Статті в журналах з теми "Multiple T-periodic solutions"

Abstract We consider a nonlinear periodic problem driven by a nonlinear nonhomogeneous differential operator and a Carathéodory reaction term f (t; x) that exhibits a (p – 1)-superlinear growth in x 2 R near 1 and near zero. A special case of the differential operator is the scalar p-Laplacian. Using a combination of variational methods based on the critical point theory with Morse theory (critical groups), we show that the problem has three nontrivial solutions, two of which have constant sign (one positive, the other negative).

In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions forn-dimensional nonautonomous functional differential systemx'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), wherehiareω-periodic intand there existω-periodic functionsαi,βi∈C(R,R+)such thatαi(t)≤(hi(t,x)/xi)≤βi(t),∫0ω‍αi(t)dt>0,forx∈R+nall withxi>0,andt∈R,limxi→0+(hi(t,x)/xi)exist fort∈R;bi∈C(R,R+)areω-periodic functions and∫0ω‍bi(t)dt>0;fi∈C(R+n,R+),fi(x)>0forx >0;τ∈(R,R)is anω-periodic function. We show that the system has multiple or no positiveω-periodic solutions for sufficiently large or smallλ>0, respectively.

The existence results of positiveω-periodic solutions are obtained for the second-order functional differential equation with multiple delaysu″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), wherea(t)∈C(ℝ)is a positiveω-periodic function,f:ℝ×[0,+∞)n+1→[0,+∞)is a continuous function which isω-periodic int, andτ1(t),…,τn(t)∈C(ℝ,[0,+∞))areω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

Abstract In this article, by using critical point theory, we prove the existence of multiple T T -periodic solutions for difference equations with the mean curvature operator: − Δ ( ϕ c ( Δ u ( t − 1 ) ) ) + q ( t ) u ( t ) = λ f ( t , u ( t ) ) , t ∈ Z , -\Delta ({\phi }_{c}\left(\Delta u\left(t-1)))+q\left(t)u\left(t)=\lambda f\left(t,u\left(t)),\hspace{1em}t\in {\mathbb{Z}}, where Z {\mathbb{Z}} is the set of integers. As a T T -periodic problem, it does not require the nonlinear term is unbounded or bounded, and thus, our results are supplements to some well-known periodic problems. Finally, we give one example to illustrate our main results.

We prove the existence of at least two T-periodic solutions, not differing from each other by an integer multiple of 2π, of the sine-curvature equation [Formula: see text] We assume that A ∈ ℝ and [Formula: see text] is a T-periodic function such that [Formula: see text] and, e.g. ‖h‖L∞ < 4/T. Our approach is variational and makes use of basic results of non-smooth critical point theory in the space of bounded variation functions.

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing typep-Laplacian equation with multiple constant delays of the form(φp(x′(t)))′+Cx′(t)+g0(t,x(t))+∑k=1ngk(t,x(t-τk))=e(t).Moreover, an example is provided to illustrate the effectiveness of the results in this paper.

By applying the fixed point theorem, we derive some new criteria for the existence of multiple positive periodic solutions for two kinds of n-dimension periodic impulsive functional differential equations with multiple delays and two parameters:xi′(t)=ai(t)xi(t)-λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e.,t>0,t≠tk,k∈Z+,xi(tk+)-xi(tk-)=μcikxi(tk),i=1,2,…,n,k∈Z+,andxi′(t)=-ai(t)xi(t)+λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e.,t>0,t≠tk,k∈Z+,xi(tk+)-xi(tk-)=μcikxi(tk),i=1,2,…,n,k∈Z+.As an application, we study some special cases of the previous systems, which have been studied extensively in the literature.

We study the stability of periodic solutions of the scalar delay differential equation where f(t) is a periodic forcing term and δ,p∈R. We study stability in the first approximation showing that the non-smooth equation (*) can be linearized along some ‘non-singular’ periodic solutions. Then the corresponding variational equation together with the Krasnosel'skij index are used to prove the existence of multiple periodic solutions to (*). Finally, we apply a generalization of Halanay's inequality to establish conditions for global attractivity in equations with maxima.

We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation(d/dt)(x'(t)/1+x't2) +∑i=1naitgxt-τit=pt. By using Mawhin's continuation theorem, a new result is obtained. Furthermore, the nonexistence of periodic solution for the equation is investigated as well.

This paper is devoted to the study of time-periodic solutions to the nonlinear one-dimensional wave equation with x-dependent coefficients u(x)ytt – (u(x)yx)x + g(x,t,y) = f(x,t) on (0,π) × ℝ under the periodic boundary conditions y(0,t) = y(π,t), yx(0,t) = yx(π,t) or anti-periodic boundary conditions y(0, t) = –y(π,t), yx[0,t) = – yx(π,t). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. Our main concept is that of the ‘weak solution’. For T, the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.

AbstractWe consider the system of difference equations$\Delta\bigg{(}\frac{\Delta u_{n-1}}{\sqrt{1-|\Delta u_{n-1}|^{2}}}\bigg{)}=% \nabla V_{n}(u_{n})+h_{n},\quad u_{n}=u_{n+T}\quad(n\in\mathbb{Z}),$with${\Delta u_{n}=u_{n+1}-u_{n}\in{\mathbb{R}}^{N}}$,${V_{n}=V_{n}(x)\in C^{2}({\mathbb{R}}^{N},\mathbb{R})}$,${V_{n+T}=V_{n}}$,${h_{n+T}=h_{n}}$for all${n\in\mathbb{Z}}$and some positive integerT,${V_{n}(x)}$is${\omega_{i}}$-periodic (${\omega_{i}>0}$) with respect to each${x_{i}}$(${i=1,\ldots,N}$) and${\sum_{j=1}^{T}h_{j}=0}$. Applying a modification argument to the corresponding problem with a left-hand member ofp-Laplacian type, and using Morse theory, we prove that if all its solutions are non-degenerate, then the difference system above has at least${2^{N}}$geometrically distinctT-periodic solutions.

By means of a variational structure andZ2-group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the formx″(t−τ)+λ(t)f(t,x(t),x(t−τ),x(t−2τ))=x(t),λ(t)>0,τ>0.

By means of variational structure andZ2group index theory, we obtain multiple periodic solutions to a class of second-order mixed-type differential equationsx''(t−τ)+f(t,x(t),x(t−τ),x(t−2τ))=0andx''(t−τ)+λ(t)f1(t,x(t),x(t−τ),x(t−2τ))=x(t−τ).

In this paper, the numerical-analytic method has been used to study the existence and approximation of the periodic solutions for the vector T-system of new nonlinear multiple integro-differential equations of mixed (Volterra-Fredholm) and (Fredholm-Volterra) types. Our main task provided sufficient conditions for investigating the family continuation theorems (numerical-analytic method and Banach fixed point theorem) in compact spaces for the existence of periodic solutions for the vector T-system of nonlinear multiple integrodifferential equations. All functions satisfies a Hölder condition (Hölder inequality) of orders α, β and γ where 0<α, β, γ<1.

In this article, we consider the following high-order p-Laplacian neutral differential equation with multiple deviating arguments:$$(\varphi_{p}(x(t)-cx(t-r))^{(m)}(t)))^{(m)}= f(x(t))x'(t)+g(t,x(t),x(t-\tau_{1}(t)),...,x(t-\tau_{k}(t)))+e(t).$$By appling the continuation theorem, theory of Fourier series, Bernoulli numbers theory and some analytic techniques, sufficient conditions for the existence of periodic solutions are established.

By applying the fixed point theorem in a cone of Banach space, we obtain an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of two kinds of generalizedn-species competition systems with multiple delays and impulses as follows:xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1ncij(t)xi(t-τij(t))-∑j=1ndij(t)xj(t-γij(t))-∑j=1neij(t)∫-σij0‍fij(s)xj(t+s)ds], a.e., t>0,t≠tk, k∈Z+, i=1,2,…,n; xi(tk+)-xi(tk-)=θikxi(tk), i=1,2,…,n, k∈Z+; and xi′(t)=xi(t)[ai(t)-bi(t)xi(t)+∑j=1ncij(t)xi(t-τij(t))-∑j=1ndij(t)xj(t-γij(t))-∑j=1neij(t)∫-σij0‍fij(s)xj(t+s)ds], a.e., t>0, t≠tk, k∈Z+, i=1,2,…,n; xi(tk+)-xi(tk-)=θikxi(tk), i=1,2,…,n, k∈Z+.It improves and generalizes a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.

By introducing subdifferentiability of lower semicontinuous convex functionφ(x(t),x(t−τ))and its conjugate function, as well as critical point theory and operator equation theory, we obtain the existence of multiple subharmonic periodic solutions to the following second-order nonlinear nonautonomous neutral nonlinear functional differential equationx″(t)+x″(t−2τ)+f(t,x(t),x(t−τ),x(t−2τ))=0,x(0)=0.

We consider the following generalizedn-species Lotka-Volterra type and Gilpin-Ayala type competition systems with multiple delays and impulses:xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1n‍cij(t)xjαij(t-ρij(t))-∑j=1n‍dij(t)xjβij(t-τij(t))-∑j=1n‍eij(t)∫-ηij0‍kij(s)xjγij(t+s)ds-∑j=1n‍fij(t)∫-θij0‍Kij(ξ)xiδij(t+ξ)xjσij(t+ξ)dξ],a.e,t>0,t≠tk;xi(tk+)-xi(tk-)=hikxi(tk),i=1,2,…,n,k∈Z+.By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. As applications, some special cases of the previous system are examined and some earlier results are extended and improved.

LetT⊂Rbe a periodic time scale in shiftsδ±with periodP∈(t0,∞)Tandt0∈Tis nonnegative and fixed. By using a multiple fixed point theorem in cones, some criteria are established for the existence and multiplicity of positive solutions in shiftsδ±for a class of higher-dimensional functional dynamic equations with impulses on time scales of the following form:xΔ(t)=A(t)x(t)+b(t)f(t,x(g(t))), t≠tj, t∈T, x(tj+)=x(tj-)+Ij(x(tj)),whereA(t)=(aij(t))n×nis a nonsingular matrix with continuous real-valued functions as its elements. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of the results.

The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and sawtooth waves) with period T and amplitude A, we investigate the performance (energetics, mean current, Stokes efficiency) of a rocking ratchet in light of thermodynamic quantities (entropy production) and the path-dependent information geometric measures. For each G(t), we calculate exact time-dependent probability density functions under different conditions by varying T, A and the strength of the stochastic noise D in an unprecedentedly wide range. Overall similar behaviours are found for different cases of G(t). In particular, in all cases, the current, Stokes efficiency and the information rate normalised by A and D exhibit one or multiple local maxima and minima as A increases. However, the dependence of the current and Stokes efficiency on A can be quite different, while the behaviour of the information rate normalised by A and D tends to resemble that of the Stokes efficiency. In comparison, the irreversibility measured by a normalised entropy production is independent of A. The results indicate the utility of the information geometry as a proxy of a motor efficiency.

The classical Hopefield neural networks have obvious symmetry, thus the study related to its dynamic behaviors has been widely concerned. This research article is involved with the neutral-type inertial neural networks incorporating multiple delays. By making an appropriate Lyapunov functional, one novel sufficient stability criterion for the existence and global exponential stability of T-periodic solutions on the proposed system is obtained. In addition, an instructive numerical example is arranged to support the present approach. The obtained results broaden the application range of neutral-types inertial neural networks.

Abstract. We consider a highly idealized model for El Niño/Southern Oscillation (ENSO) variability, as introduced in an earlier paper. The model is governed by a delay differential equation for sea-surface temperature T in the Tropical Pacific, and it combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform a theoretical and numerical study of the model in the three-dimensional space of its physically relevant parameters: propagation period τ of oceanic waves across the Tropical Pacific, atmosphere-ocean coupling κ, and strength of seasonal forcing b. Phase locking of model solutions to the periodic forcing is prevalent: the local maxima and minima of the solutions tend to occur at the same position within the seasonal cycle. Such phase locking is a key feature of the observed El Niño (warm) and La Niña (cold) events. The phasing of the extrema within the seasonal cycle depends sensitively on model parameters when forcing is weak. We also study co-existence of multiple solutions for fixed model parameters and describe the basins of attraction of the stable solutions in a one-dimensional space of constant initial model histories.

The content of this review consists of recent developments covering an advanced treatment of multiple crack problems in plane elasticity. Several elementary solutions are highlighted, which are the fundamentals for the formulation of the integral equations. The elementary solutions include those initiated by point sources or by a distributed traction along the crack face. Two kinds of singular integral equations, three kinds of Fredholm integral equations, and one kind of hypersingular integral equation are suggested for the multiple crack problems in plane elasticity. Regularization procedures are also investigated. For the solution of the integral equations, the relevant quadrature rules are addressed. A variety of methods for solving the multiple crack problems is introduced. Applications for the solution of the multiple crack problems are also addressed. The concept of the modified complex potential (MCP) is emphasized, which will extend the solution range, for example, from the multiple crack problem in an infinite plate to that in a circular plate. Many multiple crack problems are addressed. Those problems include: (i) multiple semi-infinite crack problem, (ii) multiple crack problem with a general loading, (iii) multiple crack problem for the bonded half-planes, (iv) multiple crack problem for a finite region, (v) multiple crack problem for a circular region, (vi) multiple crack problem in antiplane elasticity, (vii) T-stress in the multiple crack problem, and (viii) periodic crack problem and many others. This review article cites 187 references.

The dynamical behaviors of a two-species discrete ratio-dependent predator–prey system are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator–prey system, Indian J. Pure Appl. Math.42(1) (2011) 1–26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator–prey system with delays, Appl. Math. Comput.153 (2004) 337–351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin–Ayala competition predator–prey discrete system, Appl. Math. Comput.190 (2007) 500–509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.

AbstractWe consider the phase-locked solutions of the differential equation governing planar motion of a weakly damped pendulum driven by horizontal, periodic forcing of the pivot with maximum acceleration εg and dimensionless frequency ω. Analytical solutions for symmetric oscillations at smaller values of ε are continued into numerical solutions at larger values of ε. A wide range of stable oscillatory solutions is described, including motion that is symmetric or asymmetric, downward or inverted, and at periods equal to the forcing period T ≡ 2π/ω or integral multiples thereof. Stable running oscillations with mean angular velocity pω/q, where p and q are integers, are investigated also. Stability boundaries are calculated for swinging oscillations of period T, 2T and 4T; 3T and 6T; and for running oscillations with mean angular velocity ω. The period-doubling cascades typically culminate in nearly periodic motion followed by chaotic motion or some independent periodic motion.

By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory fork-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse:x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))], t≠tk, k∈Z+; x(tk+)=x(tk-)+θk(x(tk)), k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.

AbstractCoplanar forced oscillations of a mechanical system such as a seismometer or a fluid in a tank are modelled by the coplanar motion of periodically forced, weakly damped pendulum. We consider the phase-locked solutions of the differential equation governing planar motion of a weakly damped pendulum driven by a periodic torque. Sinusoidal approximations previously obtained for downward and inverted oscillations at small values of the dimensionless driving amplitude ε are continued into numerical solutions at larger values of ε. Resonance curves and stability boundaries are presented for downward and inverted oscillations of periods T, 2T, and 4T, where T(≡ 2π/ω) is the dimensionless forcing period. The symmetry-breaking, period-doubling sequences of oscillatory motion are found to occur in bands on the (ω, ε) plane, with the amplitudes of stable oscillations in one band differing by multiples of about π from those in the other bands, a structure similar to that of energy levels in wave mechanics. The sinusoidal approximations for symmetric T-periodic oscillations prove to be surprisingly accurate at the larger values of ε, the banded structure being related to the periodicity of the J0 Bessel function.

Introduction - Ongoing Covid-19 Calamity: As a disease, COVID-19 is still in the pandemic phase because infections continue to increasingly occur world-wide and various population groups are still susceptible. It is likely that the SARS-CoV-2 will not be eradicated but become endemic and continue to circulate and cause infections in pockets of the global populations for years to come. It may evolve into more transmissible and virulent forms with novel mutations and variants, and associated factors may worsen the overall scenario with involvement of newer population groups and world regions. Mutations, Variants and Immune Escape: The unabated prevalence increases risk of mutations, as the virus has more chances to mutate. Further, in areas where the incidence rates are high, selection pressures favour the emergence of variants that evade neutralising antibodies. Furthermore, as population groups receive vaccination, immune pressure is conjectured to facilitate and speed up the emergence of such variants by selecting for escape mutants. In due course, these selected variants would replace previous versions of the virus propelling the pandemic or the endemic disease later on. Associated Uncertainties with SARS-CoV-2: There are various associated uncertainties with the SARS-CoV-2 virus and the disease it causes. Due to evolving genomic changes, the virus elicits erratic and labile immune response. Simultaneously, the host factors are highly variable and largely uncontrollable. Further, the control measures and available vaccines for COVID-19 may not reduce the prevalence of infections drastically for multiple reasons. These epidemiological drivers would lead to persistence of the virus and endemicity of the disease interspersed by periodic outbreaks and re-emergence. The Human Life during Covid-19 Pandemic: With COVID-19 becoming an endemic disease, the SARS-CoV-2 virus would be first encountered during childhood, typically causing mild manifestations or none. The population groups will develop some immunity through natural infection or vaccination and may not suffer with severe illness, except in those with comorbid conditions or immune-compromised states, and the disease course would depend on evolving variants, efficacy of vaccines, and nature of immunity to the virus. The herd immunity against SARS-CoV-2 may remain a myth and with individual immunity being labile and waning after 6-8 months, booster doses of updated vaccine will be required at regular intervals. Future Scenario and Search for Solutions: To mitigate the spread of SARS-CoV-2 virus, various countries have implemented a wide range of control measures from time to time and likely to resort to, in future as well. There is need for genotyping and genomic sequencing capability for quick and effective utilization of epidemiological data. Simultaneously, the large deployment of COVID-19 vaccines under way needs a rapid and effective global effort. The next-generation vaccines may stimulate T cells effectively, apart from generating antibodies against the virus, and there is possibility of designing a universal coronavirus vaccine or pan-virus vaccine for immunisation against multiple variants and strains. On the therapeutic side, use of probiotics as adjuvant therapy may Improve the prognosis and clinical outcomes in COVID-19.

Electroless metal/alloy deposition can be an efficient process in certain areas of microelectronic fabrication. In fact, it is often easier to obtain coatings of uniform thickness and composition using electroless deposition than with electrodeposition, since one does not have the current density uniformity problem of the latter. For example, we were able to develop a Ni(P) process as a replacement for the final aluminum interconnect level, significantly decreasing wafer processing cycle time, by selectively depositing a Ni(P) capping layer on the Cu bitline wiring level. In STTM MRAM, we successfully employed this Ni(P) capping process to enable the evaluation of memory state retention via functional testing in an air atmosphere at elevated temperatures (1). However, there is a need to explore materials + deposition methods for rapidly developing fields, such as Quantum computing, e.g., materials with superconducting properties. Conventional electroless metal deposition, utilizing a separate reducing agent, can deposit materials with unique and useful properties, such as phosphorus-containing alloys in the case of hypophosphite reducing agents. This talk discusses work we have carried out on electroless tin deposition, including aspects of electroless solution preparation and stability, copper substrate surface preparation and catalyzation, and the mechanisms of electroless deposition and solution decomposition. Electroless processes can deposit a limited number of materials, especially pure metals. This is in part due to conventional electroless processes requiring catalytically active surfaces both to initiate the deposition reaction and to sustain it, the heterogeneous oxidation of the reducing agent being a kinetically hindered process, often with multiple reaction pathways (2). Though not possessing good catalytic activity due to its Periodic Table related, p -block element status, pure Sn, an environmentally robust, superconducting metal, can be electrolessly deposited through a disproportionation reaction involving stannous ions (3) in an alkaline aqueous medium. We achieved electroless Sn deposition rates of up to 8 – 9 μm/hr for tartrate-citrate complexed electroless Sn solutions in the temperature range 80 – 85 ⁰C with sodium and potassium hydroxides to adjust alkalinity. We found that either in-house formulated, or commercially available, immersion Sn solutions deposited a uniform Sn catalyst layer (≤ 0.5 μm) to initiate the electroless Sn deposition reaction on copper; however, improperly formulated immersion Sn solutions rapidly developed precipitates due to tin ion hydrolysis. The biggest technical challenge was minimizing unwanted electroless deposition of tin in bulk solution, i.e., deposition not associated with the catalytically active substrate surface. Tin oxide (SnO) is known to be metastable at ambient conditions and to decompose at temperatures above 300 ⁰C with “noticeable rate” into Sn and SnO2 (4). Thus, removal of filterable hydrolysis products of Sn(II) following solution preparation was important, but not always sufficient, for obtaining solutions that were viable for several days of use. The reasons for, and mechanisms of, electroless Sn solution decomposition do not appear to have been adequately addressed in the literature. We will show SIMS analysis of both immersion and electroless Sn layers along with synchrotron X-Ray analysis results of immersion Sn catalyst films on Cu to determine the extent of Sn-Cu intermetallic formation following their formation. We will discuss the current understanding of the mechanism of electroless Sn deposition including that of concomitant H2 gas evolution. We will conclude with contrasting the Ni(P) and Sn electroless processes in terms of ease of operation and reliability for routine processing. † Present address: Solvay, 1937 West Main Street, Stamford 06902, CT. ‡ Quantum intern at the IBM TJ Watson Research Center, Summer 2019, 2020 and 2021. [1]. E. J. O'Sullivan, C. Camagong et al., 2019 Meet. Abstr. MA2019-02 916; https://doi.org/10.1149/MA2019-02/15/916. [2]. E. J. O'Sullivan, Ch 5, Advances in Electrochemical Science and Engineering, Volume 7, https://doi.org/10.1002/3527600264.ch5. [3]. A. Molenaar and J. W. G. de Bakker, 1989, J. Electrochem. Soc. 136, 378 and refs therein; H. Koyano, M. Kato, and M. Uchida, 1991, Plating and Surface Finishing, 78, 68-74 and refs therein. [4]. H. Giefers et al, 2005, Solid State Ionics, 176, 199-207; https://doi.org/10.1016/j.ssi.2004.06.006. Acknowledgements The authors gratefully acknowledge the efforts of the staff of the Microelectronics Research Laboratory (MRL) at the IBM T. J. Watson Research Center, where some of the fabrication work described in this talk was carried out.

A new approach to determine stability of multiple steady-state similarity solutions corresponding to laminar flows is introduced and applied to laminar flows in cold, pure water at temperature T∞ °C (near 4 °C) adjacent to a vertical, isothermal, plane surface at temperature T0 °C when 0 < R ≡ (4−T∞)/(T0−T∞) < 0.5, the region of buoyancy-force reversals. The results show that the steady-state similarity solutions recently found in this region by El-Henawy et al. (1982) are unstable, and thus should not be observed experimentally; while those solutions found earlier by Carey, Gebhart & Mollendorf (1980) may be stable. No unstable modes corresponding to their solutions were found. Some flows for R in the range of strong buoyancy-force reversals, 0.14 < R < 0.32 at Prandtl number Pr = 11.6, have been observed, for example at R = 0.143,0.254 and 0.317 by Carey & Gebhart (1981) and Wilson & Vyas (1979). The latter found time-varying flows in this region of strongest flow reversals.The advantages of the method introduced are reduction of mathematical shortcomings of the traditional approach and relative ease of numerical calculation of the real eigenvalues and eigenfunctions. The disadvantage is that information on downstream, selective frequency, exponential growth of amplitude is lost. The theory presented may be regarded as an asymptotic limit of the standard hydrodynamic theory as the frequency of perturbations approaches zero.

The linear stability of inviscid non-diffusive density-stratified shear flow in a rotating frame is considered. A temporally periodic base flow, characterized by vertical shear S, buoyancy frequency N and rotation frequency f, is perturbed by infinitesimal inertia–gravity waves. The temporal evolution and stability characteristics of the disturbances are analysed using Floquet theory and the growth rates of unstable solutions are computed numerically. The global structure of solutions is addressed in the dimensionless parameter space (N/f, S/f, φ) where φ is the wavenumber inclination angle from the horizontal for the wave-like perturbations. Both weakly stratified rapidly rotating flows (N<f) and strongly stratified slowly rotating flows (N>f) are examined. Distinct families of unstable modes are found, each of which can be associated with nearby stable solutions of periodicity T or 2T where T is the inertial frequency 2π/f. Rotation is found to be a destabilizing factor in the sense that stable non-rotating shear flows with N2/S2>1/4 can be unstable in a rotating frame. Morever, instabilities by parametric resonance are found associated with free oscillations at half and integer multiples of the inertial frequency.

AbstractIn this paper, we study the existence of multiple periodic solutions for the following fractional equation:(-\Delta)^{s}u+F^{\prime}(u)=0,\qquad u(x)=u(x+T)\quad x\in\mathbb{R}.For an even double-well potential, we establish more and more periodic solutions for a large period T. Without the evenness of F we give the existence of two periodic solutions of the problem. We make use of variational arguments, in particular Clark’s theorem and Morse theory.

AbstractIn this article, we first investigate the linear difference operator $(Ax)(t):=x(t)-\sum_{i=1}^{n}c_{i}(t)x(t- \delta _{i}(t))$(Ax)(t):=x(t)−∑i=1nci(t)x(t−δi(t)) in a continuous periodic function space. The existence condition and some properties of the inverse of the operator A are explicitly pointed out. Afterwards, as applications of properties of the operator A, we study the existence of periodic solutions for two kinds of second-order functional differential equations with this operator. One is a kind of second-order functional differential equation, by applications of Krasnoselskii’s fixed point theorem, some sufficient conditions for the existence of positive periodic solutions are established. Another one is a kind of second-order quasi-linear differential equation, we establish the existence of periodic solutions of this equation by an extension of Mawhin’s continuous theorem.

AbstractWe provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: $$\begin{aligned} \frac{\textrm{d}}{{\textrm{d}}t}\left( \frac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\right) =\nabla V(x),\qquad x\in \Omega \subset \mathbb {R}^n, \end{aligned}$$ d d t m x ˙ 1 - | x ˙ | 2 / c 2 = ∇ V ( x ) , x ∈ Ω ⊂ R n , where $$m, c > 0$$ m , c > 0 and $$V: \Omega \rightarrow \mathbb {R}$$ V : Ω → R is a function of class $$C^1$$ C 1 . As an application, we prove the existence of multiple periodic solutions with prescribed energy for a relativistic N-centre type problem in the plane.

Two timescale harmonic balance is a semi-analytical/numerical method for deriving periodic solutions and their stability to a class of nonlinear autonomous and forced oscillator equations of the form ẍ + x = f(x,ẋ,λ) and ẍ + x = f(x,ẋ,λ,t) , where λ is a control parameter. The method incorporates salient features from both the method of harmonic balance and multiple scales, and yet does not require an explicit small parameter. Essentially periodic solutions are formally derived on the basis of a single assumption: ‘that an N harmonic, truncated, Fourier series and its first two derivatives can represent x(t) , ẋ(t) and ẍ(t) respectively’. By seeking x(t) as a series of superharmonics, subharmonics, and ultrasubharmonics it is found that the method works over a wide range of parameter space provided the above assumption holds which, in practice, imposes some ‘problem dependent’ restriction on the magnitude of the nonlinearities. Two timescales, associated with the amplitude and phase variations respectively, are introduced by means of an implicit parameter Є . These timescales permit the construction of a set of amplitude evolution equations together with a corresponding stability criterion. In Part I the method is formulated and applied to three autonomous equations, the van der Pol equation, the modified van der Pol equation, and the van der Pol equation with escape. In this case an expansion in superharmonics is sufficient to reveal Hopf, saddle node and homoclinic bifurcations which are compared with results obtained by numerical integration of the equations. In Part II the method is applied to forced nonlinear oscillators in which the solution for x(t) includes superharmonics, subharmonics, and ultrasubharmonics. The features of period doubling, symmetry breaking, phase locking and the Feigenbaum transition to chaos are examined.

The study's focus was to identify the primary causes of construction waste and the most effective methods for reducing them. In the collaborative action research methodology, a questionnaire was used as a tool. Data from 109 participants were analysed statistically using multiple regressions and descriptive statistics (percentage, mean, and t-test). Responses were collected by various stakeholders from the construction industry having different expertise, and work experience and spread across pan India. The primary causes of construction waste have been identified during material ordering, transit damage, negligent frame of mind of the working team, wrong work methodologies and improper work planning. Preparation of an appropriate waste management plan at the start and periodic review of same by senior management, use of building certification methods, correct handing and return of leftover material from the site, the trained workforce at the site and proper work methodologies are seen as being the most effective waste reduction techniques. Multiple regressions revealed that respondent work roles, experience, and type of project were substantial positive factors that influence reducing waste management at the project site. However, both the causes and solutions of construction waste were found to be human-related. Awareness of these factors must be imparted to stakeholders, which can motivate and inspire effective waste management in the construction industry.

Photo by Hush Naidoo Jade Photography on Unsplash INTRODUCTION In this collection of narratives, the authors describe their own experiences with and reflections on healthcare worker vaccine hesitancy. The narratives explore each author’s engagement with different communities experiencing vaccine hesitancy, touching on reasons for hesitancy, proposed solutions, and legal aspects. Author’s names appear above their narratives. l. Johanna T. Crane Vaccine hesitancy, defined as “a delay of acceptance or refusal of vaccination despite the availability of vaccination services,”[1] is a worldwide but locally shaped phenomenon that pre-dates the COVID-19 pandemic.[2] Contrary to some portrayals, vaccine hesitancy is not the same as the more absolute antivaccination stance, or what some call “anti-vax.” Many people who are hesitant are not ideologically opposed to vaccines. Hesitancy is also sometimes framed as anti-science, yet reluctance to vaccinate is often about managing risk, trustworthiness, and doubt in the context of uncertainty; it represents an effort to “talk back to science” about unaddressed needs and concerns.[3] In the US, the newness of the vaccines, the unprecedented speed at which they were developed, and their remaining under emergency use authorization at first complicated public confidence. Political polarization and racial and social inequality shape vaccine acceptance and public distrust as well. While vaccine acceptance has increased in the months since the vaccines first became available, many eligible individuals have not yet been vaccinated, including a significant number of healthcare workers.[4] Vaccine hesitancy among healthcare workers may seem surprising, especially given their frontline experience – I confess that it surprised me at first. But when I began interviewing health care workers for a study on COVID vaccine roll-out at community health centers, I learned to take a more complex view. Although the study was focused on patient vaccine access,[5] many of the frontline health care workers we spoke with also described hesitancy among some of their colleagues (and, in a few cases, themselves). From these conversations, I learned that these “healthcare heroes” are also regular people and members of communities. Their concerns about COVID vaccination often reflect the prevailing concerns advanced in their communities, such as worries about vaccine side effects and safety. Like other workers, some fear missing work and losing income, as not all healthcare employers offer paid time off for vaccination or recovery. (Importantly, reluctance to vaccinate is highest among healthcare workers in lower-paid positions with little job security, such as clerks, housekeepers, patient care assistants, and home health aides.)[6] For some healthcare workers of color, the protection offered by the vaccine sits in tension with both current and historical experiences of medical abuse and neglect. Some interviewees, fully vaccinated themselves, rejected the framework of “hesitancy” entirely, arguing that Black and Brown reluctance to be vaccinated first should be understood through the lens of “self-protection”. Due to the nature of their work, healthcare workers have faced great social pressure to vaccinate and vaccinate first. This is understandable, given that vaccination against COVID-19 protects not only workers themselves but aligns with the ethical duty to prevent harm to patients by reducing the risk of transmission in healthcare settings. When the FDA approved COVID-19 vaccines under emergency use authorization in December 2020, many healthcare workers were extremely grateful to be designated “1a” – the first group prioritized to receive the shots.[7] For many bioethicists, prioritization of healthcare workers represented a recognition of the extreme risks that many front-line workers had endured since the onset of the pandemic, including critical shortages in PPE. But it is important to remember that for some workers, going first may have felt like serving as guinea pigs for new vaccines that had yet to be granted full FDA approval. For these individuals, the expectation that they would vaccinate first may have felt like an additional risk rather than a reward. Healthcare workers who are hesitant to vaccinate may feel ashamed or be subject to shaming by others;[8] this may make it difficult to discuss their concerns in the workplace. Throughout the pandemic, healthcare workers have been lauded as “heroes”, and some healthcare employers have promoted vaccination among their workforce as a “heroic” action. This messaging implies that waiting to vaccinate is shameful or cowardly and is echoed in opinion pieces and op-eds describing unvaccinated people as “selfish” or “free riders.”[9] By fostering the proper dialogue, we can respond respectfully to hesitancy among healthcare workers while still working towards the goal of increased vaccination. We in the bioethics and medical community should be willing to listen to our colleagues’ concerns with respect. Top-down approaches aimed at “correcting” hesitancy cannot address the more fundamental issues of trust that are often at stake. Instead, there must be dialogue over time. Conversations with a trusted healthcare provider have a crucial role.[10] Blaming and shaming rhetoric, whether explicit or implicit, gets us nowhere – in fact, it likely moves us backward by likely exacerbating any existing distrust or resentment that workers may hold toward their employers.[11] Lastly, the onus of trust must be with institutions, not individuals. There is a lot of talk about getting communities of color, and Black people, particularly, to "trust" healthcare institutions and the COVID vaccines. This racializes trust and puts the burden on harmed communities rather than on institutions acting in trustworthy ways.[12] Dialogue, respect, and trustworthiness must guide us even in the new era of workplace mandates. Mandates make these strategies even more important as we look toward an uncertain future. As Heidi Larson, founder of the Vaccine Confidence Project, recently said, “We should not forget that we are making people's future history now. Are people going to remember that they were treated respectfully and engaged?”[13] ll. Kara Simpson Since the release of the vaccine for COVID-19 in late 2020, there have been robust discussions within the medical community, the media, and political arenas about vaccine hesitancy among healthcare workers. The public became aware that healthcare workers, the first group to become eligible for the vaccine, were not rushing to “take the shot.” Many people’s opinions were aligned by race, ethnicity, socioeconomic status, and political affiliation. People of color were one of the first groups to be labeled vaccine hesitant as our experiences of distrust of the medical community and the politicization of the vaccine explained the low turnout.[14] It was not uncommon to hear, “this vaccine just came out; let’s wait and see if there are side effects.” Interestingly, many people in the healthcare community and in the public did not understand why healthcare workers of color remained hesitant. Trust is a vital component of any viable relationship, especially in the clinical realm. To have successful health outcomes, it is essential for clinicians to build trusting relationships with their patients and peers. Many people of color are distrustful towards the medical institution due to the years of systemic racism and abuses that they have experienced, witnessed, or learned about. Healthcare workers of color are not excluded from the experiences of their communities outside of work. In fact, I assert that healthcare of color may have an additional burden of hesitation because of their lived experiences of distrust in receiving care and inequality within their professional environment. These dual traumas can work in tandem to strengthen hesitancy. I assert that building trusting clinical relationships will address hesitancy over time. Currently, many healthcare workers are worried about vaccine mandates. For a group of people that have experienced intergenerational enslavement and marginalization, mandates feel coercive and serve as a reminder of how “lesser” bodies are considered unworthy of voice, fundamental human rights, independent decision making. To call the vaccine mandate paternalistic would be an understatement. An unintended result of vaccine mandates will be the reinforcement of hesitancy and distrust of the medical institution as trust and coercion cannot coexist. This mandate will give more power to the conspiracy theories and harm those who already do not seek or receive adequate health care because of systemic inequalities. Furthermore, mandates can also dissuade people of color from becoming healthcare workers, and others may leave the field. In essence, vaccine hesitancy is a symptom of a much larger problem: the distrust of the medical establishment. As bioethicists, our mission should be to support interventions that foster “trustworthiness” of the institutions rather than those that cause trauma. Several organizations have proposed mask mandates and weekly testing as a measure to protect the population at large and still respect the autonomy of the unvaccinated.[15] lll. Jennifer Breznay I work in a very large community teaching hospital in Brooklyn, and we were extremely hard hit by COVID in March 2020. I worked on inpatient medical units and witnessed a lot of suffering. And after nine months of fear and despair about COVID’s toll, I felt tremendous frustration in December when I heard that many healthcare workers would reject the vaccine. As the co-chair of the Bioethics Committee, I drafted a statement recommending vaccination for all employees. When the draft was revised and approved by the Bioethics Committee, I began to discuss it with employees, and I appreciated different perspectives I had not heard before. In the end, rather than releasing the statement, we directed our efforts at creating a dialogue. I also volunteer at a not-for-profit which operates seven early childhood education centers in Northern Brooklyn. The Executive Director invited me to collaborate on strategies to encourage staff vaccination, and we decided to offer a Zoom conference to 20 members of the staff. I was extremely nervous about how the audience would perceive me, a white doctor whom they did not know. I felt awkward about coming to them with an agenda. And there was also the question of whether I was an appropriate messenger compared to a person of color. Yet, I felt like I shouldn't back away from this. So, I chose to simply disclose my discomfort at the beginning of the Zoom. I said, “Thanks for having me. You know, as a white physician, I understand you might have concerns about trusting what I say. Four hundred years of inequity and abuse by the healthcare system can create a lot of mistrust, but I’m here to try to answer your questions.” Ultimately the Executive Director reported that the Zoom was successful in stimulating a lot of conversation among the staff about the vaccine. I think the critical piece is the intimate but open conversation, where you can elicit values. lV. Ashley L. Stewart In the rural areas of our state, healthcare institutions are inextricably tied to their communities. Rural hospitals hire from, serve, and function in the community where they are located. Successful implementation of a vaccine roll-out in such rural areas requires explicit recognition of the role and influence of the community. After identifying issues common to the area, rural institutions can address them. Even when rural institutions find that healthcare worker concerns seem to be unique or personal, they are often related to the larger concerns of the community.[16] Community-based increased vaccine hesitancy may coincide with an underlying issue, such as lack of information rather than principled or experience-based resistance.[17] When the vaccines became available, rural vaccination coordinators encountered a wealth of misinformation that left many people initially undecided. Compounding this lack of information, workers expressed a sense of fear about the professional consequences of voicing concerns, especially in tight-knit communities. Many workers expressed concern about being judged merely for sharing their questions or decisions.[18] They also felt that saying or doing something to promote the value of vaccination might change their relationship with members of the community where they live and work.[19] As there was a fear of engaging in productive conversations, it was difficult for them to find valuable information, and the lack of information discouraged them from being vaccinated. Vaccine coordinators wanted to get information to the entire community based on the most current research and release unbiased, consistent, and timely information from sources all people in the community could trust, including from multiple sources at once. Communication must focus on answering many types of questions, which must often be done in private or anonymously. Where poorly supported or incorrect information is widely available, sharing objective information is crucial to turning the tide of distrust. If the healthcare community dismisses concerns or assumes that answering questions based on misinformation is a waste of time, the community-based institutions will further the distrust. Some may feel that vaccine coordinators should not address misinformation directly, yet avoidance has been widely unsuccessful.[20] Being respectful and non-judgmental in answering questions posed by people who do not know what is true can be hard, but in rural communities, answering completely and honestly without judgment is a critical component of any effort to inform people. Telling people to get vaccinated “for the greater good” can sound the same as being told not to get a vaccine because it is “bad” if both sources of information fail to back up their claims. Ultimately rural institutions are respected because they are a resource to their communities, a priority we must preserve. It is also critical to treat everyone respectfully regardless of vaccine status.[21] People may perceive mandates, divisive policies, or disrespectful treatment of people based on vaccination status as discriminatory or coercive, weakening the appeal of vaccination. Such practices may make people less trusting and more anchored to their position as they come to see vaccination proponents as untrustworthy or authoritarian. We must work to maintain respect for human autonomy. Using unethical means to achieve even a just end will not lead to a “greater good” but rather to the perception that people in positions of authority would achieve a result “by any means necessary.” V. David N. Hoffman The central moral quandary that arises whenever vaccine hesitancy among healthcare workers is discussed is whether workers who refuse to get vaccinated should or could be fired. We should clarify that we are applying a definition of mandate in the employment context for private employers, the violation of which results in loss of employment. Government-controlled provider organizations are just now weighing in on this topic and are generally pursuing strategies that impose periodic, usually weekly, testing requirements for those workers who decline to get vaccinated. In the private sector, employers can require their employees to do a great many things as a condition of employment, and one of them is to get vaccinated against COVID -19. In the most prominent case to date, just such a mandate gave rise to a lawsuit in Texas involving Houston Methodist Hospital. In that case, 170 employees asserted that an employer should not be allowed to force them to get vaccinated. The judge held that, while no employer can force an employee to get vaccinated, no employer is obligated to continue the employment of any employee who declines to follow rules established by that employer, including the obligation to get vaccinated.[22] In Texas, what the judge said is you are not being forced to get vaccinated, but your employer is allowed to set limits and conditions on employment, including vaccination. Employees do not have an obligation to get vaccinated, but they also have no right to their jobs. That is because of a widely misunderstood legal concept: “employment at will.” Employment at will sounds like a rule that employees can do what they want at work, but in fact, employment at will means only that you can quit your job whenever you want (we do not permit indentured servitude). At the same time, your employer can fire you at any time, for any reason or no reason, unless the reason is a pretext and involves one of the protected statuses (race, color, religion, sex, or national origin, and in some jurisdictions gender orientation, gender identity). Generally, any employers, including hospitals, can decide that if someone is not willing to get a vaccination, or if they are not willing to complete sexual harassment training or participate in the hospital’s infection control program, that is the employee’s right, but it will mean that an employer can similarly decline to continue providing employment. The evolution of this hesitancy discussion will be influenced by the narrower debate playing out in the court of public opinion, and the courts of law, over the enforceability of New York’s recently enacted vaccine mandate. Regardless of whether that mandate survives, with or without medical and religious exemptions, healthcare employers will be left with a profound ethical dilemma. At the end of all the litigation, if there is a religious exemption, employers will always be burdened with the responsibility to determine whether an individual employee has asserted a genuine and sincere religious objection to vaccination and whether the employer is able to provide an accommodation that is safe and effective in protecting the interests of co-workers and patients. The anticipated federal mandate, which reportedly will have a test/mask alternative, will only make this ethical task more challenging. This leads to the final point in this analysis, which is that while private employers, including hospitals, can deprive an individual of their employment if those individuals refuse to get vaccinated, just because an employer can do so does not mean it should do so.[23] - [1] MacDonald NE. Vaccine hesitancy: Definition, scope and determinants. Vaccine. 2015;33(34):4161-4164. doi:10.1016/j.vaccine.2015.04.036 [2] Larson HJ, de Figueiredo A, Xiahong Z, et al. The State of Vaccine Confidence 2016: Global Insights Through a 67-Country Survey. EBioMedicine. 2016;12:295-301. doi:10.1016/j.ebiom.2016.08.042 [3] Larson H. Stuck: How Vaccine Rumors Start - and Why They Don’t Go Away. Oxford University Press; 2020; Benjamin R. Informed Refusal: Toward a Justice-based Bioethics. Sci Technol Hum Values. 2016;41(6):967-990. doi:10.1177/0162243916656059 [4] Deepa Shivaram, In The Fight Against COVID, Health Workers Aren't Immune To Vaccine Misinformation September 18, 2021. NPR Special Series: The Coronavirus. https://www.npr.org/2021/09/18/1037975289/unvaccinated-covid-19-vaccine-refuse-nurses-heath-care-workers [5] Crane JT, Pacia D, Fabi R, Neuhaus C, and Berlinger N. Advancing Covid vaccination equity at Federally Qualified Health Centers: A rapid qualitative review. Accepted and awaiting publication at JGIM. [6] Ashley Kirzinger. “KFF/The Washington Post Frontline Health Care Workers Survey - Vaccine Intentions.” KFF, 22 Apr. 2021, https://www.kff.org/report-section/kff-washington-post-frontline-health-care-workers-survey-vaccine-intentions/. [7] Johanna Crane, Samuel Reis-Dennis and Megan Applewhite. “Prioritizing the ‘1a’: Ethically Allocating Scarce Covid Vaccines to Health Care Workers.” The Hastings Center, 21 Dec. 2020, https://www.thehastingscenter.org/prioritizing-the-1a-ethically-allocating-covid-vaccines-to-health-care-workers/. [8] “'I'm Not an Anti-Vaxxer, but...' US Health Workers' Vaccine Hesitancy Raises Alarm.” The Guardian, Guardian News and Media, 10 Jan. 2021, https://www.theguardian.com/world/2021/jan/10/coronavirus-covid-19-vaccine-hesitancy-us-health-workers. [9] Gerson M. If you are healthy and refuse to take the vaccine, you are a free-rider. Washington Post. April 15, 2021. [10] Crane JT, Pacia D, Fabi R, Neuhaus C, and Berlinger N. Advancing Covid vaccination equity at Federally Qualified Health Centers: A rapid qualitative review. Accepted and awaiting publication at JGIM. [11] Larson H. Stuck : How Vaccine Rumors Start - and Why They Don’t Go Away. Oxford University Press; 2020. [12] Benjamin R. Race for Cures: Rethinking the Racial Logics of ‘Trust’ in Biomedicine. Sociology Compass. 2014;8(6):755-769. doi:10.1111/soc4.12167; Warren RC, Forrow L, David Augustin Hodge S, Truog RD. Trustworthiness before Trust — Covid-19 Vaccine Trials and the Black Community. N Engl J Med. Published online October 16, 2020. doi:10.1056/NEJMp2030033 [13] Offri D. Heidi Larson, Vaccine Anthropologist. New Yorker. Published online June 12, 2021. Accessed August 11, 2021. https://www.newyorker.com/science/annals-of-medicine/heidi-larson-vaccine-anthropologist [14] Razai M S, Osama T, McKechnie D G J, Majeed A. Covid-19 Vaccine Hesitancy Among Ethnic Minority Groups. BMJ 2021; 372 :n513 doi:10.1136/bmj.n513 [15] Dasgupta, Sharoda, et al. “Differences in Rapid Increases in County-Level COVID-19 Incidence by Implementation of Statewide Closures and Mask Mandates — United States, June 1–September 30, 2020.” Annals of Epidemiology, vol. 57, Sept. 2021, pp. 46–53., https://doi.org/10.1016/j.annepidem.2021.02.006. [16] Do, Tuong Vi C et al. “COVID-19 Vaccine Acceptance Among Rural Appalachian Healthcare Workers (Eastern Kentucky/West Virginia): A Cross-Sectional Study.” Cureus vol. 13,8 e16842. 2 Aug. 2021, doi:10.7759/cureus.16842; Danabal, K.G.M., Magesh, S.S., Saravanan, S. et al. Attitude towards COVID 19 vaccines and vaccine hesitancy in urban and rural communities in Tamil Nadu, India – a community-based survey. BMC Health Serv Res 21, 994 (2021). https://doi.org/10.1186/s12913-021-07037-4 [17] Scott C. Ratzan MD, MPA, MA, Lawrence O. Gostin JD, Najmedin Meshkati PhD, CPE, Kenneth Rabin PhD & Ruth M. Parker MD (2020) COVID-19: An Urgent Call for Coordinated, Trusted Sources to Tell Everyone What They Need to Know and Do, Journal of Health Communication, 25:10, 747-749, DOI: 10.1080/10810730.2020.1894015 [18] Huang, Pien. “Some Health Care Workers Are Wary of Getting COVID-19 Vaccines.” NPR, NPR, 1 Dec. 2020, https://www.npr.org/sections/health-shots/2020/12/01/940158684/some-health-care-workers-are-wary-of-getting-covid-19-vaccines. Portnoy, Jenna. “Several Hundred Virginia Health-Care Workers Have Been Suspended or Fired over Coronavirus Vaccine Mandates.” The Washington Post, WP Company, 4 Oct. 2021, https://www.washingtonpost.com/local/covid-vaccine-mandate-hospitals-virginia/2021/10/01/b7976d16-21ff-11ec-8200-5e3fd4c49f5e_story.html. [19] Jennifer A. Lueck & Alaina Spiers (2020) Which Beliefs Predict Intention to Get Vaccinated against COVID-19? A Mixed-Methods Reasoned Action Approach Applied to Health Communication, Journal of Health Communication, 25:10, 790-798, DOI: 10.1080/10810730.2020.1865488 [20] Lockyer, Bridget, et al. “Understanding Covid-19 Misinformation and Vaccine Hesitancy in Context: Findings from a Qualitative Study Involving Citizens in Bradford, UK.” Health Expectations, vol. 24, no. 4, 4 May 2021, pp. 1158–1167., https://doi.org/10.1101/2020.12.22.20248259. Scott C. Ratzan & Ruth M. Parker (2020) Vaccine Literacy—Helping Everyone Decide to Accept Vaccination, Journal of Health Communication, 25:10, 750-752, DOI: 10.1080/10810730.2021.1875083. [21] Zimmerman, Anne. Columbia Academic Commons, 2020, Toward a Civilized Vaccination Discussion: Abandoning the False Assumption That Scientific Goals Are Shared by All, https://academiccommons.columbia.edu/doi/10.7916/d8-rzh0-1f73. [22] Bridges, et al v. Houston Methodist Hospital et al, https://docs.justia.com/cases/federal/districtcourts/texas/txsdce/4:2021cv01774/1830373/18 [23] David N. Hoffman, “Vaccine Mandates for Health Care Workers Raise Several Ethical Dilemmas,” Hasting Center Bioethics Forum. August 2021. https://www.thehastingscenter.org/vaccine-mandates-for-health-care-workers-raise-several-ethical-dilemmas/

IntroductionThe horror film Hush (2016) has attracted attention since its release due to the uniqueness of its central character—a deaf–mute author who lives in a world of silence. Maddie Young (Kate Siegel) moves into a remote cabin in the woods to recover from a breakup and finish her new novel. Aside from a cat, she is alone in the house, only engaging with loved ones via online messaging or video chats during which she uses American Sign Language (ASL). Maddie cannot hear nor speak, so writing is her primary mode of creative expression, and a key source of information for the audience. This article explores both the presence and absence of text in Hush, examining how textual “captions” of various kinds are both provided and withheld at key moments. As an author, Maddie battles the limits of written language as she struggles with writer’s block. As a person, she fights the limits of silence and isolation as a brutal killer invades her retreat. Accordingly, this article examines how the interplay between silence, text, and sound invites viewers to identify with the heroine’s experience and ultimate triumph.Hush is best described as a slasher—a horror film in which a single (usually male) killer stalks and kills a series of victims with relentless determination (Clover, Men, Women). Slashers are about close, visceral killing—blood and the hard stab of the knife. With her big brown eyes and gentle presence, quiet, deaf Maddie is clearly framed as a lamb to slaughter in the opening scenes. Indeed, throughout Hush, Maddie’s lack of hearing is leveraged to increase suspense and horror. The classic pantomime cry of “He’s behind you!” is taken to dark extremes as the audience watches a nameless man (John Gallagher Jr.) stalk the writer in her isolated house. She is unable to hear him enter the building, unable to sense him looming behind her. Neither does she hear him killing her friend outside on the porch, banging her body loudly against the French doors.And yet, despite her vulnerability, she rises to the challenge. Fighting back against her attacker using a variety of multisensory strategies, Maddie assumes the role of the “Final Girl” in this narrative. As Carol Clover has explained, the Final Girl is a key trope of slasher films, forming part of their essential structure. While others in the film are killed, “she alone looks death in the face; but she alone also finds the strength either to stay the killer long enough to be rescued (ending A) or to kill him herself (ending B)” (Clover, Her Body, Himself). However, reviews and discussions of Hush typically frame Maddie as a Final Girl with a difference. Adding disability into the equation is seen as “revolutionising” the trope (Sheppard) and “updating the Final Girl theory” for a new age (Laird). Indeed, the film presents its Final Girl as simultaneously deaf and powerful—a twist that potentially challenges the dynamics of the slasher and representations of disability more generally.My Weakness, My StrengthThe opening sequence of Hush introduces Maddie’s deafness through the use of sound, silence, and text. Following an establishing shot sweeping over the dark forest and down to her solitary cottage, the film opens to warm domesticity. Close-ups of onion, eggs, and garlic being prepared are accompanied by clear, crisp sounds of crackling, bubbling, slicing, and frying. The camera zooms out to focus on Maddie, busy at her culinary tasks. All noises begin to fade. The camera focuses on Maddie’s ear as audio is eliminated, replaced by silence. As she continues to cook, the audience experiences her world—a world devoid of sound. These initial moments also highlight the importance of digital communication technologies. Maddie moves smoothly between devices, switching from laptop computer to iPhone while sharing instant messages with a friend. Close-ups of these on-screen conversations provide viewers with additional narrative information, operating as an alternate form of captioning from within the diegesis. Snippets of text from other sources are likewise shown in passing, such as the author’s blurb on the jacket of her previous novel. The camera lingers on this book, allowing viewers to read that Maddie suffered hearing loss and vocal paralysis after contracting bacterial meningitis at 13 years old. Traditional closed captioning or subtitles are thus avoided in favour of less intrusive forms of expositional text that are integrated within the plot.While hearing characters, such as her neighbour and sister, use SimCom (simultaneous communication or sign supported speech) to communicate with her, Maddie signs in silence. Because the filmmakers have elected not to provide captions for her signs in these moments, a—typically non-ASL speaking—hearing audience will inevitably experience disruptions in comprehension and Maddie’s conversations can therefore only be partially understood. This allows for an interesting role reversal for viewers. As Katherine A. Jankowski (32) points out, deaf and hard of hearing audiences have long expressed dissatisfaction with accessing the spoken word on television and film due to a lack of closed captioning. Despite the increasing technological ease of captioning digital media in the 21st century, this barrier to accessibility continues to be an ongoing issue (Ellis and Kent). The hearing community do not share this frustrating background—television programs that include ASL are captioned to ensure hearing viewers can follow the story (see for example Beth Haller’s article on Switched at Birth in this special issue). Hush therefore inverts this dynamic by presenting ASL without captions. Whereas silence is used to draw hearing viewers into Maddie’s experience, her periodic use of ASL pushes them out again. This creates a push–pull dynamic, whereby the hearing audience identify with Maddie and empathise with the losses associated with being deaf and mute, but also realise that, as a result, she has developed additional skills that are beyond their ken.It is worth noting at this point that Maddie is not the first Final Girl with a disability. In the 1967 thriller Wait until Dark, for instance, Audrey Hepburn plays Susy Hendrix, a blind woman trapped in her home by three crooks. Martin F. Norden suggests that this film represented a “step forward” in cinematic representations of disability because its heroine is not simply an innocent victim, but “tough, resilient, and resourceful in her fight against the criminals who have misrepresented themselves to her and have broken into her apartment” (228). Susy’s blindness, at first presented as a source of vulnerability and frustration, becomes her strength in the film’s climax. Bashing out all the lights in the apartment, she forces the men to fight on her terms, in darkness, where she holds the upper hand. In a classic example of Final Girl tenacity, Susy stabs the last of them to death before help arrives. Maddie likewise uses her disability as a tactical advantage. An enhanced sense of touch allows her to detect the killer when he sneaks up behind her as she feels the lightest flutter upon the hairs of her neck. She also wields a blaring fire alarm as a weapon, deafening and disorienting her attacker, causing him to drop his knife.The similarities between these films are not coincidental. During an interview, director Mike Flanagan (who co-wrote Hush with wife Siegel) stated that they were directly informed by Wait until Dark. When asked about the choice to make Maddie’s character deaf, he explained that “it kind of happened because Kate and I were out to dinner and we were talking about movies we liked. One of the ones that we stumbled on that we both really liked was Wait Until Dark” (cited in Thurman). In the earlier film, director Terence Young used darkness to blind the audience—at times the screen is completely black and viewers must listen carefully to work out what is happening. Likewise, Flanagan and Siegel use silence to effectively deafen the audience at crucial moments. The viewers are therefore forced to experience the action as the heroines do.You’re Gonna Die Screaming But You Won’t Be HeardHorror films often depend upon sound design for impact—the most mundane visuals can be made frightening by the addition of a particular noise, effect, or tune. Therefore, in the context of the slasher genre, one of the most unique aspects of Hush is the absence of the Final Girl’s vocalisation. A mute heroine is deprived of the most basic expressive tool in the horror handbook—a good scream. “What really won me over,” comments one reviewer, “was the fact that this particular ‘final girl’ isn’t physically able to whinge or scream when in pain–something that really isn’t the norm in slasher/home invasion movies” (Gorman). Yet silence also plays an important part in this genre, “when the wind stops or the footfalls cease, death is near” (Whittington 183). Indeed, Hush’s tagline is “silence can be killer.”The arrival of the killer triggers a deep kind of silence in this particular film, because alternative captions, text, and other communicative techniques (including ASL) cease to be used or useful when the man begins terrorising Maddie. This is not entirely surprising, as the abject failure of technology is a familiar trope in slasher films. As Clover explains, “the emotional terrain of the slasher film is pretechnological” (Her Body, Himself, 198). In Hush, however, the focus on text in this context is notable. There is a sense that written modes of communication are unreliable when it counts. The killer steals her phone, and cuts electricity and Internet access to the house. She attempts to use the neighbours’ Wi-Fi via her laptop, but does not know the password. Quick thinking Maddie even scrawls backwards messages on her windows, “WON’T TELL. DIDN’T SEE FACE,” she writes in lipstick, “BOYFRIEND COMING HOME.” In response, the killer simply removes his mask, “You’ve seen it now” he says. They both know there is no boyfriend. The written word has shifted from being central to Maddie’s life, to largely irrelevant. Text cannot save her. It is only by using other strategies (and senses) that Maddie empowers herself to survive.Maddie’s struggles to communicate and take control are integral to the film’s unfolding narrative, and co-writer Siegel notes this was a conscious theme: “A lot of this movie is … a metaphor for feeling unheard. It’s a movie about asserting yourself and of course as a female writer I brought a lot to that.” In their reflection on the limits of both verbal and written communication, the writers of Hush owe a debt to another source of inspiration—Joss Whedon’s Buffy the Vampire Slayer television series. Season four, episode ten, also called Hush, was first aired on 14 December 1999 and features a critically acclaimed storyline in which the characters all lose their ability to speak. Voices from all over Sunnydale are stolen by monstrous fairytale figures called The Gentlemen, who use the silence to cut fresh hearts from living victims. Their appearance is heralded by a morbid rhyme:Can’t even shout, can’t even cry The Gentlemen are coming by. Looking in windows, knocking on doors, They need to take seven and they might take yours. Can’t call to mom, can’t say a word, You’re gonna die screaming but you won’t be heard.The theme of being “unheard” is clearly felt in this episode. Buffy and co attempt a variety of methods to compensate for their lost voices, such as hanging message boards around their necks, using basic text-to-voice computer software, and drawing on overhead projector slides. These tools essentially provide the captions for a story unfolding in silence, as no subtitles are provided. As it turns out, in many ways the friends’ non-verbal communication is more effective than their spoken words. Patrick Shade argues that the episode:celebrates the limits and virtues of both the nonverbal and the verbal. … We tend to be most readily aware of verbal means … but “Hush” stresses that we are embodied creatures whose communication consists in more than the spoken word. It reminds us that we have multiple resources we regularly employ in communicating.In a similar way, the film Hush emphasises alternative modes of expression through the device of the mute Final Girl, who must use all of her sensory and intellectual resources to survive. The evening begins with Maddie at leisure, unable to decide how to end her fictional novel. By the finale she is clarity incarnate. She assesses each real-life scene proactively and “writes” the end of the film on her own terms, showing that there is only one way to survive the night—she must fight.Deaf GainIn his discussion of disability and cinema, Norden explains that the majority of films position disabled people as outsiders and “others” because “filmmakers photograph and edit their work to reflect an able-bodied point of view” (1). The very apparatus of mainstream film, he argues, is designed to embody able-bodied experiences and encourage audience identification with able-bodied characters. He argues this bias results in disabled characters positioned as “objects of spectacle” to be pitied, feared or scorned by viewers. In Hush, however, the audience is consistently encouraged to identify with Maddie. As she fights for her life in the final scenes, sound fades away and the camera assumes a first-person perspective. The man is above, choking her on the floor, and we look up at him through her eyes. As Maddie’s groping hand finds a corkscrew and jabs the spike into his neck, we watch his death through her eyes too. The film thus assists viewers to apprehend Maddie’s strength intimately, rather than framing her as a spectacle or distanced “other” to be pitied.Importantly, it is this very core of perceived vulnerability, yet ultimate strength, that gives Maddie the edge over her attacker in the end. In this way, Maddie’s disabilities are not solely represented as a space of limitation or difference, but a potential wellspring of power. Hence the film supports, to some degree, the move to seeing deafness as gain, rather than loss:Deafness has long been viewed as a hearing loss—an absence, a void, a lack. It is virtually impossible to think of deafness without thinking of loss. And yet Deaf people do not often consider their lives to be defined by loss. Rather, there is something present in the lives of Deaf people, something full and complete. (Bauman and Murray, 3)As Bauman and Murray explain, the shift from “hearing loss” to “deaf gain” involves focusing on what is advantageous and unique about the deaf experience. They use the example of the Swiss national snowboarding team, who hired a deaf coach to boost their performance. The coach noticed they were depending too much on sound and used earplugs to teach a multi-sensory approach, “the earplugs forced them to learn to depend on the feel of the snow beneath their boards [and] the snowboarder’s performance improved markedly” (6). This idea that removing sound strengthens other senses is a thread that runs throughout Hush. For example, it is the loss of hearing and speech that are credited with inspiring Maddie’s successful writing career and innovative literary “voice”.Lennard J. Davis warns that framing people as heroic or empowered as a result of their disabilities can feed counterproductive stereotypes and perpetuate oppressive systems. “Privileging the inherent powers of the deaf or the blind is a form of patronizing,” he argues, because it traps such individuals within the concept of innate difference (106). Disparities between able and disabled people are easier to justify when disabled characters are presented as intrinsically “special” or “noble,” as this suggests inevitable divergence, rather than structural inequality. While this is something to keep in mind, Hush skirts the issue by presenting Maddie as a flawed, realistic character. She does not possess superpowers; she makes mistakes and gets injured. In short, she is a fallible human using what resources she has to the best of her abilities. As such, she represents a holistic vision of a disabled heroine rather than an overly glorified stereotype.ConclusionHush is a film about the limits of text, the gaps where language is impossible or insufficient, and the struggle to be heard as a woman with disabilities. It is a film about the difficulties surrounding both verbal and written communication, and our dependence upon them. The absence of closed captions or subtitles, combined with the use of alternative “captioning”—in the form of instant messaging, for instance—grounds the narrative in lived space, rather than providing easy extra-textual solutions. It also poses a challenge to a hearing audience, to cross the border of “otherness” and identify with a deaf heroine.Returning to the discussion of the Final Girl characterisation, Clover argues that this is a gendered device combining both traditionally feminine and masculine characteristics. The fluidity of the Final Girl is constant, “even during that final struggle she is now weak and now strong, now flees the killer and now charges him, now stabs and is stabbed, now cries out in fear and now shouts in anger” (Her Body, Himself, 221). Men viewing slasher films identify with the Final Girl’s “masculine” traits, and in the process find themselves looking through the eyes of a woman. In using a deaf character, Hush suggests that an evolution of this dynamic might also occur along the dis/abled boundary line. Maddie is a powerful survivor who shifts between weak and strong, frightened and fierce, but also between disabled and able. This portrayal encourages the audience to identify with her empowered traits and in the process look through the eyes of a disabled woman. Therefore, while slashers—and horror films in general—are not traditionally associated with progressive representations of disabilities, this evolution of the Final Girl may provide a fruitful topic of both research and filmmaking in the future.ReferencesBauman, Dirksen, and Joseph J. Murray. “Reframing: From Hearing Loss to Deaf Gain.” Trans. Fallon Brizendine and Emily Schenker. Deaf Studies Digital Journal 1 (2009): 1–10. <http://dsdj.gallaudet.edu/assets/section/section2/entry19/DSDJ_entry19.pdf>.Clover, Carol J. Men, Women, and Chain Saws: Gender in the Modern Horror Film. New Jersey: Princeton UP, 1992.———. “Her Body, Himself: Gender in the Slasher Film.” Representations 20 (1987): 187–228.Davis, Lennard J. Enforcing Normalcy: Disability, Deafness, and the Body. London: Verso, 1995.Ellis, Katie, and Mike Kent. Disability and New Media. New York: Routledge, 2011.Gorman, H. “Hush: Film Review.” Scream Horror Magazine (2016) <http://www.screamhorrormag.com/hush-film-review/>.Jankowski, Katherine A. Deaf Empowerment: Emergence, Struggle, and Rhetoric. Washington: Gallaudet UP, 1997.Laird, E.E. “Updating the Final Girl Theory.” Medium (2016) <https://medium.com/@TheFilmJournal/updating-the-final-girl-theory-b37ec0b1acf4>.Norden, M.F. Cinema of Isolation: A History of Physical Disability in the Movies. New Jersey: Rutgers UP, 1994.Shade, Patrick. “Screaming to Be Heard: Community and Communication in ‘Hush’.” Slayage 6.1 (2006). <http://www.whedonstudies.tv/uploads/2/6/2/8/26288593/shade_slayage_6.1.pdf>.Sheppard, D. “Hush: Revolutionising the Final Girl.” Eyes on Screen (2016). <https://eyesonscreen.wordpress.com/2016/06/08/hush-revolutionising-the-final-girl/>.Thurman, T. “‘Hush’ Director Mike Flanagan and Actress Kate Siegel on Their New Thriller!” Interview. Bloody Disgusting (2016). <http://bloody-disgusting.com/interviews/3384092/interview-hush-mike-flanagan-kate-siegel/>.Whittington, W. “Horror Sound Design.” A Companion to the Horror Film. Ed. Harry M. Benshoff. Oxford: John Wiley & Sons, 2014: 168–185.

Our thesis is that the city’s ambience is now an unstable dialectic in which we are watchers and watched, mirrored and refracted in a landscape of iPhone auteurs, eTags, CCTV and sousveillance. Embrace ambience! Invoking Benjamin’s spirit, this article does not seek to limit understanding through restriction to a particular theme or theoretical construct (Buck-Morss 253). Instead, it offers snapshots of interactions at the dawn of the postmodern city. That bricolage also engages how people appropriate, manipulate, disrupt and divert urban spaces and strategies of power in their everyday life. Ambient information can both liberate and disenfranchise the individual. This article asks whether our era’s dialectics result in a new personhood or merely restate the traditional spectacle of ‘bright lights, big city’. Does the virtualized city result in ambient anomie and satiation or in surprise, autonomy and serendipity? (Gumpert 36) Since the steam age, ambience has been characterised in terms of urban sound, particularly the alienation attributable to the individual’s experience as a passive receptor of a cacophony of sounds – now soft, now loud, random and recurrent–from the hubbub of crowds, the crash and grind of traffic, the noise of industrial processes and domestic activity, factory whistles, fire alarms, radio, television and gramophones (Merchant 111; Thompson 6). In the age of the internet, personal devices such as digital cameras and iPhones, and urban informatics such as CCTV networks and e-Tags, ambience is interactivity, monitoring and signalling across multiple media, rather than just sound. It is an interactivity in which watchers observe the watched observing them and the watched reshape the fabric of virtualized cities merely by traversing urban precincts (Hillier 295; De Certeau 163). It is also about pervasive although unevenly distributed monitoring of individuals, using sensors that are remote to the individual (for example cameras or tag-readers mounted above highways) or are borne by the individual (for example mobile phones or badges that systematically report the location to a parent, employer or sex offender register) (Holmes 176; Savitch 130). That monitoring reflects what Doel and Clark characterized as a pervasive sense of ambient fear in the postmodern city, albeit fear that like much contemporary anxiety is misplaced–you are more at risk from intimates than from strangers, from car accidents than terrorists or stalkers–and that is ahistorical (Doel 13; Scheingold 33). Finally, it is about cooption, with individuals signalling their identity through ambient advertising: wearing tshirts, sweatshirts, caps and other apparel that display iconic faces such as Obama and Monroe or that embody corporate imagery such as the Nike ‘Swoosh’, Coca-Cola ‘Ribbon’, Linux Penguin and Hello Kitty feline (Sayre 82; Maynard 97). In the postmodern global village much advertising is ambient, rather than merely delivered to a device or fixed on a billboard. Australian cities are now seas of information, phantasmagoric environments in which the ambient noise encountered by residents and visitors comprises corporate signage, intelligent traffic signs, displays at public transport nodes, shop-window video screens displaying us watching them, and a plethora of personal devices showing everything from the weather to snaps of people in the street or neighborhood satellite maps. They are environments through which people traverse both as persons and abstractions, virtual presences on volatile digital maps and in online social networks. Spectacle, Anomie or Personhood The spectacular city of modernity is a meme of communication, cultural and urban development theory. It is spectacular in the sense that of large, artificial, even sublime. It is also spectacular because it is built around the gaze, whether the vistas of Hausmann’s boulevards, the towers of Manhattan and Chicago, the shopfront ‘sea of light’ and advertising pillars noted by visitors to Weimar Berlin or the neon ‘neo-baroque’ of Las Vegas (Schivelbusch 114; Fritzsche 164; Ndalianis 535). In the year 2010 it aspires to 2020 vision, a panoptic and panspectric gaze on the part of governors and governed alike (Kullenberg 38). In contrast to the timelessness of Heidegger’s hut and the ‘fixity’ of rural backwaters, spectacular cities are volatile domains where all that is solid continues to melt into air with the aid of jackhammers and the latest ‘new media’ potentially result in a hypereality that make it difficult to determine what is real and what is not (Wark 22; Berman 19). The spectacular city embodies a dialectic. It is anomic because it induces an alienation in the spectator, a fatigue attributable to media satiation and to a sense of being a mere cog in a wheel, a disempowered and readily-replaceable entity that is denied personhood–recognition as an autonomous individual–through subjection to a Fordist and post-Fordist industrial discipline or the more insidious imprisonment of being ‘a housewife’, one ant in a very large ant hill (Dyer-Witheford 58). People, however, are not automatons: they experience media, modernity and urbanism in different ways. The same attributes that erode the selfhood of some people enhance the autonomy and personhood of others. The spectacular city, now a matrix of digits, information flows and opportunities, is a realm in which people can subvert expectations and find scope for self-fulfillment, whether by wearing a hoodie that defeats CCTV or by using digital technologies to find and associate with other members of stigmatized affinity groups. One person’s anomie is another’s opportunity. Ambience and Virtualisation Eighty years after Fritz Lang’s Metropolis forecast a cyber-sociality, digital technologies are resulting in a ‘virtualisation’ of social interactions and cities. In post-modern cityscapes, the space of flows comprises an increasing number of electronic exchanges through physically disjointed places (Castells 2002). Virtualisation involves supplementation or replacement of face-to-face contact with hypersocial communication via new media, including SMS, email, blogging and Facebook. In 2010 your friends (or your boss or a bully) may always be just a few keystrokes away, irrespective of whether it is raining outside, there is a public transport strike or the car is in for repairs (Hassan 69; Baron 215). Virtualisation also involves an abstraction of bodies and physical movements, with the information that represents individual identities or vehicles traversing the virtual spaces comprised of CCTV networks (where viewers never encounter the person or crowd face to face), rail ticketing systems and road management systems (x e-Tag passed by this tag reader, y camera logged a specific vehicle onto a database using automated number-plate recognition software) (Wood 93; Lyon 253). Surveillant Cities Pervasive anxiety is a permanent and recurrent feature of urban experience. Often navigated by an urgency to control perceived disorder, both physically and through cultivated dominant theory (early twentieth century gendered discourses to push women back into the private sphere; ethno-racial closure and control in the Black Metropolis of 1940s Chicago), history is punctuated by attempts to dissolve public debate and infringe minority freedoms (Wilson 1991). In the Post-modern city unprecedented technological capacity generates a totalizing media vector whose plausible by-product is the perception of an ambient menace (Wark 3). Concurrent faith in technology as a cost-effective mechanism for public management (policing, traffic, planning, revenue generation) has resulted in emergence of the surveillant city. It is both a social and architectural fabric whose infrastructure is dotted with sensors and whose people assume that they will be monitored by private/public sector entities and directed by interactive traffic management systems – from electronic speed signs and congestion indicators through to rail schedule displays –leveraging data collected through those sensors. The fabric embodies tensions between governance (at its crudest, enforcement of law by police and their surrogates in private security services) and the soft cage of digital governmentality, with people being disciplined through knowledge that they are being watched and that the observation may be shared with others in an official or non-official shaming (Parenti 51; Staples 41). Encounters with a railway station CCTV might thus result in exhibition of the individual in court or on broadcast television, whether in nightly news or in a ‘reality tv’ crime expose built around ‘most wanted’ footage (Jermyn 109). Misbehaviour by a partner might merely result in scrutiny of mobile phone bills or web browser histories (which illicit content has the partner consumed, which parts of cyberspace has been visited), followed by a visit to the family court. It might instead result in digital viligilantism, with private offences being named and shamed on electronic walls across the global village, such as Facebook. iPhone Auteurism Activists have responded to pervasive surveillance by turning the cameras on ‘the watchers’ in an exercise of ‘sousveillance’ (Bennett 13; Huey 158). That mirroring might involve the meticulous documentation, often using the same geospatial tools deployed by public/private security agents, of the location of closed circuit television cameras and other surveillance devices. One outcome is the production of maps identifying who is watching and where that watching is taking place. As a corollary, people with anxieties about being surveilled, with a taste for street theatre or a receptiveness to a new form of urban adventure have used those maps to traverse cities via routes along which they cannot be identified by cameras, tags and other tools of the panoptic sort, or to simply adopt masks at particular locations. In 2020 can anyone aspire to be a protagonist in V for Vendetta? (iSee) Mirroring might take more visceral forms, with protestors for example increasingly making a practice of capturing images of police and private security services dealing with marches, riots and pickets. The advent of 3G mobile phones with a still/video image capability and ongoing ‘dematerialisation’ of traditional video cameras (ie progressively cheaper, lighter, more robust, less visible) means that those engaged in political action can document interaction with authority. So can passers-by. That ambient imaging, turning the public gaze on power and thereby potentially redefining the ‘public’ (given that in Australia the community has been embodied by the state and discourse has been mediated by state-sanctioned media), poses challenges for media scholars and exponents of an invigorated civil society in which we are looking together – and looking at each other – rather than bowling alone. One challenge for consumers in construing ambient media is trust. Can we believe what we see, particularly when few audiences have forensic skills and intermediaries such as commercial broadcasters may privilege immediacy (the ‘breaking news’ snippet from participants) over context and verification. Social critics such as Baudelaire and Benjamin exalt the flaneur, the free spirit who gazed on the street, a street that was as much a spectacle as the theatre and as vibrant as the circus. In 2010 the same technologies that empower citizen journalism and foster a succession of velvet revolutions feed flaneurs whose streetwalking doesn’t extend beyond a keyboard and a modem. The US and UK have thus seen emergence of gawker services, with new media entrepreneurs attempting to build sustainable businesses by encouraging fans to report the location of celebrities (and ideally provide images of those encounters) for the delectation of people who are web surfing or receiving a tweet (Burns 24). In the age of ambient cameras, where the media are everywhere and nowhere (and micro-stock photoservices challenge agencies such as Magnum), everyone can join the paparazzi. Anyone can deploy that ambient surveillance to become a stalker. The enthusiasm with which fans publish sightings of celebrities will presumably facilitate attacks on bodies rather than images. Information may want to be free but so, inconveniently, do iconoclasts and practitioners of participatory panopticism (Dodge 431; Dennis 348). Rhetoric about ‘citizen journalism’ has been co-opted by ‘old media’, with national broadcasters and commercial enterprises soliciting still images and video from non-professionals, whether for free or on a commercial basis. It is a world where ‘journalists’ are everywhere and where responsibility resides uncertainly at the editorial desk, able to reject or accept offerings from people with cameras but without the industrial discipline formerly exercised through professional training and adherence to formal codes of practice. It is thus unsurprising that South Australia’s Government, echoed by some peers, has mooted anti-gawker legislation aimed at would-be auteurs who impede emergency services by stopping their cars to take photos of bushfires, road accidents or other disasters. The flipside of that iPhone auteurism is anxiety about the public gaze, expressed through moral panics regarding street photography and sexting. Apart from a handful of exceptions (notably photography in the Sydney Opera House precinct, in the immediate vicinity of defence facilities and in some national parks), Australian law does not prohibit ‘street photography’ which includes photographs or videos of streetscapes or public places. Despite periodic assertions that it is a criminal offence to take photographs of people–particularly minors–without permission from an official, parent/guardian or individual there is no general restriction on ambient photography in public spaces. Moral panics about photographs of children (or adults) on beaches or in the street reflect an ambient anxiety in which danger is associated with strangers and strangers are everywhere (Marr 7; Bauman 93). That conceptualisation is one that would delight people who are wholly innocent of Judith Butler or Andrea Dworkin, in which the gaze (ever pervasive, ever powerful) is tantamount to a violation. The reality is more prosaic: most child sex offences involve intimates, rather than the ‘monstrous other’ with the telephoto lens or collection of nastiness on his iPod (Cossins 435; Ingebretsen 190). Recognition of that reality is important in considering moves that would egregiously restrict legitimate photography in public spaces or happy snaps made by doting relatives. An ambient image–unposed, unpremeditated, uncoerced–of an intimate may empower both authors and subjects when little is solid and memory is fleeting. The same caution might usefully be applied in considering alarms about sexting, ie creation using mobile phones (and access by phone or computer monitor) of intimate images of teenagers by teenagers. Australian governments have moved to emulate their US peers, treating such photography as a criminal offence that can be conceptualized as child pornography and addressed through permanent inclusion in sex offender registers. Lifelong stigmatisation is inappropriate in dealing with naïve or brash 12 and 16 year olds who have been exchanging intimate images without an awareness of legal frameworks or an understanding of consequences (Shafron-Perez 432). Cameras may be everywhere among the e-generation but legal knowledge, like the future, is unevenly distributed. Digital Handcuffs Generations prior to 2008 lost themselves in the streets, gaining individuality or personhood by escaping the surveillance inherent in living at home, being observed by neighbours or simply surrounded by colleagues. Streets offered anonymity and autonomy (Simmel 1903), one reason why heterodox sexuality has traditionally been negotiated in parks and other beats and on kerbs where sex workers ply their trade (Dalton 375). Recent decades have seen a privatisation of those public spaces, with urban planning and digital technologies imposing a new governmentality on hitherto ambient ‘deviance’ and on voyeuristic-exhibitionist practice such as heterosexual ‘dogging’ (Bell 387). That governmentality has been enforced through mechanisms such as replacement of traditional public toilets with ‘pods’ that are conveniently maintained by global service providers such as Veolia (the unromantic but profitable rump of former media & sewers conglomerate Vivendi) and function as billboards for advertising groups such as JC Decaux. Faces encountered in the vicinity of the twenty-first century pissoir are thus likely to be those of supermodels selling yoghurt, low interest loans or sportsgear – the same faces sighted at other venues across the nation and across the globe. Visiting ‘the mens’ gives new meaning to the word ambience when you are more likely to encounter Louis Vuitton and a CCTV camera than George Michael. George’s face, or that of Madonna, Barack Obama, Kevin 07 or Homer Simpson, might instead be sighted on the tshirts or hoodies mentioned above. George’s music might also be borne on the bodies of people you see in the park, on the street, or in the bus. This is the age of ambient performance, taken out of concert halls and virtualised on iPods, Walkmen and other personal devices, music at the demand of the consumer rather than as rationed by concert managers (Bull 85). The cost of that ambience, liberation of performance from time and space constraints, may be a Weberian disenchantment (Steiner 434). Technology has also removed anonymity by offering digital handcuffs to employees, partners, friends and children. The same mobile phones used in the past to offer excuses or otherwise disguise the bearer’s movement may now be tied to an observer through location services that plot the person’s movement across Google Maps or the geospatial information of similar services. That tracking is an extension into the private realm of the identification we now take for granted when using taxis or logistics services, with corporate Australia for example investing in systems that allow accurate determination of where a shipment is located (on Sydney Harbour Bridge? the loading dock? accompanying the truck driver on unauthorized visits to the pub?) and a forecast of when it will arrive (Monmonier 76). Such technologies are being used on a smaller scale to enforce digital Fordism among the binary proletariat in corporate buildings and campuses, with ‘smart badges’ and biometric gateways logging an individual’s movement across institutional terrain (so many minutes in the conference room, so many minutes in the bathroom or lingering among the faux rainforest near the Vice Chancellery) (Bolt). Bright Lights, Blog City It is a truth universally acknowledged, at least by right-thinking Foucauldians, that modernity is a matter of coercion and anomie as all that is solid melts into air. If we are living in an age of hypersocialisation and hypercapitalism – movies and friends on tap, along with the panoptic sorting by marketers and pervasive scrutiny by both the ‘information state’ and public audiences (the million people or one person reading your blog) that is an inevitable accompaniment of the digital cornucopia–we might ask whether everyone is or should be unhappy. This article began by highlighting traditional responses to the bright lights, brashness and excitement of the big city. One conclusion might be that in 2010 not much has changed. Some people experience ambient information as liberating; others as threatening, productive of physical danger or of a more insidious anomie in which personal identity is blurred by an ineluctable electro-smog. There is disagreement about the professionalism (for which read ethics and inhibitions) of ‘citizen media’ and about a culture in which, as in the 1920s, audiences believe that they ‘own the image’ embodying the celebrity or public malefactor. Digital technologies allow you to navigate through the urban maze and allow officials, marketers or the hostile to track you. Those same technologies allow you to subvert both the governmentality and governance. You are free: Be ambient! References Baron, Naomi. Always On: Language in an Online and Mobile World. New York: Oxford UP, 2008. Bauman, Zygmunt. 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