20,818 research outputs found
On Minimal Trajectories for Mobile Sampling of Bandlimited Fields
We study the design of sampling trajectories for stable sampling and the
reconstruction of bandlimited spatial fields using mobile sensors. The spectrum
is assumed to be a symmetric convex set. As a performance metric we use the
path density of the set of sampling trajectories that is defined as the total
distance traveled by the moving sensors per unit spatial volume of the spatial
region being monitored. Focussing first on parallel lines, we identify the set
of parallel lines with minimal path density that contains a set of stable
sampling for fields bandlimited to a known set. We then show that the problem
becomes ill-posed when the optimization is performed over all trajectories by
demonstrating a feasible trajectory set with arbitrarily low path density.
However, the problem becomes well-posed if we explicitly specify the stability
margins. We demonstrate this by obtaining a non-trivial lower bound on the path
density of an arbitrary set of trajectories that contain a sampling set with
explicitly specified stability bounds.Comment: 28 pages, 8 figure
A Monte Carlo method for critical systems in infinite volume: the planar Ising model
In this paper we propose a Monte Carlo method for generating finite-domain
marginals of critical distributions of statistical models in infinite volume.
The algorithm corrects the problem of the long-range effects of boundaries
associated to generating critical distributions on finite lattices. It uses the
advantage of scale invariance combined with ideas of the renormalization group
in order to construct a type of "holographic" boundary condition that encodes
the presence of an infinite volume beyond it. We check the quality of the
distribution obtained in the case of the planar Ising model by comparing
various observables with their infinite-plane prediction. We accurately
reproduce planar two-, three- and four-point functions of spin and energy
operators. We also define a lattice stress-energy tensor, and numerically
obtain the associated conformal Ward identities and the Ising central charge.Comment: 43 pages, 21 figure
Efficient stochastic thermostatting of path integral molecular dynamics
The path integral molecular dynamics (PIMD) method provides a convenient way
to compute the quantum mechanical structural and thermodynamic properties of
condensed phase systems at the expense of introducing an additional set of
high-frequency normal modes on top of the physical vibrations of the system.
Efficiently sampling such a wide range of frequencies provides a considerable
thermostatting challenge. Here we introduce a simple stochastic path integral
Langevin equation (PILE) thermostat which exploits an analytic knowledge of the
free path integral normal mode frequencies. We also apply a recently-developed
colored-noise thermostat based on a generalized Langevin equation (GLE), which
automatically achieves a similar, frequency-optimized sampling. The sampling
efficiencies of these thermostats are compared with that of the more
conventional Nos\'e-Hoover chain (NHC) thermostat for a number of physically
relevant properties of the liquid water and hydrogen-in-palladium systems. In
nearly every case, the new PILE thermostat is found to perform just as well as
the NHC thermostat while allowing for a computationally more efficient
implementation. The GLE thermostat also proves to be very robust delivering a
near-optimum sampling efficiency in all of the cases considered. We suspect
that these simple stochastic thermostats will therefore find useful application
in many future PIMD simulations.Comment: Accepted for publication on JC
Using Bayes formula to estimate rates of rare events in transition path sampling simulations
Transition path sampling is a method for estimating the rates of rare events
in molecular systems based on the gradual transformation of a path distribution
containing a small fraction of reactive trajectories into a biased distribution
in which these rare trajectories have become frequent. Then, a multistate
reweighting scheme is implemented to postprocess data collected from the staged
simulations. Herein, we show how Bayes formula allows to directly construct a
biased sample containing an enhanced fraction of reactive trajectories and to
concomitantly estimate the transition rate from this sample. The approach can
remediate the convergence issues encountered in free energy perturbation or
umbrella sampling simulations when the transformed distribution insufficiently
overlaps with the reference distribution.Comment: 11 pages, 8 figure
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