Wave-front solution in extended quantum circuits with charge discreteness

J. C. Flores; Mauro Bologna; K. J. Chandía; Constantino A. Utreras Díaz

doi:10.1103/physrevb.74.193319

Wave-front solution behaviour for continuous neural networks with lateral inhibition

IMA Journal of Applied Mathematics ◽

10.1093/imamat/hxl007 ◽

2006 ◽

Vol 71 (4) ◽

pp. 544-564 ◽

Cited By ~ 1

Author(s):

Sittipong Ruktamatakul ◽

Jonathan Bell ◽

Yongwimon Lenbury

Keyword(s):

Neural Networks ◽

Wave Front ◽

Lateral Inhibition ◽

Front Solution ◽

Continuous Neural Networks ◽

Solution Behaviour

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Wave front solution of some competition models with migration effect

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.59.223 ◽

1983 ◽

Vol 59 (6) ◽

pp. 223-226 ◽

Cited By ~ 1

Author(s):

Yuzo Hosono ◽

Syozo Niizeki

Keyword(s):

Wave Front ◽

Front Solution ◽

Migration Effect ◽

Competition Models

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Periodic solution and wave front solution for delay equation

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2006.09.006 ◽

2007 ◽

Vol 45 (7-8) ◽

pp. 974-980 ◽

Cited By ~ 1

Author(s):

Guojian Lin ◽

Rong Yuan

Keyword(s):

Periodic Solution ◽

Wave Front ◽

Delay Equation ◽

Front Solution

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Application of Kirchhoff’s Integral Equation Formulation to an Elastic Wave Scattering Problem

Journal of Applied Mechanics ◽

10.1115/1.3607857 ◽

1967 ◽

Vol 34 (4) ◽

pp. 921-930 ◽

Cited By ~ 1

Author(s):

William L. Ko ◽

Thorbjorn Karlsson

Keyword(s):

Wave Front ◽

Integral Equations ◽

Scattering Problem ◽

Linear Matrix ◽

Infinite Length ◽

Shadow Zone ◽

Surface Integral ◽

Front Solution ◽

Frequency Wave ◽

Integral Equation Formulation

Interaction of a plane compressional step wave with a circular cylindrical obstacle embedded in an elastic medium is studied. The obstacle is rigid, stationary, and of infinite length. The incident wave travels in a direction perpendicular to the axis of the cylinder. Using Kirchhoff’s theorem, surface integral equations are formulated for the displacement potential derivatives in the scattered field and on the cylinder boundary. The wave-front solution obtained for the illuminated zone on the cylinder is identical to that obtained by high-frequency wave-front analysis. Boundary stresses in the shadow zone as well as the initial behavior of the wave-front stresses at the boundary between the illuminated and shadow zones are obtained. The integral equations for both illuminated and shadow-zone boundary stresses are reduced to successive linear matrix equations for numerical analysis. The numerical methods developed in this paper can be applied to interaction problems for obstacles of arbitrary geometrical configuration. They are also readily extended to the case where the medium exhibits bilinear or multilinear stress-strain behavior.

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Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network

Abstract and Applied Analysis ◽

10.1155/2014/753614 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Lijun Zhang ◽

Linghai Zhang ◽

Jie Yuan ◽

C. M. Khalique

Keyword(s):

Differential Equation ◽

Wave Front ◽

Model Equation ◽

Main Idea ◽

Kernel Functions ◽

Front Solution ◽

Differential Model ◽

Traveling Wave Front ◽

Front Solutions ◽

Integral Differential Equation

An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions). The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.

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Scattering of Stress Waves by a Circular Elastic Cylinder Embedded in an Elastic Medium

Journal of Applied Mechanics ◽

10.1115/1.3408512 ◽

1970 ◽

Vol 37 (2) ◽

pp. 345-355 ◽

Cited By ~ 8

Author(s):

W. L. Ko

Keyword(s):

Elastic Medium ◽

Wave Front ◽

Early Stage ◽

Elastic Cylinder ◽

Stress Waves ◽

Front Solution ◽

Integral Formulas ◽

Incident Plane ◽

Geometrical Acoustics ◽

Singular Wave

Scattering of stress waves by a circular elastic cylinder embedded in an elastic medium is investigated. The axis of the scatterer is perpendicular to the propagation vector of the incident plane compressional stress pulse wave. Making use of modified Kirchhoff’s integral formulas developed for elastodynamics by Ko [1], wave-front stresses and displacements during the early stage of interaction are obtained for both interior and exterior fields, and for the scatterer-medium interface. The solutions are valid for the whole spectrum of material properties of the scatterer ranging from void to infinitely dense materials. It is found that Kirchhoff’s method of retarded potentials predicts singular wave-front response at caustics as does the geometrical acoustics. The basic integral equations presented are applicable to a scatterer of arbitrary shape and do not only give the wave-front solution, but also the solutions after the arrival of the wave front.

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