Search results for "Diffusion equation"

Dependence of O2 diffusion dynamics on pressure and temperature in silica nanoparticles

2013

An experimental study of the molecular O2 diffusion process in high purity non-porous silica nanoparticles having 50 m2/g BET specific surface and 20 nm average radius was carried out in the temperature range from 127 to 177 °C at O2 pressure in the range from 0.2 to 66 bar. The study was performed by measuring the volume average interstitial O2 concentration by a Raman and photoluminescence technique using a 1,064 nm excitation laser to detect the singlet to triplet emission at 1,272 nm of the molecular oxygen in silica. A dependence of the diffusion kinetics on the O2 absolute pressure, in addition to temperature dependence, was found. The kinetics can be fit by the solution of Fick’s dif…

The Monotone Area-preserving Flux-Form Advection Algorithm: Reducing the Time-splitting Error in Two-Dimensional Flow Fields

1993

A time evolution model for total-variation based blind deconvolution

2007

Departamento Matematica Aplicada, Universidad de Valencia, Burjassot 46100, Spain.We propose a time evolution model for total-variation based blind deconvolution consisting of two evolution equations evolv-ing the signal by means of a nonlinear scale space method and the kernel by using a diffusion equation starting from the zerosignal and a delta function respectively. A preliminary numerical test consisting of blind deconvolution of a noiseless blurredimage is presented.

A strongly degenerate quasilinear elliptic equation

2005

Abstract We prove existence and uniqueness of entropy solutions for the quasilinear elliptic equation u - div a ( u , Du ) = v , where 0 ⩽ v ∈ L 1 ( R N ) ∩ L ∞ ( R N ) , a ( z , ξ ) = ∇ ξ f ( z , ξ ) , and f is a convex function of ξ with linear growth as ∥ ξ ∥ → ∞ , satisfying other additional assumptions. In particular, this class of equations includes the elliptic problems associated to a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics, respectively. In a second part of this work, using Crandall–Liggett's iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the corresponding…

Fully reliable a posteriori error control for evolutionary problems

2015

Geoid effects in a convecting system with lateral viscosity variations

1992

The geoid signal and the flow patterns of two-dimensional steady state convection models with exponential temperature- and depth dependent viscosity are compared with results for an equivalent stratified viscosity structure. In analogy to Richards and Hager [1989], the latter are computed by a “dynamic response” approach. The flow fields obtained with this approach are quite different from the full solution; the geoid signals are similar but the amplitudes differ significantly. The differences are analysed in the horizontal wavenumber domain and in the spatial domain. They may lead to an overestimation of the viscosity contrast of the earth's mantle derived by modeling the earth's geoid wit…

Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations

2021

We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…

Linearly implicit-explicit schemes for the equilibrium dispersive model of chromatography

2018

Abstract Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22–42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose seve…

Levy targeting and the principle of detailed balance

2011

We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …

Diffusional kinetics of metalliding zinc into solid copper

1982

The process of incorporation of zinc into a copper cathode has been experimentally studied in a molten salt system at 381±2° C and at various current densities. The process is shown to be kinetically controlled by the diffusion of Zn into the solid matrix. A galvanostatic pulse titration technique has been used to determine the chemical diffusion coefficient at various alloy compositions, and an exponential relationship has been found between the diffusivity and the third power of the zinc concentration in the alloy. This relationship was then used in the diffusion equation within the solid matrix and a numerical integration was performed. Very good agreement was found between the calculate…