Journal articles on the topic 'Rotating singular interactions'

We investigate the evolution of nearby like-sign vortices whose centres are at different vertical levels in a stably stratified rotating fluid. We employ two differently singularized representations of the potential vorticity distribution in the quasi-geostrophic equations (QG), in order to elucidate the pair-interaction behaviour previously seen in non-singular QG numerical solutions. The first is an analytically tractable conservative (Hamiltonian) elliptical-moment model (EM) for thin-core vortices, which exhibits a regime of very strong horizontal elongation of a vortex in response to the strain induced by its partner. We interpret this as an early evolutionary stage towards the irreversible dissipative merger and alignment interactions. This interpretation is strengthened by weakly dissipative numerical solutions of a thin-core contour-dynamics model (CD), which exhibit even further progress towards the completion of these vortex interactions in the same regime.In the EM model we classify the co-rotating stationary states which exist always for vertically offset thin-core vortices. However, the mutual strain field among the vortices cannot be balanced by co-rotation in a weakly elongated stationary state for a certain class of neighbouring, but substantially non-aligned, vortex configurations, and our interpretive assumption is that such configurations will rapidly evolve in non-singular QG solutions towards a more aligned configuration through significantly non-conservative reorganizations of the potential vorticity field. Both the EM and CD models show qualitatively similar regime boundaries between evolutions with weakly and strongly deformed vortices. In particular, there is a fairly close correspondence between the occurrence of strong vortex elongation in the EM solutions and significant filamentation and splitting in the CD solutions.

The fault diagnosis process is essentially a class discrimination problem. However, traditional class discrimination methods such as SVM and ANN fail to capitalize the interactions among the feature variables. Variable predictive model-based class discrimination (VPMCD) can adequately use the interactions. But the feature extraction and selection will greatly affect the accuracy and stability of VPMCD classifier. Aiming at the nonstationary characteristics of vibration signal from rotating machinery with local fault, singular value decomposition (SVD) technique based local characteristic-scale decomposition (LCD) was developed to extract the feature variables. Subsequently, combining artificial neural net (ANN) and mean impact value (MIV), ANN-MIV as a kind of feature selection approach was proposed to select more suitable feature variables as input vector of VPMCD classifier. In the end of this paper, a novel fault diagnosis model based on LCD-SVD-ANN-MIV and VPMCD is proposed and proved by an experimental application for roller bearing fault diagnosis. The results show that the proposed method is effective and noise tolerant. And the comparative results demonstrate that the proposed method is superior to the other methods in diagnosis speed, diagnosis success rate, and diagnosis stability.

The primary nonlinear dynamics of high-frequency gravity waves (HGWs) perturbed by their most prominent normal modes (NMs) or singular vectors (SVs) in a rotating Boussinesq fluid have been studied by direct numerical simulations (DNSs), with wave scales and values of viscosity and diffusivity characteristic for the upper mesosphere. The DNS is 2.5D in that it has only two spatial dimensions, defined by the direction of propagation of the HGW and the direction of propagation of the perturbation in the plane orthogonal to the HGW phase direction, but describes a fully 3D velocity field. Many results of the more comprehensive fully 3D simulations in the literature are reproduced. So it is found that statically unstable HGWs are subject to wave breaking ending in a wave amplitude with respect to the overturning threshold near 0.3. It is shown that this is a result of a perturbation of the HGW by its leading transverse NM. For statically stable HGWs, a parallel NM has the strongest effect, quite in line with previous results on the predominantly 2D instability of such HGWs. This parallel mode is, however, not the leading NM but a larger-scale pattern, seemingly driven by resonant wave–wave interactions, leading eventually to energy transfer from the HGW into another gravity wave with steeper phase propagation. SVs turn out to be less effective in triggering HGW decay but they can produce turbulence of a strength that is (as that from the NMs) within the range of measured values, however with a more pronounced spatial confinement.

Abstract The gravity waves (GWs) generated by potential vorticity (PV) anomalies in a rotating stratified shear flow are examined under the assumptions of constant vertical shear, two-dimensionality, and unbounded domain. Near a PV anomaly, the associated perturbation is well modeled by quasigeostrophic theory. This is not the case at large vertical distances, however, and in particular beyond the two inertial layers that appear above and below the anomaly; there, the perturbation consists of vertically propagating gravity waves. This structure is described analytically, using an expansion in the continuous spectrum of the singular modes that results from the presence of critical levels. Several explicit results are obtained. These include the form of the Eliassen–Palm (EP) flux as a function of the Richardson number N 2/Λ2, where N is the Brunt–Väisälä frequency and Λ the vertical shear. Its nondimensional value is shown to be approximately exp(−πN/Λ)/8 in the far-field GW region, approximately twice that between the two inertial layers. These results, which imply substantial wave–flow interactions in the inertial layers, are valid for Richardson numbers larger than 1 and for a large range of PV distributions. In dimensional form they provide simple relationships between the EP fluxes and the large-scale flow characteristics. As an illustration, the authors consider a PV disturbance with an amplitude of 1 PVU and a depth of 1 km, and estimate that the associated EP flux ranges between 0.1 and 100 mPa for a Richardson number between 1 and 10. These values of the flux are comparable with those observed in the lower stratosphere, which suggests that the mechanism identified in this paper provides a substantial gravity wave source, one that could be parameterized in GCMs.

This paper considers a free vorticity wave packet propagating within a rapidly rotating vortex in the quasi-steady regime, a long time after the wave packet strongly and unsteadily interacted with the vortex. We study a singular, nonlinear, helical and asymmetric shear mode inside a linearly stable, columnar and axisymmetric vortex on the $f$-plane. The amplitude-modulated mode enters resonance with the vortex at a certain radius $r_{c}$, where the phase angular speed is equal to the rotation frequency. The singularity in the modal equation at $r_{c}$ strongly modifies the flow in the three-dimensional helical critical layer, the region around $r_{c}$ where the wave/vortex interaction occurs. This interaction generates a vertically sheared three-dimensional mean flow of higher amplitude than the wave packet. The chosen envelope regime assumes the formation of a mean radial velocity of the same order as the wave packet amplitude, leading to the streamlines exhibiting a spiral motion in the neighbourhood of the critical layer. Radar images frequently show such spiral bands in tropical cyclones or tornadoes. Through matched asymptotic expansions, we find an analytical solution of the leading-order equations inside the critical layer. The generalized Batchelor integral condition applied to the quasi-steady, three-dimensional motion inside the separatrices yields a leading-order, non-uniform three-dimensional vorticity. The critical-layer pattern, strongly deformed by the mean radial velocity, loses its symmetries with respect to the azimuthal and radial directions, which makes the leading-order mean radial wave fluxes non-zero. Finally, a stronger wave/vortex interaction occurs with respect to previous studies where a steady neutral vortical mode or an envelope of larger extent was involved.

In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along a certain direction — the so-called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function [Formula: see text] which rotates the string to another one is a smooth function everywhere in space, except their respective strings. On the strings, [Formula: see text] is a multi-valued function. Consequently, some misunderstandings in the literature are clarified.

Vortex crystals are equilibrium states of point vortices whose relative configuration is unchanged throughout the evolution. They are examples of stationary point configurations subject to a logarithmic particle interaction energy, which give rise to phenomenological models of pattern formations in incompressible fluids, superconductors, superfluids and Bose–Einstein condensates. In this paper, we consider vortex crystals rotating at a constant speed in the latitudinal direction on the surface of a torus. The problem of finding vortex crystals is formulated as a linear null equation A Γ = 0 for a non-normal matrix A whose entities are derived from the locations of point vortices, and a vector Γ consisting of the strengths of point vortices and the latitudinal speed of rotation. Point configurations of vortex crystals are obtained numerically through the singular value decomposition by prescribing their locations and/or by moving them randomly so that the matrix A becomes rank deficient. Their strengths are taken from the null space corresponding to the zero singular values. The toroidal surface has a non-constant curvature and a handle structure, which are geometrically different from the plane and the spherical surface where vortex crystals have been constructed in the preceding studies. We find new vortex crystals that are associated with these toroidal geometry: (i) a polygonal arrangement of point vortices around the line of longitude; (ii) multiple latitudinal polygonal ring configurations of point vortices that are evenly arranged around the handle; and (iii) point configurations along helical curves corresponding to the fundamental group of the toroidal surface. We observe the strengths of point vortices and the behaviour of their distribution as the number of point vortices gets larger. Their linear stability is also examined. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

The axle box bearing is one of the core rotating components in high-speed trains, having served in complex working conditions for a long time. With the fault feature extraction of the vibration signal, the noise interference caused by the interaction between the wheels and rails becomes apparent. Especially when there is a shortwave defect in the rail, the interaction between wheels and rails will produce high-amplitude impulse interference. To solve the problem of the collected vibration signals of axle box bearings containing strong noise interference and high amplitude impact interference caused by rail shortwave irregularities, this paper proposes a method based on pre-identification via singular value decomposition technology to select the signals in sections and filter the noise, followed by feature extraction and fault diagnosis. The method is used to analyze the axle box bearing fault simulation signal and the weak fault signal collected by the railway bearing comprehensive experimental platform, and these signals are then compared with the random screening signal and the manual screening signal to verify the effectiveness of the method.

Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models, which can accommodate non-normalizable form factors provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such “singular” GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation: for this model, the result is improved via a nonperturbative approach that enables us to further extend the class of admissible form factors as well as to compute its resolvent and characterize its self-adjointness domain.

Abstract. The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector f1 of the lowest-order unstable periodic orbit over most of the attractor. Departures of the Lyapunov vector from this orientation are primarily rotations of the vector in an approximate tangent plane to the large-scale attractor structure. Exponential growth and decay rates of the Lyapunov vector during individual Poincaré section returns are an order of magnitude larger than the Lyapunov exponent l ≈ 0.016. Relatively large deviations of the Lyapunov vector from parallel to f1 are generally associated with relatively large transient decays. The transient growth and decay of the Lyapunov vector is well described by the transient growth and decay of the leading Floquet vectors of the set of unstable periodic orbits associated with the attractor. Each of these vectors is also nearly parallel to f1. The dynamical splitting of the complete sets of Floquet vectors for the higher-order cycles follows the previous results on the lowest-order cycle, with the vectors divided into wave-dynamical and decaying zonal flow modes. Singular vectors and singular values also generally follow this split. The primary difference between the leading Lyapunov and singular vectors is the contribution of decaying, inviscidly-damped wave-dynamical structures to the singular vectors.

This paper explores the three-way interactions between the Indian monsoon, the North Atlantic, and the tropical Pacific. Four climate records were analyzed: the monsoon rainfall in two Indian regions, the Southern Oscillation index for the tropical Pacific, and the NAO index for the North Atlantic. The individual records exhibit highly significant oscillatory modes with spectral peaks at 7–8 yr and in the quasi-biennial and quasi-quadrennial bands. The interactions between the three regions were investigated in the light of the synchronization theory of chaotic oscillators. The theory was applied here by combining multichannel singular-spectrum analysis (M-SSA) with a recently introduced varimax rotation of the M-SSA eigenvectors. A key result is that the 7–8-yr and 2.7-yr oscillatory modes in all three regions are synchronized, at least in part. The energy-ratio analysis, as well as time-lag results, suggests that the NAO plays a leading role in the 7–8-yr mode. It was found therewith that the South Asian monsoon is not slaved to forcing from the equatorial Pacific, although it does interact strongly with it. The time-lag analysis pinpointed this to be the case in particular for the quasi-biennial oscillatory modes. Overall, these results confirm that the approach of synchronized oscillators, combined with varimax-rotated M-SSA, is a powerful tool in studying teleconnections between regional climate modes and that it helps identify the mechanisms that operate in various frequency bands. This approach should be readily applicable to ocean modes of variability and to the problems of air–sea interaction as well.

Strato-rotational instability (SRI) is normally interpreted as the resonant interactions between normal modes of the internal or Kelvin variety in three-dimensional settings in which the stratification and rotation are orthogonal to both the background flow and its shear. Using a combination of asymptotic analysis and numerical solution of the linear eigenvalue problem for plane Couette flow, it is shown that such resonant interactions can be destroyed by certain singular critical levels. These levels are not classical critical levels, where the phase speed $c$ of a normal mode matches the mean flow speed $U$, but are a different type of singularity where $(c-U)$ matches a characteristic gravity-wave speed $\pm N/k$, based on the buoyancy frequency $N$ and streamwise horizontal wavenumber $k$. Instead, it is shown that a variant of SRI can occur due to the coupling of a Kelvin or internal wave to such ‘baroclinic’ critical levels. Two characteristic situations are identified and explored, and the conservation law for pseudo-momentum is used to rationalize the physical mechanism of instability. The critical level coupling removes the requirement for resonance near specific wavenumbers $k$, resulting in an extensive continuous band of unstable modes.

In pressure vessel applications, the accurate evaluation of the state of stress in the vicinity of nozzles or rigid attachments is of vital importance to the structural integrity of the vessel. Consequently, a number of investigations have paid attention to the problem and, through analytical and numerical approaches, provided information concerning the effect of system parameters, such as shell curvature and attachment geometry, on stress concentration and effective shell stiffness. While analytical solutions have only been able to provide information to axisymmetric problems, finite element approaches have been widely used as an attractive alternative. In evaluating the latter, one can identify the high computational cost that accompanies analyses dealing with complex systems. In this study, the performance of a boundary integral scheme is assessed as a possible analytical and/or numerical tool in dealing with spherical shells interacting with attachments. Such method hopes to achieve a close to analytical solutions representation of the stress state in the vicinity of the attachment that is accompanied by significant reduction in the computational cost. To achieve this, a set of integral equations, which satisfy the edge constraints, are reduced to a system of algebraic equations. These integral equations utilize singular solutions obtained for deep (nonshallow) spherical shells, which in turn are more representative of the shell domain. Explicit comparisons, on the basis of representative shell-attachment interaction problems, between the finite element and boundary integral computational techniques are conducted in order to assess the performance and efficiency of the new method. Finally, shell stiffnesses in the form of insert translations and rotations are presented in dimensionless form.

A matched asymptotic analysis is presented that describes the mechanical response of the vestibular semicircular canals to rotation of the head and includes the fluid–structure interaction which takes place within the enlarged ampullary region of the duct. New theoretical results detail the velocity field in a fluid boundary layer surrounding the cupula. The governing equations were linearized for small perturbations in fluid displacement from the prescribed motion of the head and reduced asymptotically by exploiting the slender geometry of the duct. The results include the pressure drop around the three-dimensional endolymphatic duct and through the transitional boundary layers within the ampulla. Results implicitly include the deflected shape of the cupular partition and provide an expression for the dynamic boundary condition acting on the two surfaces of the cupula. In this sense, the analysis reduces the three-dimensional fluid dynamics of the endolymph to a relatively simple boundary condition acting on the surfaces of the cupula. For illustrative purposes we present specific results modelling the cupula as a simple viscoelastic membrane. New results show that the multi-dimensional fluid dynamics within the enlarged ampulla has a significant influence on the pointwise deflection of the cupula near the crista. The spatially averaged displacement of the cupula is shown to agree with previous macromechanical descriptions of endolymph flow and pressure that ignore the fluid–structure interaction at the cupula. As an example, the model is applied to the geometry of the horizontal semicircular canal of the toadfish, Opsanus tau, and results for the deflection of the cupula are compared to individual semicircular canal afferent responses previously reported by Boyle & Highstein (1990). The cupular-shear-angle gain, defined by the angular slope of the cupula at the crista divided by the angular velocity of the head, is relatively constant at frequencies from 0.01 Hz up to 1 Hz. Over this same range, the phase of the cupular shear angle aligns with the angular velocity of the head. Near 10 Hz, the shear-angle gain increases slightly and the phase shows a lead of as much a 30°. Results are sensitive to the cupular stiffness and viscosity. Comparing results to the afferent responses represented within the VIIIth nerve provides additional theoretical evidence that the macromechanical displacement of the cupula accounts for the behaviour of only a subset of afferent fibres.

Abstract The development of new tools for the analysis of nonstationary currents, including tidal currents, has been the subject of recent research. In this work a method for studies of nonstationary barotropic or baroclinic currents based on empirical orthogonal function (EOF) and singular spectrum analysis (SSA) is proposed. It represents a new alternative to other methods of analysis of tidal currents in strong interaction with nontidal forcing, for example, the continuous wavelet transform. The advantage of the SSA method resides in the fact that it is fast, easy to implement, efficient for short-time records, and is based on the covariance structure of the data. If significant tidal constituents occur in the measurements, these are determined by the method itself even with short-time-series records. This is in contrast to the harmonic analysis (HA), where a large table of tidal constituents stated a priori are fitted to the data, even if the presence of some of these are spurious and not justified physically. The method is first demonstrated in the analysis of a synthetic current time series and then applied to an hourly current ADCP profile dataset of 410 days from the northeast Brazilian shelf. In both cases the SSA results were compared to the classical HA and the neoclassical short-term HA (STHA). The description of the shelf area where the ADCP was placed, the deployment and data acquisition operations, and the quality control data analysis are included for completeness. Analysis of the full ADCP quality-controlled data was done after a separation of the subtidal from the tidal high-frequency bands, although this traditional separation is not strictly necessary and was only made to better compare with HA and STHA. Analysis of the tidal band obtained from the ADCP data showed that the extracted tidal ellipse constituents present coherent oscillations dominated by the annual and 57-day periods, and changes in the sense of rotation of the current vector from anticyclonic to cyclonic in the ellipses. The subtidal band variability is shown to be also dominated by an annual and a 57-day period component, both polarized along the isobaths, which is suggestive of a nonlinear interaction of the subtidal and the tidal variability.

We present acoustic drill beams. These singular beams show a dynamic intensity distribution matching the shape of a helix. The intensity distribution rotates along the axis of the beam with a controlled direction and angular frequency, therefore resembling the shape of a mechanical drill bit. Acoustic drills emerge elegantly as the spatio-temporal interference of two confocal and detuned vortex beams. The beam parameters are fully tuneable. The detuned frequency, detuning wave number, and detuned topological charge of the composing beams control the number of arms of the drill, the winding period, the rotation velocity, and its direction. We show that elongated drill beams are obtained using two high-order Bessel beams, enabling analytical solutions for optimal overlapping. In addition, drill beams can also be synthesized by focused ultrasound vortices. Analytic, numeric, and experimental results are shown in the ultrasound regime using a low-cost device based on two confocal 1-MHz piezoelectric transducers and 3D-printed acoustic holograms. This new wave structure opens novel avenues for wave-matter interaction such as contactless particle manipulation, matter processing, or biomedical applications.

The problem of the hydrodynamic interaction of two unequal-sized spheres in a slightly rarefied gas is treated following the singular perturbation scheme of Sone & Onishi (1978), valid at small, but finite, particle Knudsen numbers. In this method the solution to the linearized BGKW transport equation governing the gas molecular motion consists of two parts: one describing a Knudsen layer where the actual microscopic boundary conditions are applied and the other describing a Hilbert region where the Stokes equations of continuum hydrodynamics hold. The Knudsen-layer solution establishes the ‘slip’ boundary conditions for the Stokes equations. Here we clearly distinguish between particle ‘slip’ due to the type of boundary conditions and particle ‘slip’ due to lengthscale effects as measured by the Knudsen number. The present analysis has been carried out to first order in particle Knudsen number for the case of diffuse reflective molecular boundary conditions. General relationships between the first- and zero-order velocity fields, both of which are written in the form of Lamb's (1932) solution to the Stokes equation, are established. It is illustrated how these general relationships can be used to determine the force and torque acting on a single sphere translating and rotating in a slightly rarefied gas. Finally, we have treated the two-sphere problem in a slightly rarefied gas using the twin multipole expansion method of Jeffrey & Onishi (1984). Here again, general relationships are established between the solutions of the first-order fluid velocity field and the zero-order velocity field, the latter being shown to recover Jeffrey & Onishi's results for stick boundary conditions. These general relationships are subsequently used to determine the complete resistance and mobility matrices of the two-sphere system. The symmetric properties of the resistance and mobility matrices are demonstrated for slip boundary conditions, in agreement with the general proof of Landau & Lifshitz (1980) and Bedeaux, Albano & Mazur (1977).

Domain branching near the boundary appears in many singularly perturbed models for microstructure in materials and was first demonstrated mathematically by Kohn and Müller for a scalar problem representing the elastic behavior of shape-memory alloys. We study here a model for shape-memory alloys based on the full vectorial problem of nonlinear elasticity, including invariance under rotations, in the case of two wells in two dimensions. We show that, for two wells with two rank-one connections, the energy is proportional to the power 2/3 of the surface energy, in agreement with the scalar model. In a case where only one rank-one connection is present, we show that the energy exhibits a different behavior, proportional to the power 4/5 of the surface energy. This lower energy is achieved by a suitable interaction of the two components of the deformations and hence cannot be reproduced by the scalar model. Both scalings are proven by explicit constructions and matching lower bounds.

Quantified Analyses of Aggression Pattern in a Captive Population of Musk Deer (Moschus Sifanicus)Alpine musk deer (Moschus sifanicus) are endangered as a result of habitat degradation and loss and centuries of widespread poaching. Consequently, musk deer farming was introduced as a measure to not only protect musk deer but also to provide a means for sustainable musk supply. An increased understanding of the social structure of captive populations is essential for both successful farming and improved welfare of individuals. This study recorded agonistic interactions between captive individuals at Xinglongshan Musk Deer Farm (XMDF), northwest China. The relationship between aggressive interactions and the individual's age and gender and opponent health was analysed. From our observations we found that stable social hierarchies developed within both captive male and gender-mixed musk deer groups. There was no significant correlation found between only age of individual and their status in the social hierarchy, and it was thus concluded, as social rank was not determined singularly by age, that a combination of other factors, such as experience and origin of the individual, better explain rank orders. Three forms of aggressive behaviour were expressed between males, in which threatening (56.38%±7.28%) was significantly more frequent than attacking (17.86%±5.94%) and displacing behaviours (25.78%±3.66%). There was no attacking behaviour observed in interactions initiated by males towards females, however displacing (70.85%±4.15%) was more common than threatening (29.15%±4.15%). Conflict-initiating male deer demonstrated more attacking and threatening behaviour towards male opponents than to female ones, however the differences were statistically insignificant. These results can be implemented into musk deer farming management practices through 1) rotating individuals within an enclosure on a frequent basis; 2) removing males from female enclosures after successful mating and 3) enclosing males in single sex enclosures. Furthermore, in order to improve musk deer farming and captive musk deer welfare, management systems should be kept relatively consistent in order to assist in establishing the stable social hierarchy patterns in captive populations.

The free surface of a viscous fluid is a source of convective flow (Marangoni convection) if its surface tension is distributed non-uniformly. Such non-uniformity arises from the dependence of the surface tension on a scalar quantity, either surfactant concentration or temperature. The surface-tension-induced velocity redistributes the scalar forming a closed-loop interaction. It is shown that under the assumptions of (i) small Reynolds number and (ii) vanishing diffusivity this nonlinear process is described by a single self-consistent two-dimensional evolution equation for the scalar field at the free surface that can be derived from the three-dimensional basic equations without approximation. The formulation of this equation for a particular system requires only the knowledge of the closure law, which expresses the surface velocity as a linear functional of the active scalar at the free surface. We explicitly derive these closure laws for various systems with a planar non-deflecting surface and infinite horizontal extent, including an infinitely deep fluid, a fluid with finite depth, a rotating fluid, and an electrically conducting fluid under the influence of a magnetic field. For the canonical problem of an infinitely deep layer we demonstrate that the dynamics of singular (point-like) surfactant or temperature distributions can be further reduced to a system of ordinary differential equations, equivalent to point-vortex dynamics in two-dimensional perfect fluids. We further show, using numerical simulations, that the dynamical evolution of initially smooth scalar fields leads in general to a finite-time singularity. The present theory provides a rational framework for a simplified modelling of strongly nonlinear Marangoni convection in high-Prandtl-number fluids or systems with high Schmidt number.

Abstract We investigate the topological excitations of rotating spin-1 ferromagnetic Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in an in-plane quadrupole field. Such a system sustains a rich variety of exotic vortex structures due to the spinor order parameter and the interplay among in-plane quadrupole field, SOC, rotation, and interatomic interaction. For the nonrotating case, with the increase of the quadrupole field strength, the system experiences a transition from a coreless polar-core vortex with a bright soliton to a singular polar-core vortex with a density hole. Without rotation but with fixed quadrupole field, when the SOC strength increases, the system transforms from a central Mermin-Ho vortex into a criss-crossed vortex-antivortex string lattice. For the rotating case, we give a phase diagram with respect to the quadrupole field strength and the SOC strength. It is shown that the rotating system supports four typical quantum phases: vortex necklace, diagonal vortex chain cluster, single diagonal vortex chain, and few vortex state. Furthermore, the system favors novel spin textures and skyrmion excitations including an antiskyrmion, a criss-crossed half-skyrmion-half-antiskyrmion lattice, a skyrmion-meron necklace, a symmetric half-skyrmion lattice, and an asymmetric skyrmion-meron lattice.

AbstractFluid dynamic equations are used to model various phenomena arising from physics, engineering, astrophysics, geophysics. One feature is that they take place at different time and length scales and it is important to understand which phenomena occur according to the use of single scales or to the interactions of them. From a mathematical point of view, these various physical behaviours give rise to different singular limits and, consequently to a different analysis of the asymptotic state of the governing equations. In this paper we will analyse a very simplified model given by a linearised continuity equation and by the classical momentum equation which include terms that take into account of rotation and we will show, according to the values of different scales, that the asymptotic behaviour of the model will be those of an incompressible fluid or of a geostrophic flow. Finally we point out, that the set of equations analysed in the paper may also fit in the artificial compressibility approximation methods.

AbstractThe impact of two tubercle leading-edge (TLE) modifications on the turbulent wake of a reference marine rudder at Reynolds number 2.26 × 106 was analysed numerically using Detached Eddy Simulations (DES). This paper studies the counter-rotating vortex pair formation around the TLE and their impact on the wake structures behind the rudder to find out if the vortex interaction can accelerate the tip vortex dissipation. According to the results, the tubercles enhanced lift for angles of attack (AOA) 10º and above, but at the cost of a drag penalty which reduced the rudders’ lift-to-drag ratio. The formation of the distinctive stream-wise counter-rotating vortex pairs occurred behind the tubercles, which then interacted with the dominant tip vortex. Due to the inherent spanwise flow component of finite-span lifting surfaces the counter-rotating vortex pairs were generated at unequal strength and soon merged into singular vortices co-rotating with the tip vortex. The vortices facilitated flow compartmentalisation over the rudder suction side which broke up the trailing-edge vortex sheet and confined the spanwise flow separation over the rudder surface as AOA increased. The tubercles confined flow separation closer to the rudder tip which reduced the lift generation in the tip area and minimised the initial tip vortex strength. Large elements of stream-wise counter-rotating vorticity formed around the localised stall cells of the TLE rudders that interacted with the tip vortex downstream, introducing elliptical instabilities further weakening the tip vortex and changing its trajectory.

In this study, a hybrid Cartesian-meshless method is first extended to deal with the thermal flows with complex immersed objects. The temperature and flow fields are governed by energy conservation equation and Navier-Stokes equations with Boussinesq approximation, respectively. The governing equations are solved by conventional finite difference scheme on Cartesian grid and generalized finite-difference (GFD) with singular value decomposition (SVD) approximation on meshless nodes, with second-order accuracy. The present thermal SVD-GFD method is applied to simulate the following six numerical examples over wide ranges of governing parameters, including that with high Prandtl number: (1) Forced convection around a circular cylinder; (2) Mixed convection around a stationary circular cylinder in a lid-driven cavity; (3) Mixed convection involving moving boundary in a cavity with two rotating circular cylinders; (4) Sedimentation of a cold circular particle in a long channel; (5) Freely falling of a sphere in viscous fluid with thermal buoyancy; (6) Sedimentation of a torus with thermal convection; (7) Flow over a heated circular cylinder. The excellent agreements between the published data and the present numerical results demonstrate the good capability of the thermal SVD-GFD method to simulate the thermal flows with complex immersed objects, especially those involving fluid-structure interaction and high Prandtl number.

In considering the vibrational properties of a crystal, a rigorous finite transformation of the particle displacements from their reference configuration is introduced. This transformation shows that an arbitrary set of such displacements may be regarded as made up of a rotation, a translation, a homogeneous deformation of the reference configuration, and a set of inhomogeneous deformational orthogonal modes. For a three-dimensional crystal, there are 3 N – 12 such inhomogeneous modes, which, in the limit of a large crystal can be considered wave-like. In the usual treatment beginning with the cyclic boundary conditions, 3 N wave-like modes are assumed and rotational displacements, for example, must be ignored. The present treatment accounts satisfactorily for all degrees of freedom, including rotational. Because of the non-singular nature of the above transformation, the transformation of the above modes to the normal modes proves that some normal modes are admixtures of inhomogeneous and homogeneous modes and therefore cannot possibly satisfy the Born cyclic boundary conditions. The vibrational hamiltonian is shown to contain the elastic energy and the elastic–phonon interaction terms as well as the usual wave energies. In the limit of a large crystal, it is shown that, for all processes involving phonons, the homogeneous coordinates may be regarded as effectively static, in much the same way as, in a simple theory of the Earth–Sun motion, the Sun, because of its large inertial mass, is considered stationary and its position coordinates static. The above transformation enables the case of a crystal, free or confined in a container, to be satisfactorily discussed. It is proved that the quantum mean value of the tensor whose independent elements define the homogeneous coordinates is, in the limit of a large crystal, equal to the strain tensor of the container, when it is being used to deform the crystal by being itself homogeneously deformed. A rigorous quantum treatment of crystal elastic constants may then be developed. For practical use, the 3 N – 12 inhomogeneous modes may be assumed to obey the cyclic boundary conditions. Thus a satisfactory complete basic treatment of lattice dynamics may be given which accounts for all degrees of freedom including rotation.

Drift: An IntroductionEntering into Drift is akin to entering—or becoming ensnared by—a hum. Projected across one wall, the work uses abstract visual forms to draw visitors into its meditational folds. Quadraphonic sound circulates in smooth, heavy pulses, like the steady rumble of a train running over deep-set tracks. A succession of vibrating lines occupy the screen, much like the horizontal static of a poorly-tuned television. Gradually, the ambient timbre darkens, the hum becomes more persistent and atmospheric undulations more frequent, until room and body expand with intensity. Throbbing vibrations connect ground to feet, roll along skin, finding their way into deep interiors until organs and sinew become subsumed by Drift’s thick, heart-gripping drone. The installation’s tight, affective grasp only becomes apparent upon the sudden release of this tension; the room lightens and hum eases as the screen whitens with faint patterns, like a window opening from a darkened room. Drift, by German artist Ulf Langheinrich, appeared in White Noise, an exhibition dedicated to abstract moving image art at the Australian Centre for the Moving Image in Melbourne (ACMI). At the time of this exhibition in 2005, I was undertaking a seven month study of ACMI’s Screen Gallery, also documenting the preceding exhibition, World without End. My research used the Gallery as a site to examine the shifting relationship between visitor experience, digital art and museums, as the space compelled unusual modalities of visitor interaction. Most notable were states of complete stillness. I aimed to investigate how art and technology might mediate visitor agency through such experiences; not only to understand how museum visitation is transforming in new and significant ways, but to also extrapolate a substantial account of an individual’s agency within this era of what Beck, Giddens and Lash have termed ‘reflexive modernisation’. However, existing studies of museum visitation are rarely informed by the subjective modalities of visitor encounter, but rather, detail how experiences are shaped by institutional practices (Bourdieu; Luhmann; Silverman; Falk; Falk and Dierking) or governmental agendas (Bennett; Hooper-Greenhill). A notable exception is Megan Hick’s phenomenological study of Sydney’s Powerhouse museum. Following this example, I developed a phenomenology of museum visitation that could privilege the visitor’s enunciation of experience, whilst also exploring how expressions of agency may be highly subjective, multifarious and nuanced. I used qualitative ethnographic techniques to gather phenomenological material. Firstly, I attended the Gallery on a fortnightly basis to conduct longitudinal participant observations. However, as observation offered no means to interpret quiet faces and still bodies I also undertook visitor interviews. I approached visitors immediately after their visitation, and attempted to capture a wide cross-sample of responses by recruiting on the basis of age, gender and reason for visitation. I undertook ten 45 minute interviews, enquiring into the factors influencing impressions of the Gallery, prior familiarity with museums, and opinions about media art and technology. This ethnographic material was central to my study, as the voices of visitors guided its thematic direction and ensuing analysis. As the first in-depth, qualitative analysis of visitation to the Screen Gallery, my study therefore makes an empirical contribution to existing visitor research by offering an original means of exploring issues of museum visitation and agency, and movement and stillness.For example, visitors often received Drift with complete stillness, lulled into a focused state of attention by the shiftings of light and sound. As interviewee Colleen reveals, this concentration arose because Drift resonated intimately, akin to a meditative encounter:There wasn’t any other emotion or feeling behind it other than feeling relieved and comfortable, and relaxed. It was almost meditative … I was actually trying not to think about anything! … I didn’t want it to be influenced by the morning’s happenings … I just thought ‘this is relaxing’.Colleen has described how stillness and movement are therefore modalities within a broad vocabulary of interaction. While theorists have long noted how the transition from painting to film marked a shift from still to more ‘active’ forms of contemplation (Benjamin), an unanticipated finding of my study reasserted stillness as a dominant modality of active reception. In this article I therefore ask how agency finds expression within states of stillness.I propose that stillness mediates a distinctive form of agency as it is laden with what Brian Massumi calls ‘potential movement.’ I explore this concept with reference to visitors’ experiences of History of a Day, a work in World Without End. I then draw upon Henri Lefebvre’s description of ‘eurrhythmic’ congruence to describe how stillness is characterised by a focused state of attention, reflecting a highly subjective form of agency. I conclude by describing how this spatial awareness enables individuals to realise their own creativity, and inspire new praxes for daily living.1. Stillness: A State of Potential MovementBy dedicating its exhibition space to time-based art, ACMI’s Screen Gallery has cultivated a new temporal paradigm for visitor participation. It mediates both stillness and movement. Visitors described how the task of negotiating multiple time-based screens in a singular space loosened the temporal boundaries of engagement. Visitors were frequently compelled to pause and wait, as there was an absence of ‘entry’ or ‘exit’ points for viewing a piece. This raises questions as to how slower, or ‘still’, forms of participation in the Gallery may elicit agency. If considering stillness as a state that exists as an inverse of movement, rather than a state lacking in movement, it becomes possible to locate agency within the process of maintaining stillness, and as a result, engender what Brian Massumi describes as ‘potential movement’.In his account of architect Lars Spuybroek’s wetGRID design, Massumi describes how Spuybroek compares the experience of viewing images with the spatial experience of moving through buildings. Spuybroek drew from the premise that while movement can be understood as “the actual content of architecture” (322), it is more difficult to draw correlations between the properties of movement and perception of still images. He developed the idea of potential movement to breach a commonality between the two, as paraphrased by Massumi: “potentials for movement are extracted from actual movement, then fed back into it via architecture. We normally think of abstraction as a distancing from the actual, but here potentials are being ‘abstracted into it’” (323). Spuybroek therefore inscribed the idea of ‘tendency’ in his work, an ‘affordance’ that manifests as “a possibility of convergence that unconsciously exerts a pull, drawing the body forward into a movement the body already feels itself performing before it actually stirs” (Gibson in Massumi 324). This idea suggests that the act of sitting and viewing an image, can be reconceived as a state laden with potential movement. As Massumi describes, “sitting still is the performance of a tendency towards movement … It is the pre-performance, in potential, of the movement and its function … It is in intensity” (324).Sitting can therefore be regarded an 'active' state, where 'tendency'—indeed intensity—charges stillness with a potential for movement, actualisation and change. Conventions that invite still forms of participation in an interactive museum are an opportunity to express one’s agency, as one cannot feel the full momentum of tendency if not having at first remained still. At one level, the process of waiting for a work to begin or end generates a potential for movement, as visitors must decide when they will move towards another work. However, the potential for agency is also articulated within a less performative, ‘internal’ shift that arises within stillness, when visitors eschew reflexive forms of interaction to maintain a focused state of attention.2. Focusing Attention in StillnessVisitors’ interaction with Simon Carrol and Martin Friedel's History of a Day (2004) demonstrated how such a focused attention arises. This work comprises five screens arranged in a pentagonal shape. Visitors engage with this work whilst moving or still, seating themselves on an ottoman set within the pentagon or viewing the work while walking around its outside perimeter. The work came to mediate a number of different types of still and playful encounters, as described by Sean:I was aware that there was other stuff going on around the gallery … could see that out the corner of your eye because there’s spaces in-between screens, but at the same time I wasn’t hurried … And Luke who was with me, he sat down and watched one particular screen, whereas I sort of moved around. When I got to the edge I could see two or three screens at once, so I was just trying to work out what the story was. On one hand, the ‘gaps’ between these screens could fragment visitors’ attention and mediate reflexive forms of perception. Sean described how he “moved around”, as he was drawn to these ‘gaps’ as he exchanged peripheries and centres of focus. However, the close arrangement of the five screens also created a veiled, intimate space that confined visitors’ attention within the spatial parameters of the work. Unlike Sean, Luke remained seated. His experience was conditioned by stillness. He sat observing a single screen and maintained a focused state of attention. By focusing their attention in this way, visitors become more receptive towards the affective experience of viewing art. For example, History of a Day flutters with time-lapse images, a soothing rhythm of night turning to day and to night again. On one hand, each screen has been allocated its own narrative, a temporal illustration of a day’s passing within natural and human-made landscapes. A fairground, for example, was shot at night and showed crowds arriving, swarming, alighting rides and departing. However, it is possible to yield to the projection’s visual and aural rhythm, and in doing so abstract the figurative signifier of each scene. Narrative logic recedes as the senses become flooded, and in turn slows the pace of reflexive perception. Without the imposition of a linear narrative the work’s images begin to unfold with a new slowness. The main ride comes to resemble the slowly beating wings of a moth in lamplight, arms lifting, rotating and dropping in the fairground floodlights. People, rides and the dark sky blend into a meditation on colour, rhythm and sound, a palette comprising the many moments that emerge and pass at a night carnival.This form of perception elicits an agency of complex, affective awareness. Sound artist Brian Eno’s account of the role of silence in ambient music provides a close analogy as to how experiences of stillness in the Screen Gallery become dynamic with enhanced affective awareness. He describes how silences—a ‘stillness’ in sound—actually draw attention to the aural experience that preceded it, as the “‘rests’ are invariably filled in by ‘echoes’ of previously heard fragments” (in Tamm 134). In other words, the experience of listening is heightened by silences, for they create a space of reflection that resonates with the impressions of sound passed. The Gallery is an ambient chamber that echoes with affective forms of experiential encounter rather than echoes of sound. The echoes of visitors’ encounters are also intensified by stillness. Stillness focuses attention, so visitors garner an affective awareness of their spatial environment. This awareness constitutes a distinctive form of agency within the museum, for it enables visitors to locate what Henri Lefebvre describes as a ‘rhythmic’ congruence between their subjective experience and conditions of external environment.3. Awareness of Rhythmic CongruenceIn his theory of rhythmnanalysis, Henri Lefebvre (16) describes how an awareness of ‘rhythmic’ congruity and incongruity can be used to inform a politics in daily life. He argues that practices of self-observation and spatial awareness can reveal how our internal and environmental rhythms are a part of a rhythmic landscape, and can be used as a political means for change. Lefebvre (20) delineates between ‘eurhythmia’ and ‘arrhythmia’ as the forms of rhythmic logic that describe states of congruity:What is certain is that harmony sometimes (often) exists: eurhythmia. The eu-rhythmic body, composed of diverse rhythms – each organ, each function, having its own – keeps them in a metastable equilibrium, which is always understood and often recovered, with the exception of disturbances (arrhythmia) that sooner of later becomes illness (the pathological state). But the surroundings of bodies, be they in nature or a social setting, are also bundles, bouquets, garlands of rhythms, to which it is necessary to listen in order to grasp the natural or produced ensembles. While Lefebvre uses these definitions to develop a Marxist critique of modernity, they also show how within the flexible temporal boundaries of stillness, visitors can express a form of agency by using their heightened affective awareness to locate eurhythmic and arrhythmic experiences. By becoming aware of the way we are conditioned by rhythms, we can begin to imprint new rhythms upon the patterns that govern cultural and social practices. Within the Screen Gallery, this rhythmic observation manifests as an attentiveness towards the temporal relationship between internal sensation and external environment.Congruence between internal and external rhythms was often described by visitors as a feeling of relaxation, even meditation. For example, Sean drew comparisons between still encounters with time-based art and his impression of quiet environments: “It’s like having background music while you’re falling asleep, or you turn the radio on so you haven’t caught the start of a song but you catch the end of it”. These associations imply a close environmental relationship between sound and body, where the rich aesthetic presence of art overrides the expectation of narrative continuity. Perhaps most telling is Sean’s analogy of falling asleep to background music, as it suggests that time-based art can maintain an ambient presence while not intruding upon natural bodily ‘rhythms’. It seems that a harmony between body and art environment allows a pull towards a state of relaxation akin to the drift of sleep, which, notably, is a point where both internal and external rhythms synchronise. Falling asleep is a crossing of thresholds into a space dominated by the activities of the unconscious. Occupying the Gallery and surrendering to a state of relaxation can therefore also be understood as crossing a threshold into a deeper, more internal realm of interaction with art.Affective awareness therefore enables visitors to cultivate a greater sensitivity towards their sensory responses. This is a highly-subjective agency, as it arises when visitors develop a keen awareness of the eurrhythmic alignment between the rhythm of external space, and their own, internal rhythm. Stillness therefore draws attention to the complexity of our own subjective experience, and the different ways we are conditioned by our environments. Yet most importantly, these experiences also generated self-reflection and a desire to creatively transform their circumstances. Matthew described how his encounter with art aroused creative inspiration: “I go there to experience something new. I would love to be able to do something like that… Maybe it’s something for me, where I wish I was doing something else in terms of my occupation.” Paul noted how expressive potential could be expanded by considering oneself an artist: “you can do it yourself as well, and I suppose that’s what draws people in to the whole thing”. Katrina suggested that aesthetic forms of interaction can challenge the conventional ways of thinking about and responding to our environment: “if it gets somebody to do something different, or, gets someone to do something in a different way maybe, expand their minds in that way, maybe that’s a use for it as well … give them something to think about, and they can see it again in a different light”. These comments show how stillness can enable a realisation of one’s own subjective, creative potential by countering the reflexive speed of the everyday.ConclusionMy study of ACMI’s Screen Gallery has shown how agency finds expression in stillness. The temporal elasticity created by artwork and institution allows visitors to appropriate time and space in a way that slows the pace of movement and focuses attention, in turn enhancing a visitor’s awareness of their presence and spatial environment. Stillness therefore heightens visitors’ awareness of sensation, sentience, the body’s occupation of time and space. This form of encounter elicits a feeling of congruence and awakens the spirit. This transformation was the mainstay of the political project set by Lefebvre, a statement on mobilising individuals to affect change by becoming more attentive towards incongruities between self and environment. In the Gallery it became possible, through immersion in an aesthetic, ambient space, for visitors to cultivate an intuition towards their own rhythms and those of surrounding environments. An important claim is to be staked on creating spaces for stillness in daily life, as opportunities for stillness are becoming increasingly scarce within the dynamics of spatial and temporal compression that characterise this era of globalisation and informationalisation. As Heidi describes, these moments given to daydreaming and reflection can become powerful conduits for realising one’s own potential:[It] gives you a new lease on life. And all the dreams you have – it’s possible … Sometimes you think ‘it’s all a bit out of reach, it’s too difficult,’ whereas you go and see something like that, and … it makes everything clear. And makes everything possible.ReferencesBeck, Ulrich, Anthony Giddens, and Scott Lash. Reflexive Modernization: Politics, Tradition and Aesthetics in the Modern Social Order. 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