Search results for " diffusion"
showing 10 items of 521 documents
Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence
2021
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full se…
A dynamic subgrid-scale tensorial eddy viscosity model
1999
In the Navier-Stokes equations the removal of the turbulent fluctuating velocities with a frequency above a certain fixed threshold, employed in the Large Eddy Simulation (LES), causes the appearance of a turbulent stress tensor that requires a number of closure assumptions. In this paper insufficiencies are demonstrated for those closure models which are based on a scalar eddy viscosity coefficient. A new model, based on a tensorial eddy viscosity, is therefore proposed; it employs the Germano identity [1] and allows dynamical evaluation of the single required input coefficient. The tensorial expression for the eddy viscosity is deduced by removing the widely used scalar assumption of the …
Critical Phenomena and Diffusion in Complex Systems
2008
Un museo de ciencia accesible a la sociedad. Contribución e impacto
2022
El conocimiento es objeto de investigación y discusión; la ciudadanía lo utiliza de manera crítica transformándolo en herramientas que les permiten mejorar su vida a nivel individual y colectivo. Las diferencias sociales y jerárquicas que históricamente determinaban el acceso al capital formativo se han difuminado en el último siglo, y cada vez más se consume una gran variedad de formas de cultura, independientemente del nivel social, económico o cultural. Entre los centros culturales más visitados por los y las ciudadanas encontramos los museos. Estos núcleos de conocimiento trabajan para que su finalidad comunicativa esté en sintonía con los contenidos que ofrecen y tratan de dar respuest…
Atmospheric dry deposition processes of particles on urban and suburban surfaces: Modelling and validation works
2019
Abstract Dry deposition process is one of the important pathways for the removal of particles from atmosphere. It is the result of a combination of different environmental and physical factors as atmospheric conditions, particle properties, characteristics of the canopy. For this latter factor, urban canopy represents unevenly combinations of different types of surface elements that increases the complexity of deposition process phenomena. Therefore, particle dry deposition on urban surfaces is not easy to configure and, although empirical or semi-empirical models in literature have been developed to address this aspect, there is not standardized and commonly accepted criteria, especially f…
Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion
2012
In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through a weakly nonlinear analysis, we are able to predict the shape and the amplitude of the pattern. For the amplitude, in the supercritical and in the subcritical case, we derive the cubic and the quintic Stuart–Landau equation respectively. When the size of the spatial domain is large, and the initial perturbation is localized, the pattern is formed sequentially and invades the whole domain as a travelin…
Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion
2013
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…
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…
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.
Comparison of 2D versus 3D diffusion analysis at Nanowire Electrodes: Finite element analysis and experimental study
2021
In electroanalysis, finite element simulations of electrochemical processes occurring at electrodes are used to provide key insight into experimental design in relation to diffusion profiles and expected currents. The diffusion domain approach (DDA) offers a means of reducing a three dimensional design to two dimensions to ease computational demands. However, the DDA approach can be limited when basic assumptions, for example that all electrodes in an array are equivalent, are incorrect. Consequently, to get a more realistic view of molecular diffusion to nanoelectrodes, it is necessary to undertake simulations in 3D. In this work, two and three dimensional models of electrodes comprising o…