Kinetic transport equations with a given confining potential and non-linear relaxation type collision operators are considered. General (monotone) energy dependent equilibrium distributions are allowed with a chemical potential ensuring mass conservation. Existence and uniqueness of solutions is proven for initial data bounded by equilibrium distributions. The diffusive macroscopic limit is car...

Diffusion tensor imaging (DTI) accurately delineates white matter pathways when the Gaussian model of diffusion is valid. However, DTI yields erroneous results when diffusion takes on a more complex distribution, as is the case in the brain when fiber tracts cross. High angular resolution diffusion imaging (HARDI) overcomes this limitation of DTI by more fully characterizing the angular depende...

In typical applications of diffusion tensor imaging (DTI), DT-derived quantities are used to make a diagnostic, therapeutic, or scientific determination. In such cases it is essential to characterize the variability of these tensor-derived quantities. Parametric and empirical methods have been proposed to estimate the variance of the estimated DT, and quantities derived from it. However, the fo...

In this paper, we discuss a stochastic analogue of Aubry–Mather theory in which a deterministic control problem is replaced by a controlled diffusion. We prove the existence of a minimizing measure (Mather measure) and discuss its main properties using viscosity solutions of Hamilton–Jacobi equations. Then we prove regularity estimates on viscosity solutions of the Hamilton–Jacobi equation usin...

in this paper, a new numerical method for solving time-fractional diffusion equations is introduced. for this purpose, finite difference scheme for discretization in time and chebyshev collocation method is applied. also, to simplify application of the method, the matrix form of the suggested method is obtained. illustrative examples show that the proposed method is very efficient and accurate.

background : these days, the antibiotic resistance of pseudomonas aeruginosa isolates to imipenem has significantly increased. therefore the study of resistance to imipenem in this organism to imipenem in determining the appropriate treatment is crucial and necessary. the goal of this study is to compare three phenotypic methods of e-test, disk diffusion and micro broth dilution in the study of...

Background and Aim:  Streptococcus sanguinis (S. sanguinis) is one of the effective bacteria in the formation of caries and periodontal diseases which are caused by dental plaque. Currently, the use of natural honey (NH) is considered as a method of reducing S. sanguinis and S. mutans in saliva, which results in reducing the dental plaque. The purpose of this study was to evaluate the effects o...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

Submitted for the DPP13 Meeting of The American Physical Society Finite Volume Scheme for Anisotropic Diffusion1 BRAM VAN ES, CWI, Amsterdam, The Netherlands; FOM Institute DIFFER, Nieuwegein, The Netherlands, BARRY KOREN, CWI, Amsterdam, The Netherlands; Eindhoven University of Technology, Eindhoven, The Netherlands, HUGO DE BLANK, FOM Institute DIFFER, Nieuwegein, The Netherlands — In fusion ...

Simple and efficient modifications of the original error-diffusion algorithm are proposed to remove the structural artifact and enhance the real structures. The input image is separated into the flatten and detailed areas based on a gradient-based measure. While a randomization is applied to remove the structural artifact in the flatten area, a gradient-based diffusion modulation is applied to ...