Search results for "Diffusion"

Cross-diffusion driven instability for a nonlinear reaction-diffusion system

2008

In this work we investigate the possibility of the pattern formation for a system of two coupled reaction-diffusion equations. The nonlinear diffusion terms has been introduced to describe the tendency of two competing species to diffuse faster (than predicted by the usual linear diffusion) toward lower densities areas. The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The system is supplemented with the initial conditions and no-flux boundary conditions. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show h…

Anomaly Detection from Network Logs Using Diffusion Maps

2011

The goal of this study is to detect anomalous queries from network logs using a dimensionality reduction framework. The fequencies of 2-grams in queries are extracted to a feature matrix. Dimensionality reduction is done by applying diffusion maps. The method is adaptive and thus does not need training before analysis. We tested the method with data that includes normal and intrusive traffic to a web server. This approach finds all intrusions in the dataset. peerReviewed

Transfer of aroma compounds in water-lipid systems: binding tendency of beta-lactoglobulin.

1998

Interactions of volatile aroma compounds with protein in aqueous solutions, especially whey proteins, have received significant attention in recent years. This work attempts to improve our understanding of the mass transfer in multiphasic systems, such as emulsions at the lipid−water interface, and to reveal the role of β-lactoglobulin in the release rate of solutes. For this purpose the rotating diffusion cell has been used. From a practical point of view it enables evaluation of the transfer through the aqueous phase, through the oil and the interfacial transfer. The effect of β-lactoglobulin, medium pH, and solute concentration has been investigated. Benzaldehyde and 2-nonanone have been…

Brainstem Anatomy of White Matter Tracts Using Diffusion Weighted Imaging

1998

Soret coefficient of trace ions determined with electrochemical impedance spectroscopy in a thin cell. Theory and measurement

2018

The tendency of a substance to migrate due to a temperature gradient is known as thermodiffusion or the Soret effect. We believe that this is the first work that describes the study of the Soret effect using electrochemical impedance spectroscopy in a non-isothermal thin cell, and shows how the Soret coefficient can be determined from these measurements. The effect of a temperature gradient in a thin cell is analyzed, both theoretically and experimentally. Our theoretical modeling of the system predicts the effect of key parameters to the impedance spectra. Experimentally we determine the Soret coefficient of the redox couple Fe(CN)64−/Fe(CN)63− in an aqueous KCl solution. It is found that …

An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology

2016

The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the i…

Transport coefficients in desalting processes by electrodialysis

2011

Abstract In this work a thermodynamic analysis on the transport equations in the processes of electrodiffusion (EF) and electrodialysis (ED) has been developed. The transport equations are classified in two sets according to the information they contain: i ) fundamental and ii ) complementary. We determine that there are four fundamental transport coefficients needed to characterize these membrane systems. We also conclude that this number is not reduced to three when the Onsager reciprocal relation (ORR) is assumed. I have also obtained a new expression for the concentration rate in EF and ED processes from the mass and volume balance. This relation provides a new way for evaluating the ap…

On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems

2018

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.

Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

2021

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …

One- and Two-Dimensional Diffusion of Metal Atoms in Graphene

2008

In the present work, individual Au or Pt atoms in layersconsisting of one or twographene planes have been monitoredin real time at high temperature by high-resolution TEM. Weobtain information about the location of metal atoms ingrapheneandthediffusionmechanisms.Activationenergiesfordiffusion are obtained in a temperature range close to thetemperature of the technically important metal-assisted CVDprocess.Thematerialwassynthesizedinanarcdischarge