12,834 research outputs found
Asymptotics of work distributions in a stochastically driven system
We determine the asymptotic forms of work distributions at arbitrary times
, in a class of driven stochastic systems using a theory developed by Engel
and Nickelsen (EN theory) (arXiv:1102.4505v1 [cond-mat.stat-mech]), which is
based on the contraction principle of large deviation theory. In this paper, we
extend the theory, previously applied in the context of deterministically
driven systems, to a model in which the driving is stochastic. The models we
study are described by overdamped Langevin equations and the work distributions
in the path integral form, are characterised by having quadratic actions. We
first illustrate EN theory, for a deterministically driven system - the
breathing parabola model, and show that within its framework, the Crooks
flucutation theorem manifests itself as a reflection symmetry property of a
certain characteristic polynomial function. We then extend our analysis to a
stochastically driven system, studied in ( arXiv:1212.0704v2
[cond-mat.stat-mech], arXiv:1402.5777v1 [cond-mat.stat-mech]) using a
moment-generating-function method, for both equilibrium and non - equilibrium
steady state initial distributions. In both cases we obtain new analytic
solutions for the asymptotic forms of (dissipated) work distributions at
arbitrary . For dissipated work in the steady state, we compare the large
asymptotic behaviour of our solution to that already obtained in (
arXiv:1402.5777v1 [cond-mat.stat-mech]). In all cases, special emphasis is
placed on the computation of the pre-exponential factor and the results show
excellent agreement with the numerical simulations. Our solutions are exact in
the low noise limit.Comment: 26 pages, 8 figures. Changes from version 1: Several typos and
equations corrected, references added, pictures modified. Version to appear
in EPJ
Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels
Optimal design under uncertainty has gained much attention in the past ten
years due to the ever increasing need for manufacturers to build robust systems
at the lowest cost. Reliability-based design optimization (RBDO) allows the
analyst to minimize some cost function while ensuring some minimal performances
cast as admissible failure probabilities for a set of performance functions. In
order to address real-world engineering problems in which the performance is
assessed through computational models (e.g., finite element models in
structural mechanics) metamodeling techniques have been developed in the past
decade. This paper introduces adaptive Kriging surrogate models to solve the
RBDO problem. The latter is cast in an augmented space that "sums up" the range
of the design space and the aleatory uncertainty in the design parameters and
the environmental conditions. The surrogate model is used (i) for evaluating
robust estimates of the failure probabilities (and for enhancing the
computational experimental design by adaptive sampling) in order to achieve the
requested accuracy and (ii) for applying a gradient-based optimization
algorithm to get optimal values of the design parameters. The approach is
applied to the optimal design of ring-stiffened cylindrical shells used in
submarine engineering under uncertain geometric imperfections. For this
application the performance of the structure is related to buckling which is
addressed here by means of a finite element solution based on the asymptotic
numerical method
Robust Estimation and Wavelet Thresholding in Partial Linear Models
This paper is concerned with a semiparametric partially linear regression
model with unknown regression coefficients, an unknown nonparametric function
for the non-linear component, and unobservable Gaussian distributed random
errors. We present a wavelet thresholding based estimation procedure to
estimate the components of the partial linear model by establishing a
connection between an -penalty based wavelet estimator of the
nonparametric component and Huber's M-estimation of a standard linear model
with outliers. Some general results on the large sample properties of the
estimates of both the parametric and the nonparametric part of the model are
established. Simulations and a real example are used to illustrate the general
results and to compare the proposed methodology with other methods available in
the recent literature
Domain Decomposition for Stochastic Optimal Control
This work proposes a method for solving linear stochastic optimal control
(SOC) problems using sum of squares and semidefinite programming. Previous work
had used polynomial optimization to approximate the value function, requiring a
high polynomial degree to capture local phenomena. To improve the scalability
of the method to problems of interest, a domain decomposition scheme is
presented. By using local approximations, lower degree polynomials become
sufficient, and both local and global properties of the value function are
captured. The domain of the problem is split into a non-overlapping partition,
with added constraints ensuring continuity. The Alternating Direction
Method of Multipliers (ADMM) is used to optimize over each domain in parallel
and ensure convergence on the boundaries of the partitions. This results in
improved conditioning of the problem and allows for much larger and more
complex problems to be addressed with improved performance.Comment: 8 pages. Accepted to CDC 201
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