363 research outputs found
Mitotic entry and exit: the rise and fall of cyclin-Cdk-Cks activity
Riele, H.P.J. te [Promotor]Wolthuis, R.M.F. [Copromotor
Effective pair potentials for spherical nanoparticles
An effective description for spherical nanoparticles in a fluid of point
particles is presented. The points inside the nanoparticles and the point
particles are assumed to interact via spherically symmetric additive pair
potentials, while the distribution of points inside the nanoparticles is taken
to be spherically symmetric and smooth. The resulting effective pair
interactions between a nanoparticle and a point particle, as well as between
two nanoparticles, are then given by spherically symmetric potentials. If
overlap between particles is allowed, the effective potential generally has
non-analytic points, but for each effective potential the expressions for
different overlapping cases can be written in terms of one analytic auxiliary
potential. Effective potentials for hollow nanoparticles (appropriate e.g. for
buckyballs) are also considered, and shown to be related to those for solid
nanoparticles. Finally, explicit expressions are given for the effective
potentials derived from basic pair potentials of power law and exponential
form, as well as from the commonly used London-Van der Waals, Morse,
Buckingham, and Lennard-Jones potential. The applicability of the latter is
demonstrated by comparison with an atomic description of nanoparticles with an
internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and
nonoverlapping particles added, as well as a comparison with an idealized
atomic descriptio
Constructing smooth potentials of mean force, radial, distribution functions and probability densities from sampled data
In this paper a method of obtaining smooth analytical estimates of
probability densities, radial distribution functions and potentials of mean
force from sampled data in a statistically controlled fashion is presented. The
approach is general and can be applied to any density of a single random
variable. The method outlined here avoids the use of histograms, which require
the specification of a physical parameter (bin size) and tend to give noisy
results. The technique is an extension of the Berg-Harris method [B.A. Berg and
R.C. Harris, Comp. Phys. Comm. 179, 443 (2008)], which is typically inaccurate
for radial distribution functions and potentials of mean force due to a
non-uniform Jacobian factor. In addition, the standard method often requires a
large number of Fourier modes to represent radial distribution functions, which
tends to lead to oscillatory fits. It is shown that the issues of poor sampling
due to a Jacobian factor can be resolved using a biased resampling scheme,
while the requirement of a large number of Fourier modes is mitigated through
an automated piecewise construction approach. The method is demonstrated by
analyzing the radial distribution functions in an energy-discretized water
model. In addition, the fitting procedure is illustrated on three more
applications for which the original Berg-Harris method is not suitable, namely,
a random variable with a discontinuous probability density, a density with long
tails, and the distribution of the first arrival times of a diffusing particle
to a sphere, which has both long tails and short-time structure. In all cases,
the resampled, piecewise analytical fit outperforms the histogram and the
original Berg-Harris method.Comment: 14 pages, 15 figures. To appear in J. Chem. Phy
An Extension of the Fluctuation Theorem
Heat fluctuations are studied in a dissipative system with both mechanical
and stochastic components for a simple model: a Brownian particle dragged
through water by a moving potential. An extended stationary state fluctuation
theorem is derived. For infinite time, this reduces to the conventional
fluctuation theorem only for small fluctuations; for large fluctuations, it
gives a much larger ratio of the probabilities of the particle to absorb rather
than supply heat. This persists for finite times and should be observable in
experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and
white
Mode-coupling theory for structural and conformational dynamics of polymer melts
A mode-coupling theory for dense polymeric systems is developed which
unifyingly incorporates the segmental cage effect relevant for structural
slowing down and polymer chain conformational degrees of freedom. An ideal
glass transition of polymer melts is predicted which becomes molecular-weight
independent for large molecules. The theory provides a microscopic
justification for the use of the Rouse theory in polymer melts, and the results
for Rouse-mode correlators and mean-squared displacements are in good agreement
with computer simulation results.Comment: 4 pages, 3 figures, Phys. Rev. Lett. in pres
Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces
Heat fluctuations over a time \tau in a non-equilibrium stationary state and
in a transient state are studied for a simple system with deterministic and
stochastic components: a Brownian particle dragged through a fluid by a
harmonic potential which is moved with constant velocity. Using a Langevin
equation, we find the exact Fourier transform of the distribution of these
fluctuations for all \tau. By a saddle-point method we obtain analytical
results for the inverse Fourier transform, which, for not too small \tau, agree
very well with numerical results from a sampling method as well as from the
fast Fourier transform algorithm. Due to the interaction of the deterministic
part of the motion of the particle in the mechanical potential with the
stochastic part of the motion caused by the fluid, the conventional heat
fluctuation theorem is, for infinite and for finite \tau, replaced by an
extended fluctuation theorem that differs noticeably and measurably from it. In
particular, for large fluctuations, the ratio of the probability for absorption
of heat (by the particle from the fluid) to the probability to supply heat (by
the particle to the fluid) is much larger here than in the conventional
fluctuation theorem.Comment: 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected
and a footnote was added on the d-dimensional cas
Fronts with a Growth Cutoff but Speed Higher than
Fronts, propagating into an unstable state , whose asymptotic speed
is equal to the linear spreading speed of infinitesimal
perturbations about that state (so-called pulled fronts) are very sensitive to
changes in the growth rate for . It was recently found
that with a small cutoff, for ,
converges to very slowly from below, as . Here we show
that with such a cutoff {\em and} a small enhancement of the growth rate for
small behind it, one can have , {\em even} in the
limit . The effect is confirmed in a stochastic lattice model
simulation where the growth rules for a few particles per site are accordingly
modified.Comment: 4 pages, 4 figures, to appear in Rapid Comm., Phys. Rev.
Velocity distributions in dissipative granular gases
Motivated by recent experiments reporting non-Gaussian velocity distributions
in driven dilute granular materials, we study by numerical simulation the
properties of 2D inelastic gases. We find theoretically that the form of the
observed velocity distribution is governed primarily by the coefficient of
restitution and , the ratio between the average number of
heatings and the average number of collisions in the gas. The differences in
distributions we find between uniform and boundary heating can then be
understood as different limits of , for and
respectively.Comment: 5 figure
The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff
The concept of pulled fronts with a cutoff has been introduced to
model the effects of discrete nature of the constituent particles on the
asymptotic front speed in models with continuum variables (Pulled fronts are
the fronts which propagate into an unstable state, and have an asymptotic front
speed equal to the linear spreading speed of small linear perturbations
around the unstable state). In this paper, we demonstrate that the introduction
of a cutoff actually makes such pulled fronts weakly pushed. For the nonlinear
diffusion equation with a cutoff, we show that the longest relaxation times
that govern the convergence to the asymptotic front speed and profile,
are given by , for
.Comment: 4 pages, 2 figures, submitted to Brief Reports, Phys. Rev.
Event-Driven Dynamics of Rigid Bodies Interacting via Discretized Potentials
A framework for performing event-driven, adaptive time step simulations of
systems of rigid bodies interacting under stepped or terraced potentials in
which the potential energy is only allowed to have discrete values is outlined.
The scheme is based on a discretization of an underlying continuous potential
that effectively determines the times at which interaction energies change. As
in most event-driven approaches, the method consists of specifying a means of
computing the free motion, evaluating the times at which interactions occur,
and determining the consequences of interactions on subsequent motion for the
terraced-potential. The latter two aspects are shown to be simply expressible
in terms of the underlying smooth potential. Within this context, algorithms
for computing the times of interaction events and carrying out efficient
event-driven simulations are discussed. The method is illustrated on system
composed of rigid rods in which the constituents interact via a terraced
potential that depends on the relative orientations of the rods.Comment: 9 pages, 5 figure
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