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Multiple scattering of polarised electromagnetic waves in diffusive media is investigated by means of radiative transfer theory. The method becomes exact in several situations of interest, such as a thick-slab experiment (slab thickness L…
A rigorous approach for solving canonical circular open-ended dielectric-lined waveguide diffraction problems is presented. This is continuation of our recent paper [1] where a simpler case of uniform dielectric filling has been considered.…
A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…
This work focuses on the length correction due to radiation effect of a duct discontinuity or at the surface of a perforated plate in the linear acoustic domain and at large wavelengths. Two results are obtained from the comparison of…
We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling…
We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the…
Shock tubes have been a crucial device, facilitating studies across a wide range of practical applications. An open-ended shock tube employing the wire-explosion technique with a rectangular cross section is used in the present study to…
We explore the oscillatory behavior observed in inversion methods applied to large-scale text-to-image diffusion models, with a focus on the "Flux" model. By employing a fixed-point-inspired iterative approach to invert real-world images,…
Most of the physically based techniques for rendering translucent objects use the diffusion theory of light scattering in turbid media. The widely used dipole diffusion model (Jensen et al. 2001) applies the diffusion-theory formula derived…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
The present work revisits the problem of modeling diffusion above a stagnant liquid interface in a capillary tube geometry. In this revisitation we elucidate a misconception found in the classical model proposed by Bird et. al. Furthermore,…
One strategy for arresting propagating detonation waves in pipes is by imposing a sudden area enlargement, which provides a rapid lateral divergence of the gases in the reaction zone and attenuates the leading shock. For sufficiently small…
We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our…
The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the…
A problem of diffraction of a symmetrical transverse magnetic mode $ \text{TM}_{0l} $ by an open-ended cylindrical waveguide corrugated inside is considered. A depth and a period of corrugations are supposed to be much less than the…
We show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We provide an estimate on the total length of time for which…
Strong nonlinear effects are known to contribute to the wave run-up caused when a progressive wave impinges on a vertical surface piercing cylinder. The magnitude of the wave run-up is largely dependent on the coupling of the cylinder…
The diffraction of ultrasound by a circular disk and an aperture of the same size have been investigated as a demonstration of Babinet's principle in the Fresnel regime. The amplitude and the phase of diffracted ultrasonic waves have been…
Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary…
Rayleigh-Bloch waves are guided acoustic waves propagating along a periodic line of inclusions placed inside an open, infinite medium. Below the sound cone, they are transversely evanescent on both sides of the line of inclusions. Guidance…