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Artículos de revistas sobre el tema "Finite speed of propagation"

Autor: Grafiati
Publicado: 10 de marzo de 2023

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1

Mariano, Paolo Maria y Marco Spadini. "Sources of Finite Speed Temperature Propagation". Journal of Non-Equilibrium Thermodynamics 47, n.º 2 (9 de febrero de 2022): 165–78. http://dx.doi.org/10.1515/jnet-2021-0078.

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Abstract The relation between heat flux and temperature gradient has been considered as a constitutive structure or as a balance law in different approaches. Both views may allow a description of heat conduction characterized by finite speed propagation of temperature disturbances. Such a result, which overcomes Fourier’s drawback of infinite speed propagation, can be obtained also by considering insufficient the representation of a conductor, even when it is considered to be rigid, rather than the sole relation between heat flux and temperature gradient. We comment this last view and describe the intersection with previous proposals. Eventually, we show how under Fourier’s law we can have traveling-wave-type temperature propagation when thermal microstructures are accounted for.
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2

Fujishima, Y. y J. Habermann. "Finite speed propagation for parabolic quasiminimizers". Nonlinear Analysis 198 (septiembre de 2020): 111891. http://dx.doi.org/10.1016/j.na.2020.111891.

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3

Roe, John. "Finite propagation speed and Connes' foliation algebra". Mathematical Proceedings of the Cambridge Philosophical Society 102, n.º 3 (noviembre de 1987): 459–66. http://dx.doi.org/10.1017/s0305004100067517.

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In [4], A. Connes has defined the convolution algebra associated to a foliation ℱ of the compact manifold M. Here is the graph or holonomy groupoid of the foliation ℱ (Winkelnkemper [15]). By forming the completion of in its regular representation, he obtains the C*-algebra C*{M, ℱ) associated to the foliation. The completeness of C*(M, ℱ) makes it easier to handle in some analytical contexts, but in others it seems to be too big, and it is necessary to consider instead some carefully selected dense subalgebra (cf. [6]). The purpose of this note is to show that certain spectral functions of leafwise elliptic operators, which might a priori be expected to belong to C*(M, ℱ), in fact belong to the more controllable dense subalgebra . We give a couple of applications, including a proof not passing through C*-algebras of Connes' index theorem for measured foliations [4]. It should be emphasized that the proof of that result offered here is essentially Connes' one, but the presentation may perhaps be more congenial to those who are not C*-algebra specialists.
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4

Andreu, F., V. Caselles, J. M. Mazón y S. Moll. "Some diffusion equations with finite propagation speed". PAMM 7, n.º 1 (diciembre de 2007): 1040101–2. http://dx.doi.org/10.1002/pamm.200700126.

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5

Harvey, B. J., J. Methven y M. H. P. Ambaum. "Rossby wave propagation on potential vorticity fronts with finite width". Journal of Fluid Mechanics 794 (6 de abril de 2016): 775–97. http://dx.doi.org/10.1017/jfm.2016.180.

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The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here, an approximate correction is derived for the case of a finite-width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.
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6

Andreu, Fuensanta, Vicent Caselles, José M. Mazón y Salvador Moll. "Finite Propagation Speed for Limited Flux Diffusion Equations". Archive for Rational Mechanics and Analysis 182, n.º 2 (3 de abril de 2006): 269–97. http://dx.doi.org/10.1007/s00205-006-0428-3.

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7

Constantin, Adrian. "Finite propagation speed for the Camassa–Holm equation". Journal of Mathematical Physics 46, n.º 2 (febrero de 2005): 023506. http://dx.doi.org/10.1063/1.1845603.

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8

McLaughlin, Joyce R. y Jeong-Rock Yoon. "Finite Propagation Speed of Waves in Anisotropic Viscoelastic Media". SIAM Journal on Applied Mathematics 77, n.º 6 (enero de 2017): 1921–36. http://dx.doi.org/10.1137/16m1099959.

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9

Bonafede, S., G. R. Cirmi y A. F. Tedeev. "Finite Speed of Propagation for the Porous Media Equation". SIAM Journal on Mathematical Analysis 29, n.º 6 (noviembre de 1998): 1381–98. http://dx.doi.org/10.1137/s0036141096298072.

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10

Remling, Christian. "Finite propagation speed and kernel estimates for Schrödinger operators". Proceedings of the American Mathematical Society 135, n.º 10 (1 de octubre de 2007): 3329–41. http://dx.doi.org/10.1090/s0002-9939-07-08857-0.

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11

Gess, Benjamin. "Finite Speed of Propagation for Stochastic Porous Media Equations". SIAM Journal on Mathematical Analysis 45, n.º 5 (enero de 2013): 2734–66. http://dx.doi.org/10.1137/120894713.

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12

Andreu, F., V. Caselles y J. M. Mazón. "A Fisher–Kolmogorov equation with finite speed of propagation". Journal of Differential Equations 248, n.º 10 (mayo de 2010): 2528–61. http://dx.doi.org/10.1016/j.jde.2010.01.005.

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13

Rosier, Carole y Lionel Rosier. "Finite speed propagation in the relaxation of vortex patches". Quarterly of Applied Mathematics 61, n.º 2 (1 de junio de 2003): 213–31. http://dx.doi.org/10.1090/qam/1976366.

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14

Gurarie, David. "Finite propagation speed and kernels of strictly elliptic operators". International Journal of Mathematics and Mathematical Sciences 8, n.º 1 (1985): 75–91. http://dx.doi.org/10.1155/s0161171285000072.

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We establish estimates of the resolvent and other related kernels and discussLp-theory for a class of strictly elliptic operators onRn. The class of operators considered in the paper is of the formA0+Bwith the leading elliptic partA0and a “singular” perturbationB, whose coefficients haveLp-type and are modeled after Schrödinger operators.
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15

Moscovici, H. y F. B. Wu. "Localization of topological pontryagin classes via finite propagation speed". Geometric and Functional Analysis 4, n.º 1 (enero de 1994): 52–92. http://dx.doi.org/10.1007/bf01898361.

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16

RENTERIA, LUCIANO ALONSO y JUAN M. PEREZ ORIA. "A MODIFIED FINITE DIFFERENCES METHOD FOR ANALYSIS OF ULTRASONIC PROPAGATION IN NONHOMOGENEOUS MEDIA". Journal of Computational Acoustics 18, n.º 01 (marzo de 2010): 31–45. http://dx.doi.org/10.1142/s0218396x10004048.

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The propagation of ultrasonic waves is generally studied in homogeneous media, although in certain industrial applications the conditions of propagation differ from the ideal conditions and the predicted results are not valid. This work is focused on the resolution of the Helmholtz equation for the study of the ultrasonic propagation in nonhomogeneous media. In this way, the solution of the Helmholtz equation has been obtained by means of Finite Differences, using a nonconventional scheme that substantially improves the results obtained with other techniques such as standard Finite Differences or Finite Elements. Moreover, it decreases the computational cost in the calculation of the coefficients about 85%. The effects on the ultrasonic echoes in propagation environments with high gradients of propagation's speed have been analyzed by simulation using the method presented, and the results obtained have been experimentally validated through a set of measurements.
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17

Kolesnik, Alexander D. "A Note on Planar Random Motion at Finite Speed". Journal of Applied Probability 44, n.º 3 (septiembre de 2007): 838–42. http://dx.doi.org/10.1239/jap/1189717549.

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18

Kolesnik, Alexander D. "A Note on Planar Random Motion at Finite Speed". Journal of Applied Probability 44, n.º 03 (septiembre de 2007): 838–42. http://dx.doi.org/10.1017/s0021900200003478.

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19

MAINI, PHILIP K., LUISA MALAGUTI, CRISTINA MARCELLI y SERENA MATUCCI. "AGGREGATIVE MOVEMENT AND FRONT PROPAGATION FOR BI-STABLE POPULATION MODELS". Mathematical Models and Methods in Applied Sciences 17, n.º 09 (septiembre de 2007): 1351–68. http://dx.doi.org/10.1142/s0218202507002303.

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Front propagation for the aggregation-diffusion-reaction equation [Formula: see text] is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling aggregating-diffusing processes. We provide necessary and sufficient conditions for the existence of traveling wave solutions and classify them according to how or if they attain their equilibria at finite times. We also show that the dynamics can exhibit the phenomena of finite speed of propagation and/or finite speed of saturation.
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20

AVITAL, ELDAD J., RICARDO E. MUSAFIR y THEODOSIOS KORAKIANITIS. "NONLINEAR PROPAGATION OF SOUND EMITTED BY HIGH SPEED WAVE PACKETS". Journal of Computational Acoustics 21, n.º 02 (29 de abril de 2013): 1250027. http://dx.doi.org/10.1142/s0218396x12500270.

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Jet's sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the source's supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervelt equation. Two- and three-dimensional sound propagations were simulated for symmetric and asymmetric supersonic wave packets. It is seen that nonlinearity in the sound field is affected by the wave packet form, an effect that cannot be captured by a 1D propagation equation. High skewness in the pressure fluctuation and its time derivative were found near the Mach direction, showing crackle-like features. Pressure time history and frequency spectra are also investigated.
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21

Schrader, Robert. "Finite propagation speed and causal free quantum fields on networks". Journal of Physics A: Mathematical and Theoretical 42, n.º 49 (20 de noviembre de 2009): 495401. http://dx.doi.org/10.1088/1751-8113/42/49/495401.

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22

Grmela, Miroslav y Georgy Lebon. "Finite-speed propagation of heat: a nonlocal and nonlinear approach". Physica A: Statistical Mechanics and its Applications 248, n.º 3-4 (enero de 1998): 428–41. http://dx.doi.org/10.1016/s0378-4371(97)00552-9.

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23

Shnaid, Isaac. "Analysis of transport phenomena with finite speed of perturbations propagation". Physica A: Statistical Mechanics and its Applications 343 (noviembre de 2004): 127–46. http://dx.doi.org/10.1016/j.physa.2004.05.054.

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24

Calvo, Juan. "On Sonic Hedgehog morphogenic action and finite propagation speed models". SeMA Journal 75, n.º 2 (23 de mayo de 2017): 173–95. http://dx.doi.org/10.1007/s40324-017-0128-y.

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25

Seredyńska, M. y Andrzej Hanyga. "Relaxation, dispersion, attenuation, and finite propagation speed in viscoelastic media". Journal of Mathematical Physics 51, n.º 9 (septiembre de 2010): 092901. http://dx.doi.org/10.1063/1.3478299.

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26

Mariano, Paolo Maria. "Finite-speed heat propagation as a consequence of microstructural changes". Continuum Mechanics and Thermodynamics 29, n.º 6 (29 de mayo de 2017): 1241–48. http://dx.doi.org/10.1007/s00161-017-0577-7.

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27

Maremonti, Paolo y Remigio Russo. "On the wave propagation property in finite elasticity". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 119, n.º 1-2 (1991): 107–16. http://dx.doi.org/10.1017/s0308210500028341.

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SynopsisBy using a mild hypothesis on the acoustic tensor, it is shown that the disturbances in a nonlinear elastic body travel with a finite speed. Moreover, a uniqueness theorem for the displacement problem of nonlinear elastodynamics is proved. No assumption is made on the extension of the body.
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28

Yin, Hao, Yu Qian, J. Riley Edwards y Kaijun Zhu. "Investigation of Relationship between Train Speed and Bolted Rail Joint Fatigue Life using Finite Element Analysis". Transportation Research Record: Journal of the Transportation Research Board 2672, n.º 10 (1 de julio de 2018): 85–95. http://dx.doi.org/10.1177/0361198118784382.

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Reducing the allowable operating speed or imposing temporary speed restrictions are common practices to prevent further damage to rail track when defects are detected related to certain track components. However, the speeds chosen for restricted operation are typically based on past experience without considering the magnitude of the impact load around the rail joints. Due to the discontinuity of geometry and track stiffness at the bolted rail joints, an impact load always exists. Thus, slower speeds may not necessarily reduce the stresses at the critical locations around the rail joint area to a safe level. Previously, the relationship between speed and the impact load around the rail joints has not been thoroughly investigated. Recent research performed at the University of Illinois at Urbana-Champaign (UIUC) has focused on investigating the rail response to load at the joint area. A finite element model (FEM) with the capability of simulating a moving wheel load has been developed to better understand the stress propagation at the joint area under different loading scenarios and track structures. This study investigated the relationship between train speed and impact load and corresponding stress propagation around the rail joints to better understand the effectiveness of speed restrictions for bolted joint track. Preliminary results from this study indicate that the contact force at the wheel–rail interface would not change monotonically with the changing train speed. In other words, when train speed is reduced, the maximum contact force at the wheel–rail interface may not necessarily reduce commensurately.
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29

Kruisová, Alena y Jiří Plešek. "Tangent Moduli of the Hencky Material Model Derived from the Stored Energy Function at Finite Strains". Materials Science Forum 482 (abril de 2005): 327–30. http://dx.doi.org/10.4028/www.scientific.net/msf.482.327.

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Tangent moduli associated with the linear logarithmic model of hyperelasticity are derived. These relations are crucial not only to theoretical analyses but also to wave propagation and ultrasonic testing. The tangent moduli as functions of stress determine the speed of propagating acoustic waves and, therefore, indirectly point to a possible occurrence of residual stress fields in elastic solids.
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30

Benoit, Antoine. "Finite speed of propagation for mixed problems in the $WR$ class". Communications on Pure and Applied Analysis 13, n.º 6 (julio de 2014): 2351–58. http://dx.doi.org/10.3934/cpaa.2014.13.2351.

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31

Finster, Felix. "Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed". Journal of Physics: Conference Series 1275 (septiembre de 2019): 012009. http://dx.doi.org/10.1088/1742-6596/1275/1/012009.

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32

Gorodtsov, V. A. "Finite speed of diffusion propagation in a two-component continuous medium". Journal of Applied Mathematics and Mechanics 65, n.º 2 (enero de 2001): 353–56. http://dx.doi.org/10.1016/s0021-8928(01)00039-9.

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33

Anker, Jean-Philippe y Alberto G. Setti. "Asymptotic finite propagation speed for heat diffusion on certain Riemannian manifolds". Journal of Functional Analysis 103, n.º 1 (enero de 1992): 50–61. http://dx.doi.org/10.1016/0022-1236(92)90133-4.

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34

Carrillo, José Antonio, Maria Pia Gualdani y Giuseppe Toscani. "Finite speed of propagation in porous media by mass transportation methods". Comptes Rendus Mathematique 338, n.º 10 (mayo de 2004): 815–18. http://dx.doi.org/10.1016/j.crma.2004.03.025.

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35

Lin, Yu-Chu, Ming-Jiea Lyu y Kung-Chien Wu. "Relativistic Boltzmann Equation: Large Time Behavior and Finite Speed of Propagation". SIAM Journal on Mathematical Analysis 52, n.º 6 (enero de 2020): 5994–6032. http://dx.doi.org/10.1137/20m1332761.

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36

Masoliver, Jaume y George H. Weiss. "Transport Equations in Chromatography with a Finite Speed of Signal Propagation". Separation Science and Technology 26, n.º 2 (febrero de 1991): 279–89. http://dx.doi.org/10.1080/01496399108050472.

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37

Sugiyama, Yoshie. "Finite speed of propagation in 1-D degenerate Keller-Segel system". Mathematische Nachrichten 285, n.º 5-6 (2 de enero de 2012): 744–57. http://dx.doi.org/10.1002/mana.200810258.

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38

Wiedemann, Emil. "Localised relative energy and finite speed of propagation for compressible flows". Journal of Differential Equations 265, n.º 4 (agosto de 2018): 1467–87. http://dx.doi.org/10.1016/j.jde.2018.04.005.

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39

Correia, Simão. "Finite speed of disturbance for the nonlinear Schrödinger equation". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, n.º 6 (27 de diciembre de 2018): 1405–19. http://dx.doi.org/10.1017/prm.2018.69.

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AbstractWe consider the Cauchy problem for the nonlinear Schrödinger equation on the whole space. After introducing a weaker concept of finite speed of propagation, we show that the concatenation of initial data gives rise to solutions whose time of existence increases as one translates one of the initial data. Moreover, we show that, given global decaying solutions with initial data u0, v0, if |y| is large, then the concatenated initial data u0 + v0(· − y) gives rise to globally decaying solutions.
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40

Franzen, Anne T. y José Natário. "Linear relativistic thermoelastic rod". Journal of Hyperbolic Differential Equations 17, n.º 04 (diciembre de 2020): 863–82. http://dx.doi.org/10.1142/s0219891620500289.

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We derive and analyze the linearized hyperbolic equations describing a relativistic heat-conducting elastic rod. We construct a decreasing energy integral for these equations, compute the associated characteristic propagation speeds and prove that the solutions decay in time by using a Fourier decomposition. For comparison purposes, we obtain analogous results for the classical system with heat waves, in which the finite propagation speed of heat is kept but the other relativistic terms are neglected and also for the usual classical system.
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41

Grinchik, N. N. y O. V. Boiprav. "High-Frequency Electrodynamics of Slow Moving Media Taking into Account the Specular Reflection". Advanced Electromagnetics 10, n.º 1 (6 de febrero de 2021): 6–14. http://dx.doi.org/10.7716/aem.v10i1.1583.

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The paper presents the results of constructing the physical and mathematical model of high-frequency electromagnetic waves propagation in slowly moving media of finite dimensions, which takes into account the phenomena of specular reflection of these waves. The constructed model is based on formulas designed to determine the speed of electromagnetic waves propagation in slowly moving media of finite dimensions, as well as on equations designed to describe these waves. The advantageous feature of these equations is that they take into account the Fresnel drag coefficient for electromagnetic waves propagation speed. The approach to solving of these equations, as well as the approach to modeling of the process of electromagnetic waves propagation in slowly moving media of finite dimensions, based on the use of a difference scheme, in which the motion of these media is taken into account, is proposed. It has been determined that the proposed model and approaches can be used in solving problems related to the construction of receiving-transmitting paths, as well as in solving problems of aeroacoustics.
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42

Song, Guangkai, Xiaolin Guo y Bohua Sun. "Scaling law for velocity of domino toppling motion in curved paths". Open Physics 19, n.º 1 (1 de enero de 2021): 426–33. http://dx.doi.org/10.1515/phys-2021-0049.

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Abstract The arranged paths of dominoes have many shapes. The scaling law for the propagation speed of domino toppling has been extensively investigated. However, in all previous investigations the scaling law for the velocity of domino toppling motion in curved lines was not taken into account. In this study, the finite-element analysis (FEA) program ABAQUS was used to discuss the scaling law for the propagation speed of domino toppling motion in curved lines. It is shown that the domino propagation speed has a rising trend with increasing domino spacing in a straight line. It is also found that domino propagation speed is linearly proportional to the square root of domino separation. This research proved that the scaling law for the speed of domino toppling motion given by Sun [Scaling law for the propagation speed of domino toppling. AIP Adv. 2020;10(9):095124] is true. Moreover, the shape of domino arrangement paths has no influence on the scaling law for the propagation speed of dominoes, but can affect the coefficient of the scaling law for the velocity. Therefore, the amendatory function for the propagation speed of dominoes in curved lines was formulated by the FEA data. On one hand, the fitted amendatory function, φ revise {\varphi }_{{\rm{revise}}} , provides the simple method for a domino player to quickly estimate the propagation speed of dominoes in curved lines; on the other hand, it is the rationale for the study of the domino effect.
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43

Sun, Baoyan. "Propagation phenomena of the solution for the relativistic BGK model". Journal of Mathematical Physics 64, n.º 2 (1 de febrero de 2023): 021507. http://dx.doi.org/10.1063/5.0120472.

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In this paper, we recognize the finite propagation speed of the solution for the relativistic Bhatnagar-Gross-Krook model of the Marle-type near equilibrium regime in the whole space [Formula: see text]. The global solutions vanish outside a modified line cone ⟨ x⟩ = aMt with a, M > 1. Moreover, one can see that the slope of the modified line cone aM can be as close as to the maximum speed of the relativistic transport part. This means that the propagation speed is optimal.
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44

Arrighi, Pablo, Giuseppe Di Molfetta y Stefano Facchini. "Quantum walking in curved spacetime: discrete metric". Quantum 2 (22 de agosto de 2018): 84. http://dx.doi.org/10.22331/q-2018-08-22-84.

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A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the(1+1)−dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operators-differently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other.
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45

Spiesberger, John L. y Dmitry Yu Mikhin. "Computing Where Perturbations Affect the Acoustic Impulse Response in the Ocean". Journal of Theoretical and Computational Acoustics 26, n.º 02 (junio de 2018): 1850004. http://dx.doi.org/10.1142/s2591728518500044.

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We compute accurate maps of oceanic perturbations affecting transient acoustic signals propagating from source to receiver. The technological advance involves coupling the one-way wave equation (OWWE) propagation model with the theory for the Differential Measure of Influence (DMI) yielding the map. The DMI requires two finite-frequency solutions of the acoustic wave equation obeying reciprocity: from source to receiver and vice versa. OWWE satisfies reciprocity at basin-scales with sound speed varying horizontally and vertically. At infinite frequency, maps of the DMI collapse into rays. Mapping the DMI is useful for understanding measurements of acoustic perturbations at finite frequencies.
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46

Djida, Jean-Daniel, Juan J. Nieto y Iván Area. "Nonlocal time-porous medium equation: Weak solutions and finite speed of propagation". Discrete & Continuous Dynamical Systems - B 24, n.º 8 (2019): 4031–53. http://dx.doi.org/10.3934/dcdsb.2019049.

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47

Ratiu, T. S., M. S. Romanov, V. N. Samokhin y G. A. Chechkin. "Existence and uniqueness theorems in two-dimensional nematodynamics. Finite speed of propagation". Doklady Mathematics 91, n.º 3 (mayo de 2015): 354–58. http://dx.doi.org/10.1134/s106456241503028x.

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48

Shnaid, Isaac. "Thermodynamically consistent description of heat conduction with finite speed of heat propagation". International Journal of Heat and Mass Transfer 46, n.º 20 (septiembre de 2003): 3853–63. http://dx.doi.org/10.1016/s0017-9310(03)00177-7.

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Liu, Xiaochuan y Changzheng Qu. "Finite speed of propagation for thin viscous flows over an inclined plane". Nonlinear Analysis: Real World Applications 13, n.º 1 (febrero de 2012): 464–75. http://dx.doi.org/10.1016/j.nonrwa.2011.08.003.

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Bostan, M. "Finite speed propagation of the solutions for the relativistic Vlasov–Maxwell system". Nonlinear Analysis: Theory, Methods & Applications 69, n.º 12 (diciembre de 2008): 4365–79. http://dx.doi.org/10.1016/j.na.2007.10.059.

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