176,442 research outputs found
Noncolliding system of continuous-time random walks
The continuous-time random walk is defined as a Poissonization of
discrete-time random walk. We study the noncolliding system of continuous-time
simple and symmetric random walks on . We show that the system is
determinantal for any finite initial configuration without multiple point. The
spatio-temporal correlation kernel is expressed by using the modified Bessel
functions. We extend the system to the noncolliding process with an infinite
number of particles, when the initial configuration has equidistant spacing of
particles, and show a relaxation phenomenon to the equilibrium determinantal
point process with the sine kernel.Comment: AMS-LaTeX, 19 pages, no figure. arXiv admin note: text overlap with
arXiv:1307.1856 by other authors. v2: AMS-LaTeX 19 pages, minor corrections
made for publication in Pacific Journal of Mathematics for Industr
A nonlinear discrete-velocity relaxation model for traffic flow
We derive a nonlinear 2-equation discrete-velocity model for traffic flow
from a continuous kinetic model. The model converges to scalar
Lighthill-Whitham type equations in the relaxation limit for all ranges of
traffic data. Moreover, the model has an invariant domain appropriate for
traffic flow modeling. It shows some similarities with the Aw-Rascle traffic
model. However, the new model is simpler and yields, in case of a concave
fundamental diagram, an example for a totally linear degenerate hyperbolic
relaxation model. We discuss the details of the hyperbolic main part and
consider boundary conditions for the limit equations derived from the
relaxation model. Moreover, we investigate the cluster dynamics of the model
for vanishing braking distance and consider a relaxation scheme build on the
kinetic discrete velocity model. Finally, numerical results for various
situations are presented, illustrating the analytical results
Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case
The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary differential equations obtained by spatial finite-element discretisation of linear parabolic initial-boundary value problems. The results are compared to the corresponding continuous-time results. The theory is illustrated for a one-dimensional and a two-dimensional model problem and checked against results obtained by numerical experiments
Combinatorial Penalties: Which structures are preserved by convex relaxations?
We consider the homogeneous and the non-homogeneous convex relaxations for
combinatorial penalty functions defined on support sets. Our study identifies
key differences in the tightness of the resulting relaxations through the
notion of the lower combinatorial envelope of a set-function along with new
necessary conditions for support identification. We then propose a general
adaptive estimator for convex monotone regularizers, and derive new sufficient
conditions for support recovery in the asymptotic setting
Crossover Time in Relative Fluctuations Characterizes the Longest Relaxation Time of Entangled Polymers
In entangled polymer systems, there are several characteristic time scales,
such as the entanglement time and the disengagement time. In molecular
simulations, the longest relaxation time (the disengagement time) can be
determined by the mean square displacement (MSD) of a segment or by the shear
relaxation modulus. Here, we propose the relative fluctuation analysis method,
which is originally developed for characterizing large fluctuations, to
determine the longest relaxation time from the center of mass trajectories of
polymer chains (the time-averaged MSDs). Applying the method to simulation data
of entangled polymers (by the slip-spring model and the simple reptation
model), we provide a clear evidence that the longest relaxation time is
estimated as the crossover time in the relative fluctuations.Comment: 17 pages, 9 figures, to appear in J. Chem. Phy
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