This paper is concerned with entropy methods for linear drift-diffusion equations with explicitly time-dependent or degenerate coefficients. Our goal is to establish a list of various qualitative properties of the solutions. The motivation for this study comes from a model for molecular motors, the so-called Brownian ratchet, and from a nonlinear equation arising in traffic flow models, for whi...

We provide the n-channel extension of the unified workload capacity space bounds for standard parallel processing models with minimum-time, maximum-time, and single-target self-terminating stopping rules. This extension enables powerful generalizations of this approach to multiple stopping rules and any number of channels of interest. Mapping the bounds onto the unified capacity space enables a...

Transport equations arise in various areas of fluid mechanics, but the precise conditions on the vector field for them to be well-posed are still not fully understood. The renormalized theory of DiPerna and Lions for linear transport equations with unsmooth coefficient uses the tools of approximation of an arbitrary weak solution by smooth functions, and the renormalization property, that is to...

refractor ambiguities are big problem in seismic refraction method especially in seismic engineering. there can be hidden subsurface geological phenomena such as hidden faults and shear zones which are not simply predicted by the travel-time graph or some geophysical methods. head wave amplitudes are used to show the resolution of refractor ambiguities and the existence of anisotropy in complex...

We prove weak-strong uniqueness results for the compressible Navier-Stokes system with degenerate viscosity coefficient and with vacuum in one dimension. In other words, we give conditions on the weak solution constructed in [20] so that it is unique. The main novelty consists in dealing with initial density ρ0 which contains vacuum, indeed the most of the results exclude this situation in orde...

It is proved that elliptic boundary value problems in divergence form can be written in many equivalent forms. This is used to prove regularity properties and maximum principles for problems with Robin boundary conditions with negative or indefinite boundary coefficient on Lipschitz domains by rewriting them as a problem with positive coefficient. It is also shown that such methods cannot be ap...

Speckle and low contrast make ultrasound image segmentation a difficult task. This paper presents an original robust active contour energy and the corresponding quasi-automatic initialization. Both are based on the coefficient of variation gradient vector fl ow. Our approach combines anisotropic diffusion with the gradient vector fl ow field. The gradient vector fl ow is calculated from a map o...

Laser diode beam divergence is the main parameter for beam shaping and fiber optic coupling. Increasing the waveguide layer thickness is the conventional method to decrease the beam divergence. In this paper, the broadened asymmetric waveguide is introduced to decrease the divergence without increasing the optical power. The asymmetric waveguide was used to shift the vertical optical field to n...

Indian Ocean is known as a source of moisture for southeast of Iran due to summer precipitation. In this study, in order to investigate the role of SST of Indian Ocean, and the convergence and divergence fields in the precipitation of southeast of Iran, precipitation data of five synoptic stations were used during 2000-2010, including Iranshahr, Khash, ChahBahar, Zabul, and Saravan. To investig...