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In order to suppress this undesirable echo, walls and ceilings have been often given absorptive surfaces which absorb sound energy or corrugated surfaces which provide wave diffusion.
The use of a time-gated reflection matrix of a scattering medium, in particular via using singular value decomposition and injecting light into the largest time-gated eigenchannel, can lead to a more than tenfold enhancement in light energy delivery in comparison with ordinary wave diffusion cases.
Solutions to the damped wave diffusion and relaxation equation in one dimension can be used to interpret a variety of biological phenomena including developmental biology, drug design, and neuroscience.
Therefore, the residual effect due to wave diffusion could be mixed up with the residual effect caused by metallic loss in two-dimensional configurations such as ours.
This analysis of the fractional wave, diffusion, and Dirac equations, fits in the general context of establish bridges between fractional calculus and the classical and quantum mechanics [44, 45].
In this regard, notice even in the absence of metallic loss that wave diffusion takes place not in three- but in two-dimensional space, albeit in unbounded domains [16, 40].
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Fractional differential equations provide an outstanding instrument to describe the complex phenomena in fields of viscoelasticity, electromagnetic waves, diffusion equations and so on [1 5].
Among the treated problems are the minimal surface problem, the dynamic analysis of elastic membranes undergoing large deflection, the heat conduction in bodies with temperature dependent conductivity, and the nonlinear fractional wave-diffusion equation.
Liemert and Kienle [18] discussed a time fractional wave-diffusion equation in an inhomogeneous half-space.
Also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace).
These reflection coefficients are found to depend upon the angle of incidence of SV wave, thermoelastic diffusion parameter and other material constants.
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