6,219 research outputs found
Multiscale analysis of a spatially heterogeneous microscopic traffic model
The microscopic Optimal Velocity (OV) model is posed on an inhomogeneous ring-road, consisting of two spatial regimes which differ by a scaled OV function. Parameters are chosen throughout for which all uniform flows are linearly stable. The large time behaviour of this discrete system is stationary and exhibits three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp interfaces. At a coarse level, these patterns are determined by simple flow and density balances, which in some cases have non-unique solutions. The theory of characteristics for the classical Lighthill–Whitham PDE model is then applied to explain which pattern the OV model selects. A global analysis of a second-order PDE model is then performed in an attempt to explain some qualitative details of interface structure. Finally, the full microscopic model is analysed at the linear level to explain features which cannot be described by the present macroscopic approache
Monte Carlo Protein Folding: Simulations of Met-Enkephalin with Solvent-Accessible Area Parameterizations
Treating realistically the ambient water is one of the main difficulties in
applying Monte Carlo methods to protein folding. The solvent-accessible area
method, a popular method for treating water implicitly, is investigated by
means of Metropolis simulations of the brain peptide Met-Enkephalin. For the
phenomenological energy function ECEPP/2 nine atomic solvation parameter (ASP)
sets are studied that had been proposed by previous authors. The simulations
are compared with each other, with simulations with a distance dependent
electrostatic permittivity , and with vacuum simulations
(). Parallel tempering and a recently proposed biased Metropolis
technique are employed and their performances are evaluated. The measured
observables include energy and dihedral probability densities (pds), integrated
autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be
unsuitable for these simulations. For all other sets, selected configurations
are minimized in search of the global energy minima. Unique minima are found
for the vacuum and the system, but for none of the ASP models.
Other observables show a remarkable dependence on the ASPs. In particular,
autocorrelation times vary dramatically with the ASP parameters. Three ASP sets
have much smaller autocorrelations at 300 K than the vacuum simulations,
opening the possibility that simulations can be speeded up vastly by
judiciously chosing details of the forceComment: 10 pages; published in "NIC Symposium 2004", eds. D. Wolf at el.
(NIC, Juelich, 2004
Heat trace asymptotics with singular weight functions II
We study the weighted heat trace asymptotics of an operator of Laplace type
with mixed boundary conditions where the weight function exhibits radial
blowup. We give formulas for the first three boundary terms in the expansion in
terms of geometrical data
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