Ballistic diffusion induced by non-Gaussian noise

In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C（t） of the non-Gaussian stochastic process,and find that they depend on the parameter q,indicating the departure of the non-Gaussian noise from Gaussian behavior：for q ≤ 1,C（t） is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit,whereas for q 〉 1,C（t） can be approximated by a second-order exponentially decaying function and converges to a non-zero constant.Due to the properties of C（t）,the particle exhibits a normal diffusion for q ≤ 1,while for q 〉 1 the non-Gaussian noise induces a ballistic diffusion,i.e.,the long-time mean square displacement of the free particle reads 〈[x（t）-]2∝t2.

High accuracy non-equidistant method for singular perturbation reaction-diffusion problem

Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.

Kinetic equation based on non-steady-state diffusion of oxygen in solid copper

The kinetics of internal oxidation of dilute Cu-Al alloys, containing 0.4475%-2.214%Al (mole fraction) was investigated over the temperature range of 1023-1273K and the depth of internal oxidation was measured by microscopy. Based on non-steady-state diffusion, a rate equation is derived to describe the kinetics of internal oxidation of plate: X=k-t-, where X is the oxidation depth, t is the oxidation time. For the internal oxidation of Cu-Al alloys employed in the synthesis of alumina dispersion strengthened copper, the permeability of oxygen in solid copper is obtained from the internal oxidation measurements. Investigation shows that the depth of the internal oxidation is a parabolic function of time, the typical shape of the front of internal oxidation is of planar morphology, and there is no evidence for preferential diffusion along grain boundaries.

Critical anomaly and finite size scaling of the self-diffusion coefficient for Lennard Jones fluids by non-equilibrium molecular dynamic simulation

We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.

Diffusion of Amino Acids in non-Newtonian Fluids

The amino acids are necessarily nutritious components, their diffusions in body fluid and blood that be- long to typical non-Newtonian fluid are of virtual importance to control the diffusive process and help clinical treatment. In this article, a holographic interferometer has been adopted to measure the diffusivity of amino acids in non-Newtonian fluid with the use of real-time holographic interference technique. In order to prove the reliability of the experimental instrument, the diffusivities of sucrose aqueous solution at 298.15K were determined. The meas- ured result displays a satisfactory accuracy of the apparatus used. Furthermore, the diffusion coefficients of glynine, L-serine, L-threonine and L-valine in polyacrylamide (PAM) aqueous solution at 298.15K were measured, respec- tively. The experimental data were fitted by a newly proposed correlation equation based on Li’s predictive model. The calculating results by the present model are at considerably good agreement with experimental values, and the maximum average deviation is only 0.5%.

Approximate Solution of Non-Linear Reaction Diffusion Equations in Homogeneous Processes Coupled to Electrode Reactions for CE Mechanism at a Spherical Electrode

A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is based on non-stationary diffusion equation containing a non-linear reaction term. This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction. In this paper the approximate analytical expressions of the non-steady-state concentrations and current at spherical electrodes for homogeneous reactions mechanisms are derived for all values of the reaction diffusion parameters. These approximate results are compared with the available analytical results and are found to be in good agreement.

Diffusion dynamics in external noise-activated non-equilibrium open system-reservoir coupling environment

The diffusion process in an external noise-activated non-equilibrium open system–reservoir coupling environment is studied by analytically solving the generalized Langevin equation. The dynamical property of the system near the barrier top is investigated in detail by numerically calculating the quantities such as mean diffusion path, invariance, barrier passing probability, and so on. It is found that, comparing with the unfavorable effect of internal fluctuations, the external noise activation is sometimes beneficial to the diffusion process. An optimal strength of external activation or correlation time of the internal fluctuation is expected for the diffusing particle to have a maximal probability to escape from the potential well.

GLOBAL BLOWUP AND BLOWUP RATE ESTIMATES OF SOLUTIONS FOR A CLASS OF NONLINEAR NON-LOCAL REACTION-DIFFUSION PROBLEMS

In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.

Non-classical diffusion model for heat and mass transfer in laser drying

A numerical analysis of the laser drying process by employing a generalized,Maxwell-Cattaneo equation to treat both heat and mass transfer was presented. Calculations wereperformed to illustrate the non-classical transport of heat and moisture. The effect of the heatflux density and the initial moisture content on water removal was also investigated. The resultsindicate that the non-equilibrium mass diffusion plays an important role during the very earlystages of moisture removal, especially at the surface of the medium. Away from the surface, thenon-Fickian model shows a delay in the reduction of the moisture content. The calculation resultsalso show that the initial moisture content of the medium has a considerable effect on waterremoval.

Non-echo-planar diffusion-weighted MRI in cholesteatoma: One typical case, one atypical case and one rare false positive finding

We present two cases of cholesteatoma and one false positive finding in non-EP DW MRI in order to highlight the differential diagnosis in imaging and emphasize the need to discuss the findings with the otologic surgeon. The first case demonstrates different MRI signal patterns encountered in a patient with cholesteatoma. The second report is a rare case of supralabyrinthine cholesteatoma with atypical clinical presentation. The third case presents a rare but important false positive finding in non-EP DW MRI. Clinical and imaging findings are discussed taking into account the current literature.

Comparison of Isobaric and Non-isobaric Operations on a Two-Phase Dynamic Model for PEFC Cathode Gas Diffusion Layer

Key words,： Two 1-D dynamical and isothermal models of cathode gas diffusion layer（GDL） with isobaric and non-isobaric operations for polymer electrolyte fuel cells（PEFCs） were developed and implemented in COMSOL Multiphysics v3.5.The artificial diffusion coefficient was introduced as well to make the numerical computation be stable.In the non-isobaric model,the pressure of gas mixture was obtained by summing up the governing equations of gaseous components,instead of Navier-Stoks equation.Comparison of the two models were carried out with the steady-states and dynamical simulations under given conditions.The corresponding analysis based on the simulated results was also given simultaneously.This paper is contributed to finding the differences between the isobaric and non-isobaric operation in the two-phase model of cathode GDL.

Travelling Wave Solution of the Fisher-Kolmogorov Equation with Non-Linear Diffusion

In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified Fisher equation and find the approximation of minimum wave speed analytically, by using the eigenvalues of the stationary states, and numerically by using COMSOL (a commercial finite element solver). The results reveal that the minimum wave speed depends on the parameter values involved in the model. We observe that when diffusion is moderately non-linear, the eigenvalue method correctly predicts the minimum wave speed in our numerical calculations, but when diffusion is strongly non-linear the eigenvalues method gives the wrong answer.

Analysis of non-linear reaction-diffusion processes with Michaelis-Menten kinetics by a new Homotopy perturbation method

This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.

Approximate analytical solution of non-linear reaction diffusion equation in fluidized bed biofilm reactor

A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to predict the biofilm density of a single bioparticle. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation.

Effect of Non-Uniform Basic Concentration Gradient on the Onset of Double-Diffusive Convection in Micropolar Fluid

The effect of non-uniform basic concentration gradient on the onset of double diffusive convection in a micropolar fluid layer heated and saluted from below and cooled from above has been studied. The linear stability analysis is performed. The eigen value of the problem is obtained using Galerkian method. The eigen values are obtained for 1) free-free 2) rigid-free 3) rigid-rigid velocity boundary combination with isothermal temperature condition on spin-vanishing permeable boundaries. The influence of various micropolar parameters on the onset of convection has been analyzed. One linear and five non linear concentration profiles are considered and their comparative influence on onset is discussed and results are depicted graphically. It is observed that fluid layer with suspended particles heated and soluted from below is more stable compare to the classical fluid without suspended particles.

Diffusion weighted imaging for the detection and evaluation of cholesteatoma

Cholesteatoma is a collection of keratinous debris and stratified squamous epithelium.It is trapped in the middle ear and can lead to bony erosion.The disease is treated surgically often followed by a second-look procedure to check for residual tissue or recurrence.Cholesteatoma has specific signal-intensity characteristics on magnetic resonance imaging with very high signal intensity on diffusion weighted imaging(DWI).Various DWI techniques exist:Echo-planar imaging(EPI)-based and non-EPI-based techniques as well as new approaches like multi-shot EPI DWI.This article summarizes all techniques,discusses the significance in detecting cholesteatoma and mentions actual studies.Further recommendations for daily clinical practise are provided.

非自治Reaction-Diffusion方程的后向紧吸引子的正则性

运用后向Gronwall型不等式及一个后向截断的方法,在g是后向绝对连续的假设条件下,证明非自治Reaction-Diffusion方程在正则p(p≥2)次可积空间上存在唯一的后向紧拉回吸引子,这种紧性体现了非自治系统关于时间依赖的独特性,展示了非自治系统和自治系统的本质区别.

MECHANISM FOR DIFFUSION OF BORON IN γ-Fe

Mechanism for diffusion of B in γ-Fe is believed to be mainly by means of boron-vacancy complexes other than as interstitial atoms previously.This was made of calculation on the ba- sis of theoretical model proposed by the authors.The calculated diffusion coefficient of B in γ-Fe after this mechanism is consistent with the experimental values.In addition,this is also supported by the non-equilibrium segregation phenomenon of B at grain boundaries of γ-Fe and the lattice constant measurement of Fe-B alloy.

Modeling of hydrogen diffusion process at a blunt notch in zirconium

The two-dimensional diffusion of interstitial hydrogen atoms in zirconium in a non-uniform stress field was simulated using the phase-field method. The interaction between hydrogen interstitials and the stress field was described by Khachaturyan＇s elastic theory. The Cahn-Hilliard diffusion equation was then solved by an explicit finite difference method. The result shows that hydrogen atoms diffuse to the high-tensile hydrostatic region near the tip of the notch. The content of hydrogen near the tip of the notch increases by 13%, while the stress distribution caused by hydrogen interstitials around the notch is modified by only 0.7%.

Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension

The persistence exponent for the simple diffusion equation , with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field at a specified spatial coordinate remains positive throughout for a certain time t behaves as for asymptotically large time t. The value of , calculated here for any integer dimension d, is for and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values for respectively.