Green's function for the lossy wave equation

Aleixo, R.; Oliveira, E. Capelas de

doi:10.1590/s1806-11172008000100003

Cited by 5 publications

(1 citation statement)

References 4 publications

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“…To cite some of them, one can note [4] where the Green's function has been sought for the problem. In [5], asymptotic simplification of the problem and asymptotic approximation methods for Fourier integrals for the subject equation have been discussed.…”

Section: Introductionmentioning

confidence: 99%

A Simple Solution for the Damped Wave Equation With a Special Class of Boundary Conditions Using the Laplace Transform

Yener¹

2011

PIER B

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Abstract-It is proven that for the damped wave equation when the Laplace transforms of boundary value functions ψ(0, t) and ( ∂ψ (z,t) ∂z ) z=0 of the solution ψ(z, t) have no essential singularities and no branch points, the solution can be constructed with relative ease. In such a case while computing the inverse Laplace transform, the integrals along the segments on the real line are shown to always cancel. The integrals along the circles C ε and C ε about the point s = −σ/ε determined by the coefficient of the time derivative in the differential equation and point s = 0 are shown to vanish unless Laplace transforms of mentioned boundary value functions have poles at these points. If such poles do exist, the problem is nevertheless one of integration along circles about these poles and then setting the radii of these circles equal to zero in the limit.

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Section: Introductionmentioning

confidence: 99%

A Simple Solution for the Damped Wave Equation With a Special Class of Boundary Conditions Using the Laplace Transform

Yener¹

2011

PIER B

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Time-domain Green’s function associated to the interface problem for the Klein–Gordon equation

Salhi,

Tlemcani

2023

Wave Motion

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A Novel Electrical Model for Advection-Diffusion-Based Molecular Communication in Nanonetworks

Azadi

Abouei

2016

IEEE Trans.on Nanobioscience

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In this paper, we propose an end-to-end electrical model to characterize the communication between two nanomachines via advection-diffusion motion along the conventional pipe medium. For this modeling, we consider three modules consisting of transmitter, advection-diffusion propagation and receiver. The modulation scheme and releasing molecules through the conventional pipe medium from the transmitter nanomachine is represented in the transmitter module. The advection-diffusion propagation of molecules along the flow-induced path is shown in advection-diffusion propagation module, and the demodulation scheme of bounded particles at the receiver nanomachine is characterized in the receiver module. Our objective is to find an electrical model of each module under the zero initial condition which enables us to represent the electrical circuit related to each module. The transmitter and the signal propagation models are built on the basis of the molecular advection-diffusion physics, whereas the receiver model is interpreted by stemming from the theory of the ligand-receptor binding chemical process. In addition, we employ the transfer function of modules to derive the normalized gain and the delay of each module. Supported by numerical results, we analyze the effect of physical parameters of the pipe medium on the total normalized gain and delay of molecular communications.

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Green's function for the lossy wave equation

Cited by 5 publications

References 4 publications

A Simple Solution for the Damped Wave Equation With a Special Class of Boundary Conditions Using the Laplace Transform

A Simple Solution for the Damped Wave Equation With a Special Class of Boundary Conditions Using the Laplace Transform

Time-domain Green’s function associated to the interface problem for the Klein–Gordon equation

A Novel Electrical Model for Advection-Diffusion-Based Molecular Communication in Nanonetworks

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