250 research outputs found
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Numerical simulation of the Langevin equation for skewed turbulence
In this paper the authors present a numerical method for the generalized Langevin equation of motion with skewed random forcing for the case of homogeneous, skewed turbulence. The authors begin by showing how the analytic solution to the Langevin equation for this case can be used to determine the relationship between the particle velocity moments and the properties of the skewed random force. They then present a numerical method that uses simple probability distribution functions to simulate the effect of the random force. The numerical solution is shown to be exact in the limit of infinitesimal time steps, and to be within acceptable error limits when practical time steps are used
Viscosity Dependence of the Folding Rates of Proteins
The viscosity dependence of the folding rates for four sequences (the native
state of three sequences is a beta-sheet, while the fourth forms an
alpha-helix) is calculated for off-lattice models of proteins. Assuming that
the dynamics is given by the Langevin equation we show that the folding rates
increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and
have a maximum at intermediate values. The Kramers theory of barrier crossing
provides a quantitative fit of the numerical results. By mapping the simulation
results to real proteins we estimate that for optimized sequences the time
scale for forming a four turn \alpha-helix topology is about 500 nanoseconds,
whereas the time scale for forming a beta-sheet topology is about 10
microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at
http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical
Review Letter
State-dependent diffusion: thermodynamic consistency and its path integral formulation
The friction coefficient of a particle can depend on its position as it does
when the particle is near a wall. We formulate the dynamics of particles with
such state-dependent friction coefficients in terms of a general Langevin
equation with multiplicative noise, whose evaluation requires the introduction
of specific rules. Two common conventions, the Ito and the Stratonovich,
provide alternative rules for evaluation of the noise, but other conventions
are possible. We show the requirement that a particle's distribution function
approach the Boltzmann distribution at long times dictates that a drift term
must be added to the Langevin equation. This drift term is proportional to the
derivative of the diffusion coefficient times a factor that depends on the
convention used to define the multiplicative noise. We explore the consequences
of this result in a number examples with spatially varying diffusion
coefficients. We also derive path integral representations for arbitrary
interpretation of the noise, and use it in a perturbative study of correlations
in a simple system.Comment: 18 pages, 8 figures, Accepted to PR
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Preliminary environmental assessments of known geothermal resource areas in the United States
The basic purpose of the Geothermal Overview Project is to identify, summarize, and assess the environmental issues of the top priority KGRAs from among the approximately 40 KGRAs currently identified by the Division of Geothermal Energy, DOE, as having high possibilities for commercial development. The Geothermal Overview Project addresses issues pertaining to air quality, ecosystems quality, noise effects, geological effects, water quality, socioeconomic effects, and health effects. For each KGRA the following functions are accomplished: identification of key issues; inventory of all available data; analysis and assessment of available data; and, identification of what additional information is required for adequate assessments. Studies at the Geysers-Calistoga KGRA in Northern California are used as an example
Hydrodynamic Coupling of Two Brownian Spheres to a Planar Surface
We describe direct imaging measurements of the collective and relative
diffusion of two colloidal spheres near a flat plate. The bounding surface
modifies the spheres' dynamics, even at separations of tens of radii. This
behavior is captured by a stokeslet analysis of fluid flow driven by the
spheres' and wall's no-slip boundary conditions. In particular, this analysis
reveals surprising asymmetry in the normal modes for pair diffusion near a flat
surface.Comment: 4 pages, 4 figure
Like-charge attraction through hydrodynamic interaction
We demonstrate that the attractive interaction measured between like-charged
colloidal spheres near a wall can be accounted for by a nonequilibrium
hydrodynamic effect. We present both analytical results and Brownian dynamics
simulations which quantitatively capture the one-wall experiments of Larsen and
Grier (Nature 385, p. 230, 1997).Comment: 10 pages, 4 figure
A unified approach for the solution of the Fokker-Planck equation
This paper explores the use of a discrete singular convolution algorithm as a
unified approach for numerical integration of the Fokker-Planck equation. The
unified features of the discrete singular convolution algorithm are discussed.
It is demonstrated that different implementations of the present algorithm,
such as global, local, Galerkin, collocation, and finite difference, can be
deduced from a single starting point. Three benchmark stochastic systems, the
repulsive Wong process, the Black-Scholes equation and a genuine nonlinear
model, are employed to illustrate the robustness and to test accuracy of the
present approach for the solution of the Fokker-Planck equation via a
time-dependent method. An additional example, the incompressible Euler
equation, is used to further validate the present approach for more difficult
problems. Numerical results indicate that the present unified approach is
robust and accurate for solving the Fokker-Planck equation.Comment: 19 page
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Final report for LDRD Project 94-ERD-037: multi-scale atmospheric simulation system
The purpose of this LDRD project was to develop a multi-scale atmospheric simulation system that could be applied to a diverse range of atmospheric problems, including key research issues related to global and regional climate change, studies of regional and local precipitation, and emergency predictions of the path and exposure concentration of toxic materials released into the atmosphere. In addition to its multi-scale nature, the new simulation system was to be designed such that the individual components of the system could be selected by users in an optimal way to support the research and operational needs of the entire Atmospheric Sciences Division
Influence of Hydrodynamic Interactions on Mechanical Unfolding of Proteins
We incorporate hydrodynamic interactions in a structure-based model of
ubiquitin and demonstrate that the hydrodynamic coupling may reduce the peak
force when stretching the protein at constant speed, especially at larger
speeds. Hydrodynamic interactions are also shown to facilitate unfolding at
constant force and inhibit stretching by fluid flows.Comment: to be published in Journal of Physics: Condensed Matte
Chaperone-assisted translocation of a polymer through a nanopore
Using Langevin dynamics simulations, we investigate the dynamics of
chaperone-assisted translocation of a flexible polymer through a nanopore. We
find that increasing the binding energy between the chaperone and
the chain and the chaperone concentration can greatly improve the
translocation probability. Particularly, with increasing the chaperone
concentration a maximum translocation probability is observed for weak binding.
For a fixed chaperone concentration, the histogram of translocation time
has a transition from long-tailed distribution to Gaussian distribution with
increasing . rapidly decreases and then almost saturates with
increasing binding energy for short chain, however, it has a minimum for longer
chains at lower chaperone concentration. We also show that has a minimum
as a function of the chaperone concentration. For different , a
nonuniversal dependence of on the chain length is also observed.
These results can be interpreted by characteristic entropic effects for
flexible polymers induced by either crowding effect from high chaperone
concentration or the intersegmental binding for the high binding energy.Comment: 10 pages, to appear in J. Am. Chem. So
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