scholarly journals Periodic solution and wave front solution for delay equation

2007 ◽  
Vol 45 (7-8) ◽  
pp. 974-980 ◽  
Author(s):  
Guojian Lin ◽  
Rong Yuan
Keyword(s):  
Periodic Solution ◽  
Wave Front ◽  
Delay Equation ◽  
Front Solution

scholarly journals Wave-front solution in extended quantum circuits with charge discreteness

2006 ◽  
Vol 74 (19) ◽  
Author(s):  
J. C. Flores ◽  
Mauro Bologna ◽  
K. J. Chandía ◽  
Constantino A. Utreras Díaz
Keyword(s):  
Wave Front ◽  
Quantum Circuits ◽  
Front Solution

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

1967 ◽  
Vol 34 (4) ◽  
pp. 921-930 ◽  
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.

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

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.

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

1970 ◽  
Vol 37 (2) ◽  
pp. 345-355 ◽  
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.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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