968 research outputs found
Two semi-Lagrangian fast methods for Hamilton-Jacobi-Bellman equations
In this paper we apply the Fast Iterative Method (FIM) for solving general
Hamilton-Jacobi-Bellman (HJB) equations and we compare the results with an
accelerated version of the Fast Sweeping Method (FSM). We find that FIM can be
indeed used to solve HJB equations with no relevant modifications with respect
to the original algorithm proposed for the eikonal equation, and that it
overcomes FSM in many cases. Observing the evolution of the active list of
nodes for FIM, we recover another numerical validation of the arguments
recently discussed in [Cacace et al., SISC 36 (2014), A570-A587] about the
impossibility of creating local single-pass methods for HJB equations
Free boundary problems describing two-dimensional pulse recycling and motion in semiconductors
An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk
n-GaAs with circular contacts is presented. A moving pulse far from contacts is
approximated by a moving free boundary separating regions where the electric
potential solves a Laplace equation with subsidiary boundary conditions. The
dynamical condition for the motion of the free boundary is a Hamilton-Jacobi
equation. We obtain the exact solution of the free boundary problem (FBP) in
simple one-dimensional and axisymmetric geometries. The solution of the FBP is
obtained numerically in the general case and compared with the numerical
solution of the full system of equations. The agreement is excellent so that
the FBP can be adopted as the basis for an asymptotic study of the
multi-dimensional Gunn effect.Comment: 19 pages, 9 figures, Revtex. To appear in Phys. Rev.
Coupling nonpolar and polar solvation free energies in implicit solvent models
Recent studies on the solvation of atomistic and nanoscale solutes indicate
that a strong coupling exists between the hydrophobic, dispersion, and
electrostatic contributions to the solvation free energy, a facet not
considered in current implicit solvent models. We suggest a theoretical
formalism which accounts for coupling by minimizing the Gibbs free energy of
the solvent with respect to a solvent volume exclusion function. The resulting
differential equation is similar to the Laplace-Young equation for the
geometrical description of capillary interfaces, but is extended to microscopic
scales by explicitly considering curvature corrections as well as dispersion
and electrostatic contributions. Unlike existing implicit solvent approaches,
the solvent accessible surface is an output of our model. The presented
formalism is illustrated on spherically or cylindrically symmetrical systems of
neutral or charged solutes on different length scales. The results are in
agreement with computer simulations and, most importantly, demonstrate that our
method captures the strong sensitivity of solvent expulsion and dewetting to
the particular form of the solvent-solute interactions.Comment: accpted in J. Chem. Phy
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
Application of the level-set method to the implicit solvation of nonpolar molecules
A level-set method is developed for numerically capturing the equilibrium
solute-solvent interface that is defined by the recently proposed variational
implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf
104}, 527 (2006) and J. Chem.\Phys. {\bf 124}, 084905 (2006)). In the level-set
method, a possible solute-solvent interface is represented by the zero
level-set (i.e., the zero level surface) of a level-set function and is
eventually evolved into the equilibrium solute-solvent interface. The evolution
law is determined by minimization of a solvation free energy {\it functional}
that couples both the interfacial energy and the van der Waals type
solute-solvent interaction energy. The surface evolution is thus an energy
minimizing process, and the equilibrium solute-solvent interface is an output
of this process. The method is implemented and applied to the solvation of
nonpolar molecules such as two xenon atoms, two parallel paraffin plates,
helical alkane chains, and a single fullerene . The level-set solutions
show good agreement for the solvation energies when compared to available
molecular dynamics simulations. In particular, the method captures solvent
dewetting (nanobubble formation) and quantitatively describes the interaction
in the strongly hydrophobic plate system
Solving the Direction Field for Discrete Agent Motion
Models for pedestrian dynamics are often based on microscopic approaches
allowing for individual agent navigation. To reach a given destination, the
agent has to consider environmental obstacles. We propose a direction field
calculated on a regular grid with a Moore neighborhood, where obstacles are
represented by occupied cells. Our developed algorithm exactly reproduces the
shortest path with regard to the Euclidean metric.Comment: 8 pages, 4 figure
Quickest Paths in Simulations of Pedestrians
This contribution proposes a method to make agents in a microscopic
simulation of pedestrian traffic walk approximately along a path of estimated
minimal remaining travel time to their destination. Usually models of
pedestrian dynamics are (implicitly) built on the assumption that pedestrians
walk along the shortest path. Model elements formulated to make pedestrians
locally avoid collisions and intrusion into personal space do not produce
motion on quickest paths. Therefore a special model element is needed, if one
wants to model and simulate pedestrians for whom travel time matters most (e.g.
travelers in a station hall who are late for a train). Here such a model
element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte
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