Search results for "Diffusion equation"

Matrix solutions of diffusion equation

2002

The relaxation-time limit in the quantum hydrodynamic equations for semiconductors

2006

Abstract The relaxation-time limit from the quantum hydrodynamic model to the quantum drift–diffusion equations in R 3 is shown for solutions which are small perturbations of the steady state. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density including the quantum Bohm potential and a momentum relaxation term. The momentum equation is highly nonlinear and contains a dispersive term with third-order derivatives. The equations are self-consistently coupled to the Poisson equation for the electrostatic potential. The relaxation-time limit is performed both in the stationary and the transient model. The main assumptions are…

External noise effects on the electron velocity fluctuations in semiconductors

2008

We investigate the modification of the intrinsic carrier noise spectral density induced in low-doped semiconductor materials by an external correlated noise source added to the driving high-frequency periodic electric field. A Monte Carlo approach is adopted to numerically solve the transport equation by considering all the possible scattering phenomena of the hot electrons in the medium. We show that the noise spectra are strongly affected by the intensity and the correlation time of the external random electric field. Moreover this random field can cause a suppression of the total noise power.

Fractional-order theory of heat transport in rigid bodies

2014

Abstract The non-local model of heat transfer, used to describe the deviations of the temperature field from the well-known prediction of Fourier/Cattaneo models experienced in complex media, is framed in the context of fractional-order calculus. It has been assumed (Borino et al., 2011 [53] , Mongiovi and Zingales, 2013 [54] ) that thermal energy transport is due to two phenomena: ( i ) A short-range heat flux ruled by a local transport equation; ( ii ) A long-range thermal energy transfer proportional to a distance-decaying function, to the relative temperature and to the product of the interacting masses. The distance-decaying function is assumed in the functional class of the power-law …

On the dynamics of dislocation patterning

1997

Recent computer simulations on dislocation patterning have provided remarkable results in accordance with empirical laws. Moreover, several analytical models on dislocation dynamics have provided qualitative insight on dislocation patterning. However, a model, based on partial differential equations, which gives a dynamical evolution of dislocation patterns in function of measurable variables still missing. Here, we give a re-formulation of a model proposed some years ago. From this formulation, we obtained that the onset of a dislocation instability is related to the applied stress. The analytical and numerical results reported are partial and studies on this direction are under developmen…

A Langevin Approach to the Diffusion Equation

2002

We propose a generalized Langevin equation as a model for the diffusion equation of air pollution in the atmosphere. We write down a partial stochastic differential equation for the pollutant concentration, which we solve exactly obtaining the first and the second moment of the pollutant concentration. We obtain a linear multiplicative stochastic differential equation for the Fourier components of the concentration, which can be used to calculate higher moments of the concentration. We obtain the exact steady state solution in the case of neutral atmosphere and a general expression of the mean concentration as a function of the fluctuation intensity of the wind speed, the diffusion coeffici…

Axial dispersion model for solid flow in liquid suspension in system of two mixers in total recycle

2006

The measurement of residence time distribution of solid particles in solid-liquid suspension is experimentally difficult. However, the twin system approach is particularly suited for the assessment of particle RTD in flow systems as it allows overcoming some of the usual difficulties generally encountered in this kind of measurement. Twin system consists of two vessels and external piping in total recycle. Experimental results from this system can be evaluated using Z-transforms to derive particle RTD for subsequent testing of alternative flow models. Recently, the axial dispersion model was applied using the "advection diffusion equation" (sometimes called the"diffusion with bulk flow equa…

Validation of a Microscale Pollution Dispersal Model

1996

The three-dimensional numerical model MISCAM (Micro Scale Air Pollution Model) has been developed to study wind flow and pollutant dispersal in densely built-up urban areas (Eichhorn, 1989). The model has been successfully applied for planning purposes by a variety of institutions in Germany. MISCAM consists of the non-hydrostatic Eulerian equations of motion and a transport equation for pollutants. Turbulence closure is carried out by means of a k-e-model. To reduce numerical diffusion errors, Smolarkiewicz and Grabowski’s (1989) scheme may be used for the calculation of advective transport. Additionally, sedimentation and dry deposition of pollutants may be taken into account.

FINITE ELEMENT RESOLUTION OF CONVECTION-DIFFUSION EQUATIONS WITH INTERIOR AND BOUNDARY LAYERS

1996

We present a new algorithm for the resolution of both interior and boundary layers present in the convection-diffusion equation in laminar regimes, based on the formulation of a family of polynomial-exponential elements. We have carried out an adaptation of the standard variational methods (finite element method and spectral element method), obtaining an algorithm which supplies non-oscillatory and accurate solutions. The algorithm consists of generating a coupled grid of polynomial standard elements and polynomial-exponential elements. The latter are able to represent the high gradients of the solution, while the standard elements represent the solution in the areas of smooth variation.

Noise Filtering Using Edge-Driven Adaptive Anisotropic Diffusion

2008

This paper presents a method aimed to noise removal in MRI (Magnetic Resonance Imaging). We propose an improvement of Perona and Malik's anisotropic diffusion filter. In our schema, the diffusion equation of the filter has been modified to take into account the edges direction, This allows the filter to blur uniform areas, while it better preserves the edges. Both quantitative and qualitative evaluation is presented and the results are compared with other methods.