16,590 research outputs found
Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
We investigate the motion of a run-and-tumble particle (RTP) in one
dimension. We find the exact probability distribution of the particle with and
without diffusion on the infinite line, as well as in a finite interval. In the
infinite domain, this probability distribution approaches a Gaussian form in
the long-time limit, as in the case of a regular Brownian particle. At
intermediate times, this distribution exhibits unexpected multi-modal forms. In
a finite domain, the probability distribution reaches a steady state form with
peaks at the boundaries, in contrast to a Brownian particle. We also study the
relaxation to the steady state analytically. Finally we compute the survival
probability of the RTP in a semi-infinite domain. In the finite interval, we
compute the exit probability and the associated exit times. We provide
numerical verifications of our analytical results
First-passage and first-exit times of a Bessel-like stochastic process
We study a stochastic process related to the Bessel and the Rayleigh
processes, with various applications in physics, chemistry, biology, economics,
finance and other fields. The stochastic differential equation is , where is the Wiener process. Due to the
singularity of the drift term for , different natures of boundary at
the origin arise depending on the real parameter : entrance, exit, and
regular. For each of them we calculate analytically and numerically the
probability density functions of first-passage times or first-exit times.
Nontrivial behaviour is observed in the case of a regular boundary.Comment: 15 pages, 6 figures, submitted to Physical Review
MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
Molecular dynamics (MD) simulations can model the interactions between
macromolecules with high spatiotemporal resolution but at a high computational
cost. By combining high-throughput MD with Markov state models (MSMs), it is
now possible to obtain long-timescale behavior of small to intermediate
biomolecules and complexes. To model the interactions of many molecules at
large lengthscales, particle-based reaction-diffusion (RD) simulations are more
suitable but lack molecular detail. Thus, coupling MSMs and RD simulations
(MSM/RD) would be highly desirable, as they could efficiently produce
simulations at large time- and lengthscales, while still conserving the
characteristic features of the interactions observed at atomic detail. While
such a coupling seems straightforward, fundamental questions are still open:
Which definition of MSM states is suitable? Which protocol to merge and split
RD particles in an association/dissociation reaction will conserve the correct
bimolecular kinetics and thermodynamics? In this paper, we make the first step
towards MSM/RD by laying out a general theory of coupling and proposing a first
implementation for association/dissociation of a protein with a small ligand (A
+ B C). Applications on a toy model and CO diffusion into the heme cavity
of myoglobin are reported
Comparing hitting time behaviour of Markov jump processes and their diffusion approximations
Markov jump processes can provide accurate models in many applications, notably chemical and biochemical kinetics, and population dynamics. Stochastic differential equations offer a computationally efficient way to approximate these processes. It is therefore of interest to establish results that shed light on the extent to which the jump and diffusion models agree. In this work we focus on mean hitting time behavior in a thermodynamic limit. We study three simple types of reactions where analytical results can be derived, and we find that the match between mean hitting time behavior of the two models is vastly different in each case. In particular, for a degradation reaction we find that the relative discrepancy decays extremely slowly, namely, as the inverse of the logarithm of the system size. After giving some further computational results, we conclude by pointing out that studying hitting times allows the Markov jump and stochastic differential equation regimes to be compared in a manner that avoids pitfalls that may invalidate other approaches
An accurate and efficient Lagrangian sub-grid model
A computationally efficient model is introduced to account for the sub-grid
scale velocities of tracer particles dispersed in statistically homogeneous and
isotropic turbulent flows. The model embeds the multi-scale nature of turbulent
temporal and spatial correlations, that are essential to reproduce
multi-particle dispersion. It is capable to describe the Lagrangian diffusion
and dispersion of temporally and spatially correlated clouds of particles.
Although the model neglects intermittent corrections, we show that pair and
tetrad dispersion results nicely compare with Direct Numerical Simulations of
statistically isotropic and homogeneous turbulence. This is in agreement
with recent observations that deviations from self-similar pair dispersion
statistics are rare events
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