scholarly journals Poroacoustic Traveling Waves under the Rubin–Rosenau–Gottlieb Theory of Generalized Continua

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 807
Author(s):  
Pedro M. Jordan
Keyword(s):  
Traveling Waves ◽  
Experimental Tests ◽  
Periodic Boundary Conditions ◽  
Artificial Viscosity ◽  
Type Solution ◽  
Piston Problem ◽  
Generalized Continua ◽  
Von Neumann ◽  
Asymptotic Expressions ◽  
The Cauchy Problem

We investigate linear and nonlinear poroacoustic waveforms under the Rubin–Rosenau– Gottlieb (RRG) theory of generalized continua. Working in the context of the Cauchy problem, on both the real line and the case with periodic boundary conditions, exact and asymptotic expressions are obtained. Numerical simulations are also presented, von Neumann–Richtmyer “artificial” viscosity is used to derive an exact kink-type solution to the poroacoustic piston problem, and possible experimental tests of our findings are noted. The presentation concludes with a discussion of possible follow-on investigations.

Spherical piston problem in water

1969 ◽  
Vol 39 (3) ◽  
pp. 587-600 ◽  
Author(s):  
P. L. Bhatnagar ◽  
P. L. Sachdev ◽  
Phoolan Prasad
Keyword(s):  
Shock Wave ◽  
Initial Velocity ◽  
Artificial Viscosity ◽  
Initial Radius ◽  
Viscosity Method ◽  
Piston Problem ◽  
Interesting Phenomenon ◽  
Von Neumann ◽  
Finite Velocity ◽  
Cavity Boundary

In this paper, we study the propagation of a shock wave in water, produced by the expansion of a spherical piston with a finite initial radius. The piston path in the x, t plane is a hyperbola. We have considered the following two cases: (i) the piston accelerates from a zero initial velocity and attains a finite velocity asymptotically as t tends to infinity, and (ii) the piston decelerates, starting from a finite initial velocity. Since an analytic approach to this problem is extremely difficult, we have employed the artificial viscosity method of von Neumann & Richtmyer after examining its applicability in water. For the accelerating piston case, we have studied the effect of different initial radii of the piston, different initial curvatures of the piston path in the x, t plane and the different asymptotic speeds of the piston. The decelerating case exhibits the interesting phenomenon of the formation of a cavity in water when the deceleration of the piston is sufficiently high. We have also studied the motion of the cavity boundary up to 550 cycles.

On the stability of lattice boltzmann equations for one-dimensional diffusion equation

2017 ◽  
Vol 08 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Gerasim Vladimirovich Krivovichev
Keyword(s):  
Lattice Boltzmann ◽  
Initial Conditions ◽  
Kinetic Equations ◽  
Differential Approximation ◽  
Boltzmann Equations ◽  
Von Neumann ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
The Cauchy Problem ◽  
Lattice Boltzmann Equations

Stability analysis of lattice Boltzmann equations (LBEs) on initial conditions for one-dimensional diffusion is performed. Stability of the solution of the Cauchy problem for the system of linear Bhatnaghar–Gross–Krook kinetic equations is demonstrated for the cases of D1Q2 and D1Q3 lattices. Stability of the scheme for D1Q2 lattice is analytically analyzed by the method of differential approximation. Stability of parametrical scheme is numerically investigated by von Neumann method in parameter space. As a result of numerical analysis, the correction of the hypothesis on transfer of stability conditions of the scheme for macroequation to the system of LBEs is demonstrated.

ATTENUATION OF SPURIOUS OSCILLATIONS IN THE NUMERICAL CAPTURE OF SHOCK WAVES

2006 ◽  
Vol 17 (10) ◽  
pp. 1403-1413
Author(s):  
D. PORTES ◽  
H. RODRIGUES ◽  
S. B. DUARTE
Keyword(s):  
Shock Wave ◽  
Continuous Solution ◽  
Artificial Viscosity ◽  
Plane Shock ◽  
Hydrodynamic Equations ◽  
Von Neumann ◽  
One Dimensional ◽  
First Derivative ◽  
Spurious Oscillations ◽  
Steady Plane

Artificial viscosity is often expressed as a superposition of linear and quadratic terms in the first derivative of the velocity field. In trying to find a continuous solution for the hydrodynamic equations, we propose an alternative one-term artificial viscosity which is a linear form of the derivative of the specific volume. It is shown that this artificial viscosity is able to capture the profile of the steady plane shock wave, largely removing the non-physical oscillations originated by the artificial viscosity of von Neumann and Richtmyer. Analytical and numerical calculations for one-dimensional shock using both artificial viscosities are compared.

Strongly Nonlinear Spatially Periodic Traveling Waves in Granular Dimer Chains

2012 ◽  
Author(s):  
K. R. Jayaprakash ◽  
Alexander F. Vakakis ◽  
Yuli Starosvetsky
Keyword(s):  
Traveling Waves ◽  
Periodic Boundary Conditions ◽  
Mass Ratio ◽  
Efficient Energy ◽  
Periodic Traveling Waves ◽  
Strongly Nonlinear ◽  
Spatial Periodicity ◽  
Spatially Periodic ◽  
New Formulation ◽  
Primary Pulse

In the present work we study the dynamics of spatially periodic traveling waves in granular 1:1 (each bead is followed and preceded by a bead of different mass and/or stiffness) dimer chain with no pre-compression. The dynamics of a 1:1 dimer chain is governed by a single parameter, the mass ratio of the two beads forming each dimer pair of the chain. In particular, we demonstrate numerically the formation of special families of traveling waves with spatially periodic waveforms that are realized in semi-infinite dimer chains with the application of an arbitrary impulse. These traveling waves were first observed in the form of oscillatory tails in the trail of the propagating primary pulse. The energy radiated by the propagating primary pulse manifests in the form of traveling waves of varying spatial periodicity depending on the mass ratio. These traveling waves depend only on the mass ratio and are rescalable with respect to any arbitrary applied energy. The dynamics of these families of traveling waves is systematically studied by considering finite dimer chains (termed the ‘reduced systems’) subject to periodic boundary conditions. We demonstrate that these waves may exhibit interesting bifurcations or loss of stability as the system parameter varies. In turn, these bifurcations and stability exchanges in infinite dimer chains are correlated to previous studies of pulse attenuation in finite dimer chains through efficient energy radiation from the propagating pulse to the far field, mainly in the form of traveling waves. Based on these results a new formulation of attenuation and propagation zones (stop and pass bands) in semi-infinite granular dimer chains is proposed.

scholarly journals NONLINEAR EXTENSIONS OF SCHRÖDINGER–VON NEUMANN QUANTUM DYNAMICS: A SET OF NECESSARY CONDITIONS FOR COMPATIBILITY WITH THERMODYNAMICS

2005 ◽  
Vol 20 (13) ◽  
pp. 977-984 ◽  
Author(s):  
GIAN PAOLO BERETTA
Keyword(s):  
Quantum Dynamics ◽  
Necessary Conditions ◽  
Experimental Tests ◽  
Microscopic Level ◽  
General Description ◽  
Von Neumann ◽  
Nonequilibrium States ◽  
Nonlinear Extensions ◽  
Isolated Systems ◽  
True Quantum

We propose a list of conditions that consistency with thermodynamics imposes on linear and nonlinear generalizations of standard unitary quantum mechanics that assume a set of true quantum states without the restriction ρ2 = ρ even for strictly isolated systems and that are to be considered in experimental tests of the existence of intrinsic (spontaneous) decoherence at the microscopic level. As part of the discussion, we present a general description of nonequilibrium states.

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