LATTICE GAS WAVE PROPAGATION MODELS INCLUDING DISSIPATION

1995 ◽  
Vol 03 (01) ◽  
pp. 69-93 ◽  
Author(s):  
YASUSHI SUDO ◽  
VICTOR W. SPARROW
Keyword(s):  
Wave Propagation ◽  
Random Walk ◽  
Diffusion Equation ◽  
Lattice Gas ◽  
Sound Propagation ◽  
Two Dimensional ◽  
Propagation Models ◽  
One Dimensional ◽  
Lattice Gas Models ◽  
Wave Models

New lattice gas models for one-dimensional (1D) and two-dimensional (2D) sound propagation have been recently proposed by the authors. These models were dissipationless and deterministic. In this paper, it will be shown how dissipation effects can be included into these lattice gas wave models. To simulate these dissipation effects, the lattice gas particles are assumed to take a random walk. The resulting models combine the authors' lattice gas wave models with published lattice gas models for the diffusion equation. The formulations are stable and consistent.

scholarly journals Quantum walks and elliptic integrals

2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Elliptic Integral ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Elliptic Integrals ◽  
Two Dimensional ◽  
One Dimensional ◽  
Similar Expression ◽  
Return Probability

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

Numerical simulation of contaminant dispersion in estuary flows

1982 ◽  
Vol 381 (1780) ◽  
pp. 179-194 ◽  
Keyword(s):  
Numerical Simulation ◽  
Random Walk ◽  
Shear Flow ◽  
Diffusion Equation ◽  
New Method ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Turbulent Shear Flow ◽  
Oscillatory Flows ◽  
Contaminant Dispersion

The paper examines in detail the dispersion of a passive contaminant in steady and oscillatory turbulent shear flow in a two-dimensional channel. The aim of this examination is to understand dispersion in estuaries. A new method of analysing and predicting concentration distributions has been developed from work of Sullivan ( J. Fluid Mech . 49, 551–576 (1971)). A random walk technique is used, the contaminant being represented by a large number of marked particles whose paths are tracked as they move through the fluid. The technique seeks to model the physics of dispersion more realistically than the standard diffusion equation, and results from the simulation, with input based on data taken in the Mersey, show it to be a useful and versatile method of studying dispersion in oscillatory flows.

A General Continuum Theory With Microstructure for Wave Propagation in Elastic Laminated Composites

1974 ◽  
Vol 41 (1) ◽  
pp. 101-105 ◽  
Author(s):  
G. A. Hegemier ◽  
T. C. Bache
Keyword(s):  
Wave Propagation ◽  
Continuum Model ◽  
Laminated Composites ◽  
Continuum Theory ◽  
Velocity Spectrum ◽  
Two Dimensional ◽  
One Dimensional ◽  
General Continuum ◽  
Hierarchy Of Models ◽  
Dimensional Wave

A continuum theory with microstructure for wave propagation in laminated composites, proposed in previous works concerning propagation normal and parallel to the laminates, is extended herein to the general two-dimensional case. Continuum model construction is based upon an asymptotic scheme in which dominant signal wavelengths are assumed large compared to typical composite microdimensions. A hierarchy of models is defined by the order of truncation of the obtained asymptotic sequence. Particular attention is given to the lowest order dispersive theory. The phase velocity spectrum of the general theory is investigated for one-dimensional wave propagation at various propagation angles with respect to the laminates. Retention of all terms in the asymptotic sequence is found to yield the exact elasticity spectrum, while spectral collation of the lowest order dispersive theory with the first three modes of the exact theory gives excellent agreement.

Numerical Solution for Two-Dimensional Elastic Wave Propagation in Finite Bars

1967 ◽  
Vol 34 (3) ◽  
pp. 725-734 ◽  
Author(s):  
L. D. Bertholf
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Numerical Solutions ◽  
Step Change ◽  
Two Dimensional ◽  
One Dimensional ◽  
Elastic Bar ◽  
The One ◽  
The Impact

Numerical solutions of the exact equations for axisymmetric wave propagation are obtained with continuous and discontinuous loadings at the impact end of an elastic bar. The solution for a step change in stress agrees with experimental data near the end of the bar and exhibits a region that agrees with the one-dimensional strain approximation. The solution for an applied harmonic displacement closely approaches the Pochhammer-Chree solution at distances removed from the point of application. Reflections from free and rigid-lubricated ends are studied. The solutions after reflection are compared with the elementary one-dimensional stress approximation.

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