Search results for " diffusion"
showing 10 items of 521 documents
Effective diffusion coefficient and diffusion-controlled reactions in insulating solids with defects
1995
Abstract The expressions for effective diffusion coefficient are obtained in the mean field approximation for two-phase system for spatial dimensions of 1, 2 and 3. The existence of potential barrier for diffusion on the phase boundary was taken into account via the boundary conditions. Obtained formulae could be applied in the theory of diffusion-controlled reactions and for interpreting the experimental data on defect diffusion in two-phase media.
Oxygen Diffusion Constants D and K of Tumor Tissue (DS-Carcinosarcoma) and Their Temperature Dependence
1978
To understand more thoroughly the tumor O2 supply conditions, knowledge of O2 diffusivity in tumor tissue is required. Since exact measurements of the O2 diffusion constants of tumor tissue have not been carried out to date, previous investigations of tumor O2 supply had to employ estimated values (6 – 8, 10). The results of these studies are in part contradictory.
A mechanical picture of fractional-order Darcy equation
2015
Abstract In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0 ⩽ β ≤ 1 . If, instead, the physical properties of the media show a power-law increase from the control sectio…
Mathematical and numerical analysis of initial boundary valueproblem for a linear nonlocal equation
2019
We propose and study a numerical scheme for bounded distributional solutions of the initial boundary value problem for the anomalous diffusion equation ∂t u +Lμu = 0 in a bounded domain supplemented with inhomogeneous boundary conditions. Here Lμ is a class of nonlocal operators including fractional Laplacian. ⃝c 2019 InternationalAssociation forMathematics andComputers in Simulation (IMACS). Published by ElsevierB.V.All rights reserved.
An iterative method for pricing American options under jump-diffusion models
2011
We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou@?s and Merton@?s jump-diffusion models show that the resulting iteration converges rapidly.
Monotonic solution of heterogeneous anisotropic diffusion problems
2013
Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of…
A velocity–diffusion method for a Lotka–Volterra system with nonlinear cross and self-diffusion
2009
The aim of this paper is to introduce a deterministic particle method for the solution of two strongly coupled reaction-diffusion equations. In these equations the diffusion is nonlinear because we consider the cross and self-diffusion effects. The reaction terms on which we focus are of the Lotka-Volterra type. Our treatment of the diffusion terms is a generalization of the idea, introduced in [P. Degond, F.-J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Stat. Comput. 11 (1990) 293-310] for the linear diffusion, of interpreting Fick's law in a deterministic way as a prescription on the particle velocity. Time discretization is based on the …
Potential application of lactic acid bacteria in the biopreservation of red grape from mycotoxigenic fungi
2021
Background Filamentous fungi are the main contamination agent in the viticultural sector. Use of synthetic fungicides is the regular answer to these contaminations. Nevertheless, due to several problems associated with the use of synthetic compounds the industry demands new and safer methods. In the present work, the biopreservation potential of four lactic acid bacteria (LAB) strains was studied against the principal grape contaminant fungi. Results Agar diffusion test evidenced that all four culture-free supernatant (CFS) had antifungal properties against all tested fungi. The Minimum Inhibitory Concentration (MIC) and Minimum Fungicidal Concentration (MFC) test values evidenced that medi…
Prediction of mass fluxes in the pervaporation process of the ethanol dehydration, based on the free volume theory
2014
Metodę obliczania współczynników dyfuzji Maxwella-Stefana opartą na współczynnikach dyfuzji własnej przewidywanych wg zależności wynikających z teorii wolnych objętości, zastosowano do obliczania strumieni masy w procesie perwaporacyjnego odwadniania etanolu na membranie z alkoholu poliwinylowego PVA. Parametry metody wolnych objętości dla badanego układu wyznaczono oraz obliczono stężenia równowagowe w PVA stosując zmodyfikowaną metodę UNIFAC-FV a następnie obliczono udziały masowe w permeacie oraz współczynniki wzbogacenia. Obliczenia przeprowadzono dla danych eksperymentalnych opublikowanych w pracy [3]. Wyniki obliczeń porównano z wynikami uzyskanymi na instalacji doświadczalnej.
Diffusion-weighted imaging in oncology: An update
2020
To date, diffusion weighted imaging (DWI) is included in routine magnetic resonance imaging (MRI) protocols for several cancers. The real additive role of DWI lies in the “functional” information obtained by probing the free diffusivity of water molecules into intra and inter-cellular spaces that in tumors mainly depend on cellularity. Although DWI has not gained much space in some oncologic scenarios, this non-invasive tool is routinely used in clinical practice and still remains a hot research topic: it has been tested in almost all cancers to differentiate malignant from benign lesions, to distinguish different malignant histotypes or tumor grades, to predict and/or assess treatment resp…