90,596 research outputs found
Pedestrian flows in bounded domains with obstacles
In this paper we systematically apply the mathematical structures by
time-evolving measures developed in a previous work to the macroscopic modeling
of pedestrian flows. We propose a discrete-time Eulerian model, in which the
space occupancy by pedestrians is described via a sequence of Radon positive
measures generated by a push-forward recursive relation. We assume that two
fundamental aspects of pedestrian behavior rule the dynamics of the system: On
the one hand, the will to reach specific targets, which determines the main
direction of motion of the walkers; on the other hand, the tendency to avoid
crowding, which introduces interactions among the individuals. The resulting
model is able to reproduce several experimental evidences of pedestrian flows
pointed out in the specialized literature, being at the same time much easier
to handle, from both the analytical and the numerical point of view, than other
models relying on nonlinear hyperbolic conservation laws. This makes it
suitable to address two-dimensional applications of practical interest, chiefly
the motion of pedestrians in complex domains scattered with obstacles.Comment: 25 pages, 9 figure
Time-evolving measures and macroscopic modeling of pedestrian flow
This paper deals with the early results of a new model of pedestrian flow,
conceived within a measure-theoretical framework. The modeling approach
consists in a discrete-time Eulerian macroscopic representation of the system
via a family of measures which, pushed forward by some motion mappings, provide
an estimate of the space occupancy by pedestrians at successive time steps.
From the modeling point of view, this setting is particularly suitable to
treat nonlocal interactions among pedestrians, obstacles, and wall boundary
conditions. In addition, analysis and numerical approximation of the resulting
mathematical structures, which is the main target of this work, follow more
easily and straightforwardly than in case of standard hyperbolic conservation
laws, also used in the specialized literature by some Authors to address
analogous problems.Comment: 27 pages, 6 figures -- Accepted for publication in Arch. Ration.
Mech. Anal., 201
Global existence for semilinear reaction-diffusion systems on evolving domains
We present global existence results for solutions of reaction-diffusion
systems on evolving domains. Global existence results for a class of
reaction-diffusion systems on fixed domains are extended to the same systems
posed on spatially linear isotropically evolving domains. The results hold
without any assumptions on the sign of the growth rate. The analysis is valid
for many systems that commonly arise in the theory of pattern formation. We
present numerical results illustrating our theoretical findings.Comment: 24 pages, 3 figure
An adaptive multi-level model for multi-scale ductile fracture analysis in heterogeneous aluminum alloys
This paper addresses the multi-scale modeling of ductile fracture in microstructures characterized by a dispersion of hard and brittle heterogeneities in a softer ductile matrix. An adaptive multi-level model is developed with different inter-scale transfer operators and interfaces. Micro-mechanical analysis in regions of dominant damage is performed to capture the important micro-mechanical damage modes that are responsible for deterring the overall failure properties of these alloys. Regions of macroscopic homogeneity are otherwise modeled with constitutive relations derived from homogenization of evolving variables in representative volume elements. These two length scales of analysis, in conjunction with an intermediate swing level, form a three-level coupled multi-scale model to capture ductile crack propagation. The capabilities of the proposed model are demonstrated for a cast aluminum alloy
Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces
The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface
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