We study the evolution of non-linear spherically symmetric inhomogeneities in string cosmology. Friedmann solutions of different spatial curvature are matched to produce solutions which describe the evolution of non-linear density and curvature inhomogeneities. The evolution of bound and unbound inhomogeneities are studied. The problem of primordial black hole formation is discussed in the stri...

We consider the transmission eigenvalue problem for an inhomogeneous medium containing a finite number of diametrically small inhomogeneities of different refractive index. We prove a convergence result for the transmission eigenvalues and eigenvectors corresponding to media with small homogeneities as the diameter of small inhomogeneities goes to zero. In addition we derive rigorously a formul...

Here n denotes the unit outward normal to the domain Ω. Let ω denote a set of “inhomogeneities” inside Ω. The geometric assumptions about the set of “inhomogeneities” are very simple: we suppose the set ω is measurable, and separated away from the boundary, (i.e., dist(ω , ∂Ω) > d0 > 0). Most importantly, we suppose that 0 < |ω | gets arbitrarily small, where |ω | denotes the Lebesgue measure o...

Interaction of charged particles with each other and/or with external fields results in emission of electromagnetic radiation. This article considers the emission arising as fast (nonthermal) particles move through media with random inhomogeneities. The nature of these inhomogeneities might be rather arbitrary. One of the simplest examples of inhomogeneities is a distribution of the microscopic...

Nonlinear waves of the reaction-diffusion (RD) type occur in many biophysical systems, including the heart, where they initiate cardiac contraction. Such waves can form vortices called scroll waves, which result in the onset of life-threatening cardiac arrhythmias. The dynamics of scroll waves is affected by the presence of inhomogeneities, which, in a very general way, can be of (i) ionic type...

background: polymer gel dosimetry is still the only dosimetry method for direct measuring of threedimensional dose distributions. mri polymer gel dosimeters are tissue equivalent and can act as a phantom material. in this study the obtained isodose maps with pagat polymer gel dosimeter were compared to those calculated with egsnrs for singleshot irradiations of 8 and 18 mm collimators of gamma ...