82,682 research outputs found
A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel
The Trotter-Suzuki approximation leads to an efficient algorithm for solving
the time-dependent Schr\"odinger equation. Using existing highly optimized CPU
and GPU kernels, we developed a distributed version of the algorithm that runs
efficiently on a cluster. Our implementation also improves single node
performance, and is able to use multiple GPUs within a node. The scaling is
close to linear using the CPU kernels, whereas the efficiency of GPU kernels
improve with larger matrices. We also introduce a hybrid kernel that
simultaneously uses multicore CPUs and GPUs in a distributed system. This
kernel is shown to be efficient when the matrix size would not fit in the GPU
memory. Larger quantum systems scale especially well with a high number nodes.
The code is available under an open source license.Comment: 11 pages, 10 figure
Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation
In cosmic shear likelihood analyses the covariance is most commonly assumed
to be constant in parameter space. Therefore, when calculating the covariance
matrix (analytically or from simulations), its underlying cosmology should not
influence the likelihood contours. We examine whether the aforementioned
assumption holds and quantify how strong cosmic shear covariances vary within a
reasonable parameter range. Furthermore, we examine the impact on likelihood
contours when assuming different cosmologies in the covariance. We find that
covariances vary significantly within the considered parameter range
(Omega_m=[0.2;0.4], sigma_8=[0.6;1.0]) and that this has a non-negligible
impact on the size of likelihood contours. This impact increases with
increasing survey size, increasing number density of source galaxies,
decreasing ellipticity noise, and when using non-Gaussian covariances. To
improve on the assumption of a constant covariance we present two methods. The
adaptive covariance is the most accurate method, but it is computationally
expensive. To reduce the computational costs we give a scaling relation for
covariances. As a second method we outline the concept of an iterative
likelihood analysis. Here, we additionally account for non-Gaussianity using a
ray-tracing covariance derived from the Millennium simulation.Comment: 11 pages, 8 figure
Dissipative quantum mechanics beyond Bloch-Redfield: A consistent weak-coupling expansion of the ohmic spin boson model at arbitrary bias
We study the time dynamics of the ohmic spin boson model at arbitrary bias
and small coupling to the bosonic bath. Using perturbation
theory and the real-time renormalization group (RG) method we present a
consistent zero-temperature weak-coupling expansion for the time evolution of
the reduced density matrix one order beyond the Bloch-Redfield solution. We
develop a renormalized perturbation theory and present an analytical solution
covering the whole range from small to large times, including further results
for exponentially small or large times. Resumming all secular terms in all
orders of perturbation theory we find exponential decay for all terms of the
time evolution. We determine the preexponential functions and find slowly
varying logarithmic terms with the renormalized Rabi frequency as
energy scale together with strongly varying parts falling off asymptocially as
in leading order, in contrast to the unbiased case. Resumming all
logarithmic terms in all orders of perturbation theory via real-time RG we find
the correct renormalized tunneling and a power-law behaviour for the
oscillating modes with exponent crossing over from for exponentially
small times to a bias-dependent value for
exponentially large times. Furthermore, we present a degenerate perturbation
theory to calculate consistently the purely decaying mode one order beyond
Bloch-Redfield.Comment: 27 pages, 2 figure
Fast MCMC sampling for Markov jump processes and extensions
Markov jump processes (or continuous-time Markov chains) are a simple and
important class of continuous-time dynamical systems. In this paper, we tackle
the problem of simulating from the posterior distribution over paths in these
models, given partial and noisy observations. Our approach is an auxiliary
variable Gibbs sampler, and is based on the idea of uniformization. This sets
up a Markov chain over paths by alternately sampling a finite set of virtual
jump times given the current path and then sampling a new path given the set of
extant and virtual jump times using a standard hidden Markov model forward
filtering-backward sampling algorithm. Our method is exact and does not involve
approximations like time-discretization. We demonstrate how our sampler extends
naturally to MJP-based models like Markov-modulated Poisson processes and
continuous-time Bayesian networks and show significant computational benefits
over state-of-the-art MCMC samplers for these models.Comment: Accepted at the Journal of Machine Learning Research (JMLR
A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations
Implementing multicomponent diffusion models in reacting-flow simulations is
computationally expensive due to the challenges involved in calculating
diffusion coefficients. Instead, mixture-averaged diffusion treatments are
typically used to avoid these costs. However, to our knowledge, the accuracy
and appropriateness of the mixture-averaged diffusion models has not been
verified for three-dimensional turbulent premixed flames. In this study we
propose a fast,efficient, low-memory algorithm and use that to evaluate the
role of multicomponent mass diffusion in reacting-flow simulations. Direct
numerical simulation of these flames is performed by implementing the
Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the
computational expense of inverting the full multicomponent ordinary diffusion
array while maintaining accuracy and fidelity. We first verify the method by
performing one-dimensional simulations of premixed hydrogen flames and compare
with matching cases in Cantera. We demonstrate the algorithm to be stable, and
its performance scales approximately with the number of species squared. Then,
as an initial study of multicomponent diffusion, we simulate premixed,
three-dimensional turbulent hydrogen flames, neglecting secondary Soret and
Dufour effects. Simulation conditions are carefully selected to match
previously published results and ensure valid comparison. Our results show that
using the mixture-averaged diffusion assumption leads to a 15% under-prediction
of the normalized turbulent flame speed for a premixed hydrogen-air flame. This
difference in the turbulent flame speed motivates further study into using the
mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz
number flames.Comment: 36 pages, 14 figure
Asymptotic behavior of memristive circuits
The interest in memristors has risen due to their possible application both
as memory units and as computational devices in combination with CMOS. This is
in part due to their nonlinear dynamics, and a strong dependence on the circuit
topology. We provide evidence that also purely memristive circuits can be
employed for computational purposes. In the present paper we show that a
polynomial Lyapunov function in the memory parameters exists for the case of DC
controlled memristors. Such Lyapunov function can be asymptotically
approximated with binary variables, and mapped to quadratic combinatorial
optimization problems. This also shows a direct parallel between memristive
circuits and the Hopfield-Little model. In the case of Erdos-Renyi random
circuits, we show numerically that the distribution of the matrix elements of
the projectors can be roughly approximated with a Gaussian distribution, and
that it scales with the inverse square root of the number of elements. This
provides an approximated but direct connection with the physics of disordered
system and, in particular, of mean field spin glasses. Using this and the fact
that the interaction is controlled by a projector operator on the loop space of
the circuit. We estimate the number of stationary points of the approximate
Lyapunov function and provide a scaling formula as an upper bound in terms of
the circuit topology only.Comment: 20 pages, 8 figures; proofs corrected, figures changed; results
substantially unchanged; to appear in Entrop
Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
This article reviews recent developments in the theoretical understanding and
the numerical implementation of variational renormalization group methods using
matrix product states and projected entangled pair states.Comment: Review from 200
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