On accretion from an inhomogeneous medium

Nonergodic subdiffusion from Brownian motion in an inhomogeneous medium.

Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random diffusivities. The particle is never trapped but rather performs continuous Brownian motion with the local diffusion constant. Under simple assumptions on t...

Casimir stress in an inhomogeneous medium

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz’s theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wi...

On the Propagation of Calcium Waves in an Inhomogeneous Medium

Although the exact details are disputed, it is well established that propagating waves of increased intracellular free Ca2+ concentration arise from a positive feedback or autocatalytic mechanism whereby Ca2+ stimulates its own release. Most previous modeling of the propagation of Ca2+ waves has assumed that the sites of autocatalytic Ca2+ release, the activation sites, are homogeneously distri...

Wave Propagation in an Inhomogeneous Medium

On the existence of transmission eigenvalues in an inhomogeneous medium

We prove the existence of transmission eigenvalues corresponding to the inverse scattering problem for isotropic and anisotropic media for both scalar Helmholtz equation and Maxwell’s equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Päivärinta and Sylvester [15] to prove the existence of transmission eigenvalues for a larger class of interior ...