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Journal articles on the topic 'Zero-dispersion limit'

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Published: 7 July 2024
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1

David Levermore, C. "The hyperbolic nature of the zero dispersion Kdv limit." Communications in Partial Differential Equations 13, no. 4 (January 1988): 495–514. http://dx.doi.org/10.1080/03605308808820550.

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2

Lax, Peter D. "The zero dispersion limit, a deterministic analogue of turbulence." Communications on Pure and Applied Mathematics 44, no. 8-9 (October 1991): 1047–56. http://dx.doi.org/10.1002/cpa.3160440815.

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3

GLASS, OLIVIER, and SERGIO GUERRERO. "UNIFORM CONTROLLABILITY OF A TRANSPORT EQUATION IN ZERO DIFFUSION–DISPERSION LIMIT." Mathematical Models and Methods in Applied Sciences 19, no. 09 (September 2009): 1567–601. http://dx.doi.org/10.1142/s0218202509003899.

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In this paper, we consider the controllability of a transport equation perturbed by small diffusion and dispersion terms. We prove that for a sufficiently large time, the cost of the null-controllability tends to zero exponentially as the perturbation vanishes. For small times, on the contrary, we prove that this cost grows exponentially.
4

Akhmedova, V. E., and A. V. Zabrodin. "Elliptic parameterization of Pfaff integrable hierarchies in the zero-dispersion limit." Theoretical and Mathematical Physics 185, no. 3 (December 2015): 1718–28. http://dx.doi.org/10.1007/s11232-015-0374-z.

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5

Lin, Chi-Kun, and Yau-Shu Wong. "Zero-dispersion limit of the short-wave–long-wave interaction equations." Journal of Differential Equations 228, no. 1 (September 2006): 87–110. http://dx.doi.org/10.1016/j.jde.2006.03.027.

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6

Holden, H., K. H. Karlsen, and D. Mitrovic. "Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function." International Journal of Differential Equations 2009 (2009): 1–33. http://dx.doi.org/10.1155/2009/279818.

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We consider multidimensional conservation laws with discontinuous flux, which are regularized with vanishing diffusion and dispersion terms and with smoothing of the flux discontinuities. We use the approach ofH-measures to investigate the zero diffusion-dispersion-smoothing limit.
7

Berendt-Marchel, M., and A. Wawrzynczak. "Does the Zero Carry Essential Information for Artificial Neural Network learning to simulate the contaminant transport in Urban Areas?" Journal of Physics: Conference Series 2090, no. 1 (November 1, 2021): 012027. http://dx.doi.org/10.1088/1742-6596/2090/1/012027.

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Abstract The release of hazardous materials in urbanized areas is a considerable threat to human health and the environment. Therefore, it is vital to detect the contamination source quickly to limit the damage. In systems localizing the contamination source based on the measured concentrations, the dispersion models are used to compare the simulated and registered point concentrations. These models are run tens of thousands of times to find their parameters, giving the model output’s best fit to the registration. Artificial Neural Networks (ANN) can replace in localization systems the dispersion models, but first, they need to be trained on a large, diverse set of data. However, providing an ANN with a fully informative training data set leads to some computational challenges. For example, a single simulation of airborne toxin dispersion in an urban area might contain over 90% of zero concentration in the positions of the sensors. This leads to the situation when the ANN target includes a few percent positive values and many zeros. As a result, the neural network focuses on the more significant part of the set - zeros, leading to the non-adaptation of the neural network to the studied problem. Furthermore, considering the zero value of concentration in the training data set, we have to face many questions: how to include zero, scale a given interval to hide the zero in the set, and include zero values at all; or limit their number? This paper will try to answer the above questions and investigate to what extend zero carries essential information for the ANN in the contamination dispersion simulation in urban areas. For this purpose, as a testing domain, the center of London is used as in the DAPPLE experiment. Training data is generated by the Quick Urban & Industrial Complex (QUIC) Dispersion Modeling System.
8

Tian, Fei Ran. "Oscillations of the zero dispersion limit of the korteweg-de vries equation." Communications on Pure and Applied Mathematics 46, no. 8 (September 1993): 1093–129. http://dx.doi.org/10.1002/cpa.3160460802.

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9

Tovbis, Alexander, Stephanos Venakides, and Xin Zhou. "On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation." Communications on Pure and Applied Mathematics 57, no. 7 (April 16, 2004): 877–985. http://dx.doi.org/10.1002/cpa.20024.

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10

Ercolani, Nicholas M., C. David Levermore, and Taiyan Zhang. "The behavior of the weyl function in the zero-dispersion KdV limit." Communications in Mathematical Physics 183, no. 1 (January 1997): 119–43. http://dx.doi.org/10.1007/bf02509798.

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11

Fokas, A. S., and S. Kamvissis. "Zero-dispersion limit for integrable equations on the half-line with linearisable data." Abstract and Applied Analysis 2004, no. 5 (2004): 361–70. http://dx.doi.org/10.1155/s1085337504306093.

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We study the zero-dispersion limit for certain initial boundary value problems for the defocusing nonlinear Schrödinger (NLS) equationand for the Korteweg-de Vries (KdV)equation with dominant surface tension. These problems are formulated on the half-line and they involve linearisable boundaryconditions.
12

Novokshenov, V. Yu. "Zero-dispersion limit to the Korteweg-de Vries equation: a dressing chain approach." Regular and Chaotic Dynamics 13, no. 5 (October 2008): 424–30. http://dx.doi.org/10.1134/s1560354708050043.

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13

Grava, Tamara, and Fei-Ran Tian. "The generation, propagation, and extinction of multiphases in the KdV zero-dispersion limit." Communications on Pure and Applied Mathematics 55, no. 12 (September 27, 2002): 1569–639. http://dx.doi.org/10.1002/cpa.10050.

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14

Venakides, Stephanos. "The zero dispersion limit of the Korteweg-de Vries equation with periodic initial data." Transactions of the American Mathematical Society 301, no. 1 (January 1, 1987): 189. http://dx.doi.org/10.1090/s0002-9947-1987-0879569-7.

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15

Miller, Peter D., and Zhengjie Xu. "The Benjamin-Ono hierarchy with asymptotically reflectionless initial data in the zero-dispersion limit." Communications in Mathematical Sciences 10, no. 1 (2012): 117–30. http://dx.doi.org/10.4310/cms.2012.v10.n1.a6.

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16

Pierce, Virgil, and Fei-Ran Tian. "Large time behavior of the zero dispersion limit of the fifth order KdV equation." Dynamics of Partial Differential Equations 4, no. 1 (2007): 87–109. http://dx.doi.org/10.4310/dpde.2007.v4.n1.a3.

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17

Wright, Otis C. "Korteweg–de vries zero dispersion limit: Through first breaking for cubic-like analytic initial data." Communications on Pure and Applied Mathematics 46, no. 3 (March 1993): 423–40. http://dx.doi.org/10.1002/cpa.3160460306.

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18

Miller, Peter D., and Zhengjie Xu. "On the zero-dispersion limit of the benjamin-ono cauchy problem for positive initial data." Communications on Pure and Applied Mathematics 64, no. 2 (September 16, 2010): 205–70. http://dx.doi.org/10.1002/cpa.20345.

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19

Gassot, Louise. "Lax Eigenvalues in the Zero-Dispersion Limit for the Benjamin–Ono Equation on the Torus." SIAM Journal on Mathematical Analysis 55, no. 5 (October 6, 2023): 5782–822. http://dx.doi.org/10.1137/23m154635x.

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20

Tovbis, Alexander, Stephanos Venakides, and Xin Zhou. "On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case." Communications on Pure and Applied Mathematics 59, no. 10 (2006): 1379–432. http://dx.doi.org/10.1002/cpa.20142.

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21

ROSENHOUSE-DANTSKER, A., A. D. WILSON-GORDON, and H. FRIEDMANN. "ON THE PUMP INTENSITY DEPENDENCE OF PROBE NOISE, ABSORPTION AND DISPERSION IN A DRIVEN TWO-LEVEL SYSTEM AT POINTS OF ZERO ABSORPTION AND IN THE DEAD-ZONE." Journal of Nonlinear Optical Physics & Materials 05, no. 04 (October 1996): 899–909. http://dx.doi.org/10.1142/s0218863596000635.

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We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system at points of zero absorption and in the dead-zone. We find that in the Doppler-limit, maximum noise is obtained at the extremum point of the probe dispersion curve as a function of the pump intensity. This implies that in this limit, the noise is maximal at the transition point between focusing and defocusing. On the other hand, in the absence of Doppler broadening, this is true only for the case of a resonant pump.
22

Nse Biyoghe, S., Th B. Ekogo, and A. B. Moubissi. "Collective variable analysis of the nonlinear Schrödinger equation for soliton molecules in fibers." Journal of Nonlinear Optical Physics & Materials 26, no. 02 (June 2017): 1750023. http://dx.doi.org/10.1142/s0218863517500230.

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We present a description of soliton molecules in terms of its collective variables namely temporal separation between two consecutive pulses, peak-power of each pulse, center-of-mass, chirp, frequency and phase of the whole molecule. Assuming the Hermite–Gaussian ansatz to represent the temporal profile of the molecule, we derive a set of six differential equations for the evolution of the collective variables in the limit of the bare or variational approximation. Then we perform numerical experiments to confirm the ability of the proposed approach for two-soliton molecule propagating along a Dispersion-managed fiber for anomalous, zero or normal averaged dispersion.
23

Spydell, Matthew S., and Falk Feddersen. "The effect of a non-zero Lagrangian time scale on bounded shear dispersion." Journal of Fluid Mechanics 691 (December 13, 2011): 69–94. http://dx.doi.org/10.1017/jfm.2011.443.

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AbstractPrevious studies of shear dispersion in bounded velocity fields have assumed random velocities with zero Lagrangian time scale (i.e. velocities are$\delta $-function correlated in time). However, many turbulent (geophysical and engineering) flows with mean velocity shear exist where the Lagrangian time scale is non-zero. Here, the longitudinal (along-flow) shear-induced diffusivity in a two-dimensional bounded velocity field is derived for random velocities with non-zero Lagrangian time scale${\tau }_{L} $. A non-zero${\tau }_{L} $results in two-time transverse (across-flow) displacements that are correlated even for large (relative to the diffusive time scale${\tau }_{D} $) times. The longitudinal (along-flow) shear-induced diffusivity${D}_{S} $is derived, accurate for all${\tau }_{L} $, using a Lagrangian method where the velocity field is periodically extended to infinity so that unbounded transverse particle spreading statistics can be used to determine${D}_{S} $. The non-dimensionalized${D}_{S} $depends on time and two parameters: the ratio of Lagrangian to diffusive time scales${\tau }_{L} / {\tau }_{D} $and the release location. Using a parabolic velocity profile, these dependencies are explored numerically and through asymptotic analysis. The large-time${D}_{S} $is enhanced relative to the classic Taylor diffusivity, and this enhancement increases with$ \sqrt{{\tau }_{L} } $. At moderate${\tau }_{L} / {\tau }_{D} = 0. 1$this enhancement is approximately a factor of 3. For classic shear dispersion with${\tau }_{L} = 0$, the diffusive time scale${\tau }_{D} $determines the time dependence and large-time limit of the shear-induced diffusivity. In contrast, for sufficiently large${\tau }_{L} $, a shear time scale${\tau }_{S} = \mathop{ ({\tau }_{L} {\tau }_{D} )}\nolimits ^{1/ 2} $, anticipated by a simple analysis of the particle’s domain-crossing time, determines both the${D}_{S} $time dependence and the large-time limit. In addition, the scalings for turbulent shear dispersion are recovered from the large-time${D}_{S} $using properties of wall-bounded turbulence.
24

GAZOL, A., T. PASSOT, and P. L. SULEM. "Nonlinear dynamics of obliquely propagating Alfvén waves." Journal of Plasma Physics 60, no. 1 (August 1998): 95–109. http://dx.doi.org/10.1017/s0022377898006394.

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The long-wave, small-amplitude dynamics of obliquely propagating Alfvén waves is shown, using a reductive perturbative expansion, to be purely linear not only in one space dimension but also in the dispersionless limit in higher dimensions. Furthermore, in the context of multidimensional wave-train modulation, all the diffraction coefficients are found to tend to zero with the dispersion, while the non-linear terms in the envelope equation remain finite. In this ‘semiclassical’ limit, the envelope dynamics results in the formation of growing regions of finite-amplitude oscillations with a typical scale intermediate between the size of the wave packet and its wavelength.
25

Bassey, Uduak E., Mary I. Akinyemi, and Kelechi F. Njoku. "On Zero inflated models with applications to maternal healthcare utilization." International Journal of Mathematical Analysis and Optimization: Theory and Applications 7, no. 2 (March 28, 2022): 65–75. http://dx.doi.org/10.52968/28309288.

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We consider the problem of modelling count data with excess zeros and over-dispersion which are commonly encountered in various disciplines that limit the use of traditional models for count outcomes. Our research work applies the Zero-inflated Poisson and Negative Binomial models in modelling Maternal Health Care (MHC) utilization in Nigeria, employing the Andersen’s behavioural model to examine the effect of predisposing, enabling, and need factors on MHC utilization. The performance of these models are compared to the traditional Poisson and negative binomial models. The Vuong test and AIC suggests that the Zero-inflated Negative Binomial model provided the most significant improvement over traditional models for count outcomes.
26

M. KARFAA, YASIN, M. ISMAIL, F. M. ABBOU, and A. S. SHAARI. "THEORETICAL EVALUATION OF NONLINEAR EFFECTS ON OPTICAL WDM NETWORKS WITH VARIOUS FIBER TYPES." IIUM Engineering Journal 9, no. 2 (September 29, 2010): 53–66. http://dx.doi.org/10.31436/iiumej.v9i2.100.

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A theoretical study is carried out to evaluate the performance of an opticalwavelength division multiplexing (WDM) network transmission system in the presenceof crosstalk due to optical fiber nonlinearities. The most significant nonlinear effects inthe optical fiber which are Cross-Phase Modulation (XPM), Four-Wave Mixing (FWM),and Stimulated Raman Scattering (SRS) are investigated. Four types of optical fiber areincluded in the analysis; these are: single-mode fiber (SMF), dispersion compensationfiber (DCF), non-zero dispersion fiber (NZDF), and non-zero dispersion shifted fiber(NZDSF). The results represent the standard deviation of nonlinearity induced crosstalknoise power due to FWM and SRS, XPM power penalty for SMF, DCF, NZDF, andNZDSF types of fiber, besides the Bit Error Rate (BER) for the three nonlinear effectsusing standard fiber type (SMF). It is concluded that three significant fiber nonlinearitiesare making huge limitations against increasing the launched power which is desired,otherwise, lower values of launched power limit network expansion including length,distance, covered areas, and number of users accessing the WDM network, unlesssuitable precautions are taken to neutralize the nonlinear effects. Besides, various fibertypes are not behaving similarly towards network parameters.
27

Strelko, Oleh, Oleh Pylypchuk, Yuliia Berdnychenko, and Svitlana Isaienko. "COMPARING DISPERSION COMPENSATION METHODS FOR 120 GB/S OPTICAL TRANSMISSION: PRE, POST, AND SYMMETRICAL SCHEMES." Journal of Engineering Research [TJER] 19, no. 2 (April 5, 2023): 163–79. http://dx.doi.org/10.53540/tjer.vol19iss2pp163-179.

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One of the major factors that limit the performance of an optical fiber communication system is dispersion. In order to get a high transmission range with high data rates, techniques must be in place to compensate for the dispersion caused by fiber nonlinearity. Dispersion Compensating Fiber (DCF) and Fiber Bragg Grating (FBG) are the trending dispersion compensation techniques in optical fiber communication. The use of DCF and FBG as a method of dispersion compensation can notably enhance the overall performance of the system. Broadening is a function of distance as well as the Dispersion parameter (D). The dispersion parameter is given in ps/nm/km and changes from fiber to fiber and also is a function of wavelength. In this paper, we investigate pre-, post-, and symmetrical compensating schemes in three different compensating models: DCF, FBG, and DCF cascaded to FBG. The system performance was evaluated in terms of Q-factor and Bit Error Rate (BER) for one optical channel communication system at 120 Gbps Return to Zero (RZ) signal launched over Single-Mode Fiber (SMF) of 100 km by using OptiSystem 7.0 software.
28

Glass, O., and S. Guerrero. "Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit." Asymptotic Analysis 60, no. 1-2 (2008): 61–100. http://dx.doi.org/10.3233/asy-2008-0900.

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29

Glass, Olivier, and Sergio Guerrero. "Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit." PAMM 7, no. 1 (December 2007): 1041601–2. http://dx.doi.org/10.1002/pamm.200701006.

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30

Wu, Reng-Lai, Ye-Jun Long, Hong-Jie Xue, Yabin Yu, and Hui-Fang Hu. "Plasmon dispersions in ultrathin metallic films." International Journal of Modern Physics B 28, no. 27 (October 30, 2014): 1450189. http://dx.doi.org/10.1142/s0217979214501896.

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We present an eigen-equation for plasmon of ultrathin films based on the self-consistent linear response approximation (SCLRA). The calculations for plasmon dispersion in both single and multilayer systems are reported. There are two types of plasmon in the plasmon spectrum, two-dimensional (2D) and bulk-like (BL) modes. The plasmon energy of the 2D mode is zero in the long wave limit, while the one of BL mode is nonzero in the long-wave limit. Given a surface electron density, with the decrease of the wave vector the dispersions of the 2D plasmon of different layer systems become equal to each other, and approach results of the pure 2D system.
31

Leibovich, S., S. N. Brown, and Y. Patel. "Bending waves on inviscid columnar vortices." Journal of Fluid Mechanics 173 (December 1986): 595–624. http://dx.doi.org/10.1017/s0022112086001283.

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Bending waves, perturbation modes leading to deflections of the vortex centreline, are considered for an infinitely long straight vortex embedded in an irrotational flow of unlimited extent. We first establish the general form of the dispersion relation for long waves on columnar vortices with arbitrary distributions of axial and azimuthal vorticity by a singular perturbation analysis of the Howard-Gupta equation. The asymptotic results are shown to compare favourably with numerical solutions of the Howard-Gupta equation for wavelengths comparable to the vortex core radius and longer. Dispersion relations are then found numerically for specific models of vortex core structures observed experimentally; here no restrictions are placed on wavelength. The linear dispersion relation has an infinite number of branches, falling into two families; one with infinite phase speed at zero wavenumber (which we call ‘fast’ waves), the other with zero phase speed (‘slow’ waves). In the long-wave limit, slow waves have zero group velocity, while the fast waves may have finite non-zero group speeds that depend on the form of the velocity profiles on the axis of rotation. Weakly nonlinear waves are described under most circumstances by the nonlinear Schrödinger equation. Solitons are possible in certain ‘windows’ of wavenumbers of the carrier waves. An example has already been presented by Leibovich & Ma (1983), who compute solitons and soliton windows on a fast-wave branch for a vortex with a particular core structure. Experimental data of Maxworthy, Hopfinger & Redekopp (1985) reveal solitons which appear to be associated with the slow branch, and these are computed for velocity profiles fitting their data. The nonlinear Schrödinger equation is shown to fail for long waves, and to be replaced by a nonlinear integro-differential equation.
32

MIRZANEJHAD, SAEED, BEHROUZ MARAGHECHI, FARSHAD SOHBATZADEH, and IMAN KAMEL-JAHROMI. "Space-charge waves in a relativistic electron beam with ion-channel guiding." Journal of Plasma Physics 77, no. 3 (November 5, 2010): 419–29. http://dx.doi.org/10.1017/s0022377810000632.

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AbstractSpace-charge waves in a relativistic electron beam that completely fills a cylindrical metallic waveguide and is guided by an ion channel are analyzed numerically. Equilibrium consists of a uniform and rigid rotation without betatron oscillations. Using cold fluid equations a differential equation and boundary conditions are derived that constitute an eigenvalue problem. This eigenvalue problem is solved, numerically, with the finite difference scheme using shooting method. Dispersion characteristics and electrostatic potential structures of azimuthally symmetric and nonsymmetric space-charge waves are studied. Perfect agreement with analytical results at asymptotic limit of zero axial velocity is found. It was found that relativistic effects modify the dispersion characteristics of the space-charge waves considerably and can concentrate the electric field energy of the wave into a thin and small shell around the axis.
33

Venakides, Stephanos. "The zero dispersion limit of the korteweg-de vries equation for initial potentials with non-trivial reflection coefficient." Communications on Pure and Applied Mathematics 38, no. 2 (March 1985): 125–55. http://dx.doi.org/10.1002/cpa.3160380202.

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34

Chase, G. William, and Brian Thompson. "Accelerated Solvent Extraction of Vitamin K1 in Medical Foods in Conjunction with Matrix Solid-Phase Dispersion." Journal of AOAC INTERNATIONAL 83, no. 2 (March 1, 2000): 407–10. http://dx.doi.org/10.1093/jaoac/83.2.407.

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Abstract An extraction technique is described for vitamin K1 in medical foods, using accelerated solvent extraction (ASE) in conjunction with matrix solid-phase dispersion (MSPD). The medical food sample is treated as it would be with MSPD extraction, followed by ASE for a hands-free automated extraction. The vitamin K1 in the ASE extract is then quantitated by reversed-phase liquid chromatography with fluorescence detection. The chromatography specifications are identical to those in previous work that used MSPD only, with a limit of detection of 6.6 pg and a limit of quantitation of 22 pg on column. Recoveries, which were determined for an analyte-fortified zero control reference material for medical foods, averaged 97.6% (n = 25) for vitamin K1. The method provides a rapid, automatic, specific, and easily controlled assay for vitamin K1 in fortified medical foods with minimal solvent usage.
35

Salasnich, Luca. "Electrodynamics of Superconductors: From Lorentz to Galilei at Zero Temperature." Entropy 26, no. 1 (January 12, 2024): 69. http://dx.doi.org/10.3390/e26010069.

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We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law of thermodynamics, the entropy of the system is zero. In the nonrelativistic limit, we obtain a Galilei-invariant superconducting system, which differs with respect to the familiar Schrödinger-like one. From this point of view, there are similarities with the Pauli equation of fermions, which is derived from the Dirac equation in the nonrelativistic limit and has a spin-magnetic field term in contrast with the Schrödinger equation. One of the peculiar effects of our model is the decay of a static electric field inside a superconductor exactly with the London penetration length. In addition, our theory predicts a modified D’Alembert equation for the massive electromagnetic field also in the case of nonrelativistic superconducting matter. We emphasize the role of the Nambu–Goldstone phase field, which is crucial to obtain the collective modes of the superconducting matter field. In the special case of a nonrelativistic neutral superfluid, we find a gapless Bogoliubov-like spectrum, while for the charged superfluid we obtain a dispersion relation that is gapped by the plasma frequency.
36

Asselin, Olivier, and William R. Young. "An improved model of near-inertial wave dynamics." Journal of Fluid Mechanics 876 (August 1, 2019): 428–48. http://dx.doi.org/10.1017/jfm.2019.557.

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The YBJ equation (Young & Ben Jelloul, J. Marine Res., vol. 55, 1997, pp. 735–766) provides a phase-averaged description of the propagation of near-inertial waves (NIWs) through a geostrophic flow. YBJ is obtained via an asymptotic expansion based on the limit $\mathit{Bu}\rightarrow 0$, where $\mathit{Bu}$ is the Burger number of the NIWs. Here we develop an improved version, the YBJ+ equation. In common with an earlier improvement proposed by Thomas, Smith & Bühler (J. Fluid Mech., vol. 817, 2017, pp. 406–438), YBJ+ has a dispersion relation that is second-order accurate in $\mathit{Bu}$. (YBJ is first-order accurate.) Thus both improvements have the same formal justification. But the dispersion relation of YBJ+ is a Padé approximant to the exact dispersion relation and with $\mathit{Bu}$ of order unity this is significantly more accurate than the power-series approximation of Thomas et al. (2017). Moreover, in the limit of high horizontal wavenumber $k\rightarrow \infty$, the wave frequency of YBJ+ asymptotes to twice the inertial frequency $2f$. This enables solution of YBJ+ with explicit time-stepping schemes using a time step determined by stable integration of oscillations with frequency $2f$. Other phase-averaged equations have dispersion relations with frequency increasing as $k^{2}$ (YBJ) or $k^{4}$ (Thomas et al. 2017): in these cases stable integration with an explicit scheme becomes impractical with increasing horizontal resolution. The YBJ+ equation is tested by comparing its numerical solutions with those of the Boussinesq and YBJ equations. In virtually all cases, YBJ+ is more accurate than YBJ. The error, however, does not go rapidly to zero as the Burger number characterizing the initial condition is reduced: advection and refraction by geostrophic eddies reduces in the initial length scale of NIWs so that $\mathit{Bu}$ increases with time. This increase, if unchecked, would destroy the approximation. We show, however, that dispersion limits the damage by confining most of the wave energy to low $\mathit{Bu}$. In other words, advection and refraction by geostrophic flows does not result in a strong transfer of initially near-inertial energy out of the near-inertial frequency band.
37

BÜHLER, OLIVER, and MIRANDA HOLMES-CERFON. "Particle dispersion by random waves in rotating shallow water." Journal of Fluid Mechanics 638 (October 14, 2009): 5–26. http://dx.doi.org/10.1017/s0022112009991091.

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We present a theoretical and numerical study of wave-induced particle dispersion due to random waves in the rotating shallow-water system, as part of an ongoing study of particle dispersion in the ocean. Specifically, the effective particle diffusivities in the sense of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, p. 196) are computed for a small-amplitude wave field modelled as a stationary homogeneous isotropic Gaussian random field whose frequency spectrum is bounded away from zero. In this case, the leading-order diffusivity depends crucially on the nonlinear, second-order corrections to the linear velocity field, which can be computed using the methods of wave–mean interaction theory. A closed-form analytic expression for the effective diffusivity is derived and carefully tested against numerical Monte Carlo simulations. The main conclusions are that Coriolis forces in shallow water invariably decrease the effective particle diffusivity and that there is a peculiar choking effect for the second-order particle flow in the limit of strong rotation.
38

Shaban, Ali, Murad Obaid Abed, Ehab Abdul Razzaq Hussein, and H. J. Abd. "A mitigation of channel crosstalk effect in dispersion shifted fiber based on durability of modulation technique." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 1 (February 1, 2020): 891. http://dx.doi.org/10.11591/ijece.v10i1.pp891-899.

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In fiber optics the Four Wave Mixing (FWM) has the harmful effect of an optical transmission system that can severely limit Wavelength Division Multiplexing (WDM) and reduce the transmission aptness. This work preset the durability of the different modulation format was tested to FWM by using Dispersion Shifted Fiber (DSF). Moreover, the performance of the proposed system is surveyed by changing the fiber length and applying an information rate of 200 Gb/s. The experimental results show that the FWM capacity has decreased significantly by more than 14 dB when applying Return to Zero (RZ) modulation form. In addition, in terms of the propsed system performance in the first channel and with 700 km distance, it was observed that the lower Bit Error Rate (BER) in the normal RZ modulation is equal to 1.3×10-13. As well as it is noticeable when applied the Non Return to Zero (NRZ), the Modified Duobinary Return to Zero (MDRZ) and Gaussian modulation, the system performance will be quickly changed and getting worse, where the BERs increased to 1.3×10-4, 1.3×10-6 and 1.3×10-2 consecutively at same channel and for the same parameters.
39

Movchan, A. B., N. V. Movchan, and R. C. McPhedran. "Bloch–Floquet bending waves in perforated thin plates." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2086 (July 17, 2007): 2505–18. http://dx.doi.org/10.1098/rspa.2007.1886.

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This paper presents a mathematical model describing propagation of bending waves in a perforated thin plate. It is assumed that the holes are circular and form a doubly periodic square array. A spectral problem for the biharmonic operator is formulated in a unit cell containing a single defect, and its analytical solution is constructed using a multipole method. The overall system for the coefficients in the multipole expansion is then solved numerically. We generate dispersion diagrams for the two cases where the boundaries of holes are either clamped or free. We show that in the clamped case, there is a total low-frequency band gap in the limit of inclusions of zero radius, and give a simple formula describing the corresponding band diagram in this limit. We show that in the free-edge case, the band diagram of the vibrating plate is much closer to that of plane waves in a uniform plate than for the clamped case.
40

Page, A. Freddie, Tim W. Pickering, Joachim M. Hamm, Sebastian M. Wuestner, and Ortwin Hess. "Dynamics of Plasmonic Stopped-Light Nanolasing and Condensation." MRS Advances 1, no. 23 (2016): 1671–76. http://dx.doi.org/10.1557/adv.2016.125.

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ABSTRACTBy reducing the number of dimensions that light can propagate in from three down to two, one may gain control over the characteristics of propagation. This control can allow for “Stopped Light” (SL), where wavepackets of light are slowed down to a zero group velocity. This is achieved by designing planar metal-dielectric structures that are stacked in one dimension allowing for waveguide modes in the other two, and engineering the dispersion relation of these structures. Stopped light structures can be further optimized to reduce their dispersion and increase the number of spatial frequencies supported, which allows for confinement of electromagnetic energy over volumes smaller than the diffraction limit over fixed regions in space. If this electromagnetic energy is confined over a region that provides gain, the question arises, can amplification of this light energy occur? and indeed can a regime of lasing be entered into? We show that stopped light lasing is indeed possible, despite there being no resonant cavity in 2d to confine the light, and explore the properties of this new type of laser.
41

Chase, G. William, Ronald R. Eitenmiller, and Austin R. Long. "Analysis of β-Carotene in Medical Food by Liquid Chromatography with Matrix Solid-Phase Dispersion." Journal of AOAC INTERNATIONAL 82, no. 3 (May 1, 1999): 663–65. http://dx.doi.org/10.1093/jaoac/82.3.663.

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Abstract A liquid chromatographic method is described for analysis of β-carotene in medical food. The nutrient is extracted from medical food without saponification by matrix solid-phase dispersion and quantitated by isocratic normal-phase chromatography with a Si 60 column and a mobile phase of hexane containing 0.125% (v/v) isopropyl alcohol. The limit of quantitation is 0.02 μg/mL at 436 nm. Standard response was linear over the concentration range of 0.02μ1.0 μg/ml(r2 = 0.99998). Recoveries were determined on a zero control reference material containing added β-carotene at various levels. Recoveries averaged 91.2% (n = 25) with coefficients of variation from 0.50 to 3.10%. The method provides a rapid, specific, sensitive, and easily controlled assay for analysis of β-carotene in fortified medical food. In addition, retinyl palmitate can be assayed simultaneously with an in-line fluorescence detector.
42

Koch, Donald L., and John F. Brady. "Dispersion in fixed beds." Journal of Fluid Mechanics 154 (May 1985): 399–427. http://dx.doi.org/10.1017/s0022112085001598.

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A macroscopic equation of mass conservation is obtained by ensemble-averaging the basic conservation laws in a porous medium. In the long-time limit this ‘macro-transport’ equation takes the form of a macroscopic Fick's law with a constant effective diffusivity tensor. An asymptotic analysis in low volume fraction of the effective diffusivity in a bed of fixed spheres is carried out for all values of the Péclet number ℙ = Ua/Df, where U is the average velocity through the bed. a is the particle radius and Df is the molecular diffusivity of the solute in the fluid. Several physical mechanisms causing dispersion are revealed by this analysis. The stochastic velocity fluctuations induced in the fluid by the randomly positioned bed particles give rise to a convectively driven contribution to dispersion. At high Péclet numbers, this convective dispersion mechanism is purely mechanical, and the resulting effective diffusivities are independent of molecular diffusion and grow linearly with ℙ. The region of zero velocity in and near the bed particles gives rise to non-mechanical dispersion mechanisms that dominate the longitudinal diffusivity at very high Péclet numbers. One such mechanism involves the retention of the diffusing species in permeable particles, from which it can escape only by molecular diffusion, leading to a diffusion coefficient that grows as ℙ2. Even if the bed particles are impermeable, non-mechanical contributions that grow as ℙ ln ℙ and ℙ2 at high ℙ arise from a diffusive boundary layer near the solid surfaces and from regions of closed streamlines respectively. The results for the longitudinal and transverse effective diffusivities as functions of the Péclet number are summarized in tabular form in §6. Because the same physical mechanisms promote dispersion in dilute and dense fixed beds, the predicted Péclet-number dependences of the effective diffusivities are applicable to all porous media. The theoretical predictions are compared with experiments in densely packed beds of impermeable particles, and the agreement is shown to be remarkably good.
43

Farhood, Ahmed Saleh, and Dakhil Nassir Taha. "A New Flow Injection System with Merging-Zone Technique for the Determination of Copper(II) by Neocuproine Reagent in Aqueous Solution." Indonesian Journal of Chemistry 22, no. 1 (April 26, 2022): 770. http://dx.doi.org/10.22146/ijc.70799.

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A fast, simple, and high throughput sample merging-zone flow injection design was developed to determine copper(II) in aqueous solution. The procedure is based on the reduction of copper(II) to copper(I) by uric acid followed by a direct reaction with Neocuproine reagent (NC). The orange-yellow complex that forms absorb light at 454 nm. All conditions of the new flow injection unit were investigated. The analytical curve of copper(II) was linear with (r2) value of 0.9978, in the range of 0.4 to 40 mg/L with a detection limit of 0.1 mg/L and a quantification limit of 0.3 mg/L. the molar absorptivity was 1.661 × 105 L/mol cm and the recovery range was between 104.9 and 97%. The homemade acrylic valve was low-cost with zero dead volume and high repeatability (n = 7) with an RSD of 2.31%. The dispersion coefficient values were 1.8,1.62, and 1.31 for the concentrations of 5, 15, and 25 mg/L, respectively. The sample throughput was 69 h–1.
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Dagan, Gedeon. "Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations." Journal of Fluid Mechanics 233 (December 1991): 197–210. http://dx.doi.org/10.1017/s0022112091000459.

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An inert solute is convected by a steady random velocity field, which is associated with flow through a heterogeneous porous formation. The log conductivity and the velocity are stationary random space functions. The log conductivity Y is assumed to be normal, with an isotropic two-point correlation of variance σY2 and of finite integral scale I. The solute cloud is of a finite input zone of lengthscale l. The transport is characterized with the aid of the spatial moments of the solute body. The effective dispersion coefficient is defined as half of the rate of change with time of the second spatial moment with respect to the centroid. Under the ergodic hypothesis, which is bound to be satisfied for l/I [Gt ] 1, the centroid moves with the mean velocity U and the longitudinal dispersion coefficient [dscr ]L tends to its constant, Fickian, limit. Under a Lagrangian first-order analysis in σY2 it has been found that [dscr ]L = σY2UI.This study addresses the computation of the effective longitudinal dispersion coefficient for a finite input zone, for which ergodic conditions may not be satisfied. In this case the centroid trajectory and the second spatial moments are random variables. In line with a previous work (Dagan 1990) the effective dispersion coefficient DL is defined as half the rate of change of the expected value of the second spatial moment for large transport time. The aim of the study is to derive DL and its dependence upon l/I and in particular to determine the conditions under which it tends to the ergodic limit [dscr ]L. The computation is carried out separately for a thin body aligned with the mean flow and one transverse to it. In the first case it is found that DL is equal to zero, i.e. the streamlined body does not disperse in the mean. This result is explained by the correlation between the trajectories of the leading and trailing edges, respectively, once the latter reaches the position of the first. The relatively modest increase of the mean second spatial moment is effectively computed. In the case of a thin body initially transverse to the mean flow, DL may reach the ergodic limit [dscr ]L for a ratio l/I of the order 102. For smaller values, DL is found to be bounded from above, and its maximum depends on l but not on I. The uncertainty caused by the randomness of the velocity field is manifested in the trajectory of the centroid rather than in the effective dispersion.
45

Ballester, Manuel, Marcos García, Almudena P. Márquez, Eduardo Blanco, Susana M. Fernández, Dorian Minkov, Aggelos K. Katsaggelos, Oliver Cossairt, Florian Willomitzer, and Emilio Márquez. "Application of the Holomorphic Tauc-Lorentz-Urbach Function to Extract the Optical Constants of Amorphous Semiconductor Thin Films." Coatings 12, no. 10 (October 14, 2022): 1549. http://dx.doi.org/10.3390/coatings12101549.

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The Tauc–Lorentz–Urbach (TLU) dispersion model allows us to build a dielectric function from only a few parameters. However, this dielectric function is non-analytic and presents some mathematical drawbacks. As a consequence of this issue, the model becomes inaccurate. In the present work, we will adopt a procedure to conveniently transform the TLU model into a self-consistent dispersion model. The transformation involves the integration of the original TLU imaginary dielectric function ϵ2 by using a Lorentzian-type function of semi-width, Γ. This novel model is analytic and obeys the other necessary mathematical requirements of the optical constants of solid-state materials. The main difference with the non-analytic TLU model occurs at values of the photon energy near or lower than that of the bandgap energy (within the Urbach absorption region). In particular, this new model allows us to reliably extend the optical characterization of amorphous-semiconductor thin films within the limit to zero photon energy. To the best of our knowledge, this is the first time that the analytic TLU model has been successfully used to accurately determine the optical constants of unhydrogenated a-Si films using only their normal-incidence transmission spectra.
46

Frankel, I., and H. Brenner. "Generalized Taylor dispersion phenomena in unbounded homogeneous shear flows." Journal of Fluid Mechanics 230 (September 1991): 147–81. http://dx.doi.org/10.1017/s0022112091000745.

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Generalized Taylor dispersion theory is extended so as to enable the analysis of the transport in unbounded homogeneous shear flows of Brownian particles possessing internal degrees of freedom (e.g. rigid non-spherical particles possessing orientational degrees of freedom, flexible particles possessing conformational degrees of freedom, etc.). Taylor dispersion phenomena originate from the coupling between the dependence of the translational velocity of such particles in physical space upon the internal variables and the stochastic sampling of the internal space resulting from the internal diffusion process.Employing a codeformational reference frame (i.e. one deforming with the sheared fluid) and assuming that the eigenvalues of the (constant) velocity gradient are purely imaginary, we establish the existence of a coarse-grained, purely physical-space description of the more detailed physical-internal space (microscale) transport process. This macroscale description takes the form of a convective–diffusive ‘model’ problem occurring exclusively in physical space, one whose formulation and solution are independent of the internal (‘local’-space) degrees of freedom.An Einstein-type diffusion relation is obtained for the long-time limit of the temporal rate of change of the mean-square particle displacement in physical space. Despite the nonlinear (in time) asymptotic behaviour of this displacement, its Oldroyd time derivative (which is the appropriate one in the codeformational view adopted) tends to a constant, time-independent limit which is independent of the initial internal coordinates of the Brownian particle at zero time.The dyadic dispersion-like coefficient representing this asymptotic limit is, in general, not a positive-definite quantity. This apparently paradoxical behaviour arises due to the failure of the growth in particle spread to be monotonic with time as a consequence of the coupling between the Taylor dispersion mechanism and the shear field. As such, a redefinition of the solute's dispersivity dyadic (appearing as a phenomenological coefficient in the coarse-grained model constitutive equation) is proposed. This definition provides additional insight into its physical (Lagrangian) significance as well as rendering this dyadic coefficient positive-definite, thus ensuring that solutions of the convective–diffusive model problem are well behaved. No restrictions are imposed upon the magnitude of the rotary Péclet number, which represents the relative intensities of the respective shear and diffusive effects upon which the solute dispersivity and mean particle sedimentation velocity both depend.The results of the general theory are illustrated by the (relatively) elementary problem of the sedimentation in a homogeneous unbounded shear field of a size-fluctuating porous Brownian sphere (which body serves to model the behaviour of a macromolecular coil). It is demonstrated that the well-known case of the translational diffusion in a homogeneous shear flow of a rigid, non- fluctuating sphere (for which the Taylor mechanism is absent) is a particular case thereof.
47

Cho, Ikuo, Shigeki Senna, Atsushi Wakai, Kaoru Jin, and Hiroyuki Fujiwara. "Basic performance of a spatial autocorrelation method for determining phase velocities of Rayleigh waves from microtremors, with special reference to the zero-crossing method for quick surveys with mobile seismic arrays." Geophysical Journal International 226, no. 3 (April 16, 2021): 1676–94. http://dx.doi.org/10.1093/gji/ggab149.

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SUMMARY We theoretically and empirically demonstrate the usability of the zero-crossing method for quick microtremor surveys in earthquake engineering (i.e. microtremor array surveys), namely shallow (< a few kilometres) surveys with small-scale (< 1 kilometre in radius) mobile seismic arrays with a short observation time (< a few hours). The zero-crossing method is a type of spatial autocorrelation (SPAC) method that determines phase velocities based on multiple frequencies at which the SPAC coefficient curve crosses zero. It is theoretically shown that the zero-crossing method is robust against incoherent noise and that the use of the first zero crossings (i.e. those at the lowest frequencies) is more robust against inadequate conditions of the microtremor wavefield than the use of later zero crossings (i.e. those at higher frequencies). We used microtremor array data with maximum array radii and observation durations of 400 m and 120 min on average, respectively, at 445 observation sites in the Kanto Plain, Japan, for validating the practicality of using the first zero crossings. As an illustration of the robustness against low signal-to-noise ratios (SNRs), we show that with the zero-crossing method, low-sensitivity (i.e. low-SNR) seismometers provide the same analysis results as those obtained with high-sensitivity seismometers, even when the power spectral densities for the low-sensitivity seismometers are close to the self-noise level. We then show that a reference phase velocity dispersion curve (RPVDC), created mainly based on the first zero crossings at each site, has a spatial distribution that well corresponds to the geology and topography and is consistent with that obtained in a previous study. We inverted five RPVDCs to model 1-D S-wave profiles and validated them using S-wave profiles obtained from velocity logs at nearby deep (e.g. hundreds of metres) boring wells. The accuracy of phase velocities at the later zero crossings for three-sensor/four-sensor arrays and all zero crossings for two-sensor arrays are statistically examined (maximum of 9805 data) based on a comparison with the RPVDCs. The disadvantage of the zero-crossing method is that it can only provide information on phase velocities at discrete wavelengths up to a maximum wavelength of 2.6r (i.e. corresponding to the first zero-crossing point), where r is the radius of a seismic array. Therefore, the RPVDCs were then used to examine the upper limit of the analysable wavelength ranges for the conventional SPAC method for microtremor array surveys. Based on a few hundred three-sensor/four-sensor arrays, it was found that for arrays with radii larger than several tens of metres, three-quarters of the upper limit wavelengths (ULWs) stayed within 5r. For arrays with radii smaller than this value, the ULWs strongly depended on the array radius; the ULWs dramatically increased with decreasing array radius. For example, for arrays with an r value of 0.6 m, half of 336 data ranged between 26r and 54r, and the maximum ULW reached 186r. This strong size dependence can be explained by differences in SNR.
48

McL Mathieson, A. "Concerning Single Crystal Reflectivity Curves." Australian Journal of Physics 41, no. 3 (1988): 393. http://dx.doi.org/10.1071/ph880393.

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The extinguished reflectivity curve of a Bragg single crystal reflection represents the basic experimental evidence for the determination of accurate structure factors. In normal measurement procedures of one-dimensional (ID) 'counter' profiles, information on such curves is obscured by the presence of other, more dominant components. It is therefore difficult to separate out these curves so that a realistic correction for extinction can be applied. By considering the 'shape' of a Bragg reflection in the plane of diffraction from the ~w, ~2e viewpoint, procedures have been deduced for practical zero wavelength dispersion measurement of reflectivity curves for virtually any e value and, with these curves, corrections can be applied to produce extinction-free structure factor values. Attention is drawn to the fact that the width of the experimental reflectivity curve (say at half maximum) can provide a valuable criterion to assist in attaining the 'kinematical limit'.
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Das, Debanik, Chandriker Kavir Dass, Piyush J. Shah, Robert Bedford, and L. R. Ram-Mohan. "Tapered resonator-based phononic crystal: Avoided level crossings, robust self-collimation, and bi-refringence." Journal of Applied Physics 133, no. 5 (February 7, 2023): 055103. http://dx.doi.org/10.1063/5.0128957.

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In search of novel phononic crystals to effectively control the propagation of elastic waves, we propose a new single-material phononic crystal (PnC) with unit cells containing tapered resonators (TRs). The thickness of the circular taper radially decreases outward from the center. The device modulates dispersion of the wave by a local resonance mechanism and by slowly varying the group velocity of elastic waves. The TRs are layered on the top of a conventional PnC slab with a square arrangement of air holes. The band structure of the PnC is theoretically studied and a comparison is drawn between the avoided level crossings and the symmetry-protected ordinary degeneracies. In the absence of a bandgap, the zero group velocity at the band maximum restricts the waves from propagating. Moreover, the design shows anomalous dispersion phenomena such as self-collimation and bi-refringence, which are rare in conventional PnCs. We trace the origins of these phenomena by analyzing equifrequency contours associated with relevant frequencies. We show that the self-collimation effect persists even with a small variation in the angle of incidence and a perturbative hole at the center of each of the TRs. Within the classical limit, the scale invariance of the elastic wave equation makes the device useful in both the low frequency ultrasonic and the high frequency phononic regime.
50

Sansón, L. Zavala. "Simple Models of Coastal-Trapped Waves Based on the Shape of the Bottom Topography." Journal of Physical Oceanography 42, no. 3 (March 1, 2012): 420–29. http://dx.doi.org/10.1175/jpo-d-11-053.1.

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Abstract Solutions of barotropic coastal-trapped waves in the shallow-water context are discussed for different shapes of the bottom topography. In particular, an infinite family of topographic waves over continental shelves characterized by a shape parameter is considered. The fluid depth is proportional to xs, where x is the offshore coordinate and s is a real, positive number. The model assumes the rigid-lid approximation and a semi-infinite domain 0 ≤ x ≤ ∞. The wave structure and the dispersion relation depend explicitly on the shape parameter s. Essentially, waves over steeper shelves possess higher frequencies and phase speeds. In addition, the wave frequency is independent of the alongshore wavenumber k, implying a zero group velocity component along the coast. The advantages and limitations of this formulation, as well as some comparisons with other models, are discussed in light of numerical simulations for waves over arbitrary topography within a finite domain. The numerical calculations show that the frequency of the waves present a nondispersive regime at small wavenumbers (observed by several authors), followed by a constant value predicted by the analytical solutions for larger k. It is concluded that these frequencies can be considered as an upper limit reached by barotropic coastal-trapped waves over the infinite family of xs-bottom profiles, regardless of the horizontal and vertical scales of the system. The modification of the dispersion curves in a stratified ocean is briefly discussed.

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