Search results for "Diffusion"
showing 10 items of 1615 documents
Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment
2015
International audience; The micro-convection caused by the ponderomotive forces of the self-magnetic field in a magnetic fluid is studied here both numerically and experimentally. The theoretical approach based on the general Brinkman model substantially improves the description with respect to the previously proposed Darcy model. The predictions of both models are here compared to finely controlled experiments. The Brinkman model, in contrast to the Darcy model, allows us to describe the formation of mushrooms on the plumes of the micro-convective flow and the width of the fingers. In the Brinkman approach, excellent quantitative agreement is also obtained for the finger velocity dynamics …
Two-Dimensional Modeling of a Flat-Plate Photocatalytic Reactor for Oxidation of Indoor Air Pollutants
2007
In this paper we present a two-dimensional (2-D) analysis of a narrow-slit, flat-plate, single-pass, flow-through photocatalytic reactor for air purification. The continuity equation for convection and diffusion in two dimensions, under un-steady-state conditions, was coupled with radiation field modeling and photocatalytic reaction kinetics to model the transient and steady-state behavior of the reactor. The model was applied to the photocatalytic oxidation of trichloroethylene (TCE) in humidified air streams under different experimental conditions. The kinetic parameters determined by a three-dimensional (3-D) computational fluid dynamics model of the reactor were used in the 2-D model si…
Breakdown of Burton-Prime-Slichter approach and lateral solute segregation in radially converging flows
2005
A theoretical study is presented of the effect of a radially converging melt flow, which is directed away from the solidification front, on the radial solute segregation in simple solidification models. We show that the classical Burton-Prim-Slichter (BPS) solution describing the effect of a diverging flow on the solute incorporation into the solidifying material breaks down for the flows converging along the solidification front. The breakdown is caused by a divergence of the integral defining the effective boundary layer thickness which is the basic concept of the BPS theory. Although such a divergence can formally be avoided by restricting the axial extension of the melt to a layer of fi…
From classical to operatorial models
2023
Mathematical models for the collective dynamics of interacting and spatially distributed populations find applications in several contexts (biology, ecology, social sciences). Their formulation depends primarily on the (continuous or discrete) description of the space. Reaction-diffusion equations have been widely used in bioecology (morphogenesis, migration of biological species, tumor growth, neuro-degenerative diseases) and in the social sciences (diffusion of opinions or decisionmaking processes), and exhibit complex behaviors (propagation of oscillatory phenomena, pattern formation caused by instability). A reaction–diffusion system exhibits diffusion-driven instability, sometimes call…
Plasmon de surface de particules métalliques toroïdales
2006
This thesis deals with the optical properties of small metal torii. A method of resolution of the equation of Laplace in toroidal coordinates is introduced and the radiative properties of the metal toric nanoparticules are studied within the electrostatic framework. The study on the eigenmodes spatial distribution suggests that metal nanotorus can carry a non-zero magnetic dipole moment at optical frequencies. Analytical expressions for the extinction and scattering cross sections of the torus are also found and compared with numerical simulations and experimental results obtained with collaborations. The sensitivity of the plasmon frequency to the refraction index of the external medium an…
Scaling behaviour of non-hyperbolic coupled map lattices
2006
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of a given expectation value.…
Monte Carlo study of surface critical behavior in the XY model.
1989
We have used Monte Carlo simulations to study the behavior of $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D$ slabs containing classical spins which interact via nearest-neighbor $\mathrm{XY}$ coupling. The coupling constant ${J}_{S}$ for spins in the surface layer is fixed at $0.5J$. Finite-size scaling is used to analyze data for $D=59$ and to extract estimates for the surface critical exponents. We find that ${\ensuremath{\beta}}_{1}$ is in good agreement with theoretical predictions.
Coupling of lattice-Boltzmann solvers with suspended particles using the MPI intercommunication framework
2017
Abstract The MPI intercommunication framework was used for coupling of two lattice-Boltzmann solvers with suspended particles, which model advection and diffusion respectively of these particles in a carrier fluid. Simulation domain was divided into two parts, one with advection and diffusion, and the other with diffusion only (no macroscopic flow). Particles were exchanged between these domains at their common boundary by a direct process to process communication. By analysing weak and strong scaling, it was shown that the linear scaling characteristics of the lattice-Boltzmann solvers were not compromised by their coupling.
Automatic Extraction of Blood Vessels, Bifurcations and End Points in the Retinal Vascular Tree
2008
In this paper we present an effective algorithm for automated extraction of the vascular tree in retinal images, including bifurcations, crossovers and end-points detection. Correct identification of these features in the ocular fundus helps the diagnosis of important systematic diseases, such as diabetes and hypertension. The pre-processing consists in artefacts removal based on anisotropic diffusion filter. Then a matched filter is applied to enhance blood vessels. The filter uses a full adaptive kernel because each vessel has a proper orientation and thickness. The kernel of the filter needs to be rotated for all possible directions. As a consequence, a suitable kernel has been designed …
Cross-diffusion effects on stationary pattern formation in the FitzHugh-Nagumo model
2022
<p style='text-indent:20px;'>We investigate the formation of stationary patterns in the FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on the effects of cross-diffusion on the Turing mechanism. Linear stability analysis indicates that positive values of the inhibitor cross-diffusion enlarge the region in the parameter space where a Turing instability is excited. A sufficiently large cross-diffusion coefficient of the inhibitor removes the requirement imposed by the classical Turing mechanism that the inhibitor must diffuse faster than the activator. In an extended region of the parameter space a new phenomenon occurs, namely the exis…