6,335 research outputs found
Importance sampling large deviations in nonequilibrium steady states. I
Large deviation functions contain information on the stability and response
of systems driven into nonequilibrium steady states, and in such a way are
similar to free energies for systems at equilibrium. As with equilibrium free
energies, evaluating large deviation functions numerically for all but the
simplest systems is difficult, because by construction they depend on
exponentially rare events. In this first paper of a series, we evaluate
different trajectory-based sampling methods capable of computing large
deviation functions of time integrated observables within nonequilibrium steady
states. We illustrate some convergence criteria and best practices using a
number of different models, including a biased Brownian walker, a driven
lattice gas, and a model of self-assembly. We show how two popular methods for
sampling trajectory ensembles, transition path sampling and diffusion Monte
Carlo, suffer from exponentially diverging correlations in trajectory space as
a function of the bias parameter when estimating large deviation functions.
Improving the efficiencies of these algorithms requires introducing guiding
functions for the trajectories.Comment: Published in JC
Free energy reconstruction from steered dynamics without post-processing
Various methods achieving importance sampling in ensembles of nonequilibrium
trajectories enable to estimate free energy differences and, by
maximum-likelihood post-processing, to reconstruct free energy landscapes.
Here, based on Bayes theorem, we propose a more direct method in which a
posterior likelihood function is used both to construct the steered dynamics
and to infer the contribution to equilibrium of all the sampled states. The
method is implemented with two steering schedules. First, using non-autonomous
steering, we calculate the migration barrier of the vacancy in Fe-alpha.
Second, using an autonomous scheduling related to metadynamics and equivalent
to temperature-accelerated molecular dynamics, we accurately reconstruct the
two-dimensional free energy landscape of the 38-atom Lennard-Jones cluster as a
function of an orientational bond-order parameter and energy, down to the
solid-solid structural transition temperature of the cluster and without
maximum-likelihood post-processing.Comment: Accepted manuscript in Journal of Computational Physics, 7 figure
Evaluating the Differences of Gridding Techniques for Digital Elevation Models Generation and Their Influence on the Modeling of Stony Debris Flows Routing: A Case Study From Rovina di Cancia Basin (North-Eastern Italian Alps)
Debris \ufb02ows are among the most hazardous phenomena in mountain areas. To cope
with debris \ufb02ow hazard, it is common to delineate the risk-prone areas through
routing models. The most important input to debris \ufb02ow routing models are the
topographic data, usually in the form of Digital Elevation Models (DEMs). The quality
of DEMs depends on the accuracy, density, and spatial distribution of the sampled
points; on the characteristics of the surface; and on the applied gridding methodology.
Therefore, the choice of the interpolation method affects the realistic representation
of the channel and fan morphology, and thus potentially the debris \ufb02ow routing
modeling outcomes. In this paper, we initially investigate the performance of common
interpolation methods (i.e., linear triangulation, natural neighbor, nearest neighbor,
Inverse Distance to a Power, ANUDEM, Radial Basis Functions, and ordinary kriging)
in building DEMs with the complex topography of a debris \ufb02ow channel located
in the Venetian Dolomites (North-eastern Italian Alps), by using small footprint full-
waveform Light Detection And Ranging (LiDAR) data. The investigation is carried
out through a combination of statistical analysis of vertical accuracy, algorithm
robustness, and spatial clustering of vertical errors, and multi-criteria shape reliability
assessment. After that, we examine the in\ufb02uence of the tested interpolation algorithms
on the performance of a Geographic Information System (GIS)-based cell model for
simulating stony debris \ufb02ows routing. In detail, we investigate both the correlation
between the DEMs heights uncertainty resulting from the gridding procedure and
that on the corresponding simulated erosion/deposition depths, both the effect of
interpolation algorithms on simulated areas, erosion and deposition volumes, solid-liquid
discharges, and channel morphology after the event. The comparison among the tested
interpolation methods highlights that the ANUDEM and ordinary kriging algorithms
are not suitable for building DEMs with complex topography. Conversely, the linear
triangulation, the natural neighbor algorithm, and the thin-plate spline plus tension and completely regularized spline functions ensure the best trade-off among accuracy
and shape reliability. Anyway, the evaluation of the effects of gridding techniques on
debris \ufb02ow routing modeling reveals that the choice of the interpolation algorithm does
not signi\ufb01cantly affect the model outcomes
Steered Transition Path Sampling
We introduce a path sampling method for obtaining statistical properties of
an arbitrary stochastic dynamics. The method works by decomposing a trajectory
in time, estimating the probability of satisfying a progress constraint,
modifying the dynamics based on that probability, and then reweighting to
calculate averages. Because the progress constraint can be formulated in terms
of occurrences of events within time intervals, the method is particularly well
suited for controlling the sampling of currents of dynamic events. We
demonstrate the method for calculating transition probabilities in barrier
crossing problems and survival probabilities in strongly diffusive systems with
absorbing states, which are difficult to treat by shooting. We discuss the
relation of the algorithm to other methods.Comment: 11 pages, 8 figure
Efficient path sampling on multiple reaction channels
Due to the time scale problem, rare events are not accessible by straight
forward molecular dynamics. The presence of multiple reaction channels
complicates the problem even further. The feasibility of the standard free
energy based methods relies strongly on the success in finding a proper
reaction coordinate. This can be very difficult task in high-dimensional
complex systems and even more if several distinct reaction channels exist.
Moreover, even if a proper reaction coordinate can be found, ergodic sampling
will be a challenge. In this article, we discuss the recent advancements of
path sampling methods to tackle this problem. We argue why the path sampling
methods, via the transition interface sampling technique, is less sensitive to
the choice of reaction coordinate. Moreover, we review a new algorithm,
parallel path swapping, that can dramatically improve the ergodic sampling of
trajectories for the multiple reaction channel systems.Comment: 7 pages, 4 figures. Article submitted for the proceedings of the
Conference on Computational Physics, Brussels 200
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