5,588 research outputs found
Techniques for the Fast Simulation of Models of Highly dependable Systems
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system
New advances in H∞ control and filtering for nonlinear systems
The main objective of this special issue is to
summarise recent advances in H∞ control and filtering
for nonlinear systems, including time-delay, hybrid and
stochastic systems. The published papers provide new
ideas and approaches, clearly indicating the advances
made in problem statements, methodologies or applications
with respect to the existing results. The special
issue also includes papers focusing on advanced and
non-traditional methods and presenting considerable
novelties in theoretical background or experimental
setup. Some papers present applications to newly
emerging fields, such as network-based control and
estimation
Optimized auxiliary oscillators for the simulation of general open quantum systems
A method for the systematic construction of few-body damped harmonic
oscillator networks accurately reproducing the effect of general bosonic
environments in open quantum systems is presented. Under the sole assumptions
of a Gaussian environment and regardless of the system coupled to it, an
algorithm to determine the parameters of an equivalent set of interacting
damped oscillators obeying a Markovian quantum master equation is introduced.
By choosing a suitable coupling to the system and minimizing an appropriate
distance between the two-time correlation function of this effective bath and
that of the target environment, the error induced in the reduced dynamics of
the system is brought under rigorous control. The interactions among the
effective modes provide remarkable flexibility in replicating non-Markovian
effects on the system even with a small number of oscillators, and the
resulting Lindblad equation may therefore be integrated at a very reasonable
computational cost using standard methods for Markovian problems, even in
strongly non-perturbative coupling regimes and at arbitrary temperatures
including zero. We apply the method to an exactly solvable problem in order to
demonstrate its accuracy, and present a study based on current research in the
context of coherent transport in biological aggregates as a more realistic
example of its use; performance and versatility are highlighted, and
theoretical and numerical advantages over existing methods, as well as possible
future improvements, are discussed.Comment: 23 + 9 pages, 11 + 2 figures. No changes from previous version except
publication info and updated author affiliation
Problems in the numerical simulation of models with heterogeneous agents and economic distortions
Our work has been concerned with the numerical simulation of dynamic economies with heterogeneous agents and economic distortions. Recent research has drawn attention to inherent difficulties in the computation of competitive equilibria for these economies: A continuous Markovian solution may fail to exist, and some commonly used numerical algorithms may not deliver accurate approximations. We consider a reliable algorithm set forth in Feng et al. (2009), and discuss problems related to the existence and computation of Markovian equilibria, as well as convergence and accuracy properties. We offer new insights into numerical simulation.Econometric models
Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach
The non-Markovian dynamics of a three-level quantum system coupled to a
bosonic environment is a difficult problem due to the lack of an exact dynamic
equation such as a master equation. We present for the first time an exact
quantum trajectory approach to a dissipative three-level model. We have
established a convolutionless stochastic Schr\"{o}dinger equation called
time-local quantum state diffusion (QSD) equation without any approximations,
in particular, without Markov approximation. Our exact time-local QSD equation
opens a new avenue for exploring quantum dynamics for a higher dimensional
quantum system coupled to a non-Markovian environment.Comment: 4 pages, 2 figure
Some advances in importance sampling of reliability models based on zero variance approximation
We are interested in estimating, through simulation, the probability of entering a rare failure state before a regeneration state. Since this probability is typically small, we apply importance sampling. The method that we use is based on finding the most likely paths to failure. We present an algorithm that is guaranteed to produce an estimator that meets the conditions presented in [10] [9] for vanishing relative error. We furthermore demonstrate how the procedure that is used to obtain the change of measure can be executed a second time to achieve even further variance reduction, using ideas from [5], and also apply this technique to the method of failure biasing, with which we compare our results
Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency
We study origin, parameter optimization, and thermodynamic efficiency of
isothermal rocking ratchets based on fractional subdiffusion within a
generalized non-Markovian Langevin equation approach. A corresponding
multi-dimensional Markovian embedding dynamics is realized using a set of
auxiliary Brownian particles elastically coupled to the central Brownian
particle (see video on the journal web site). We show that anomalous
subdiffusive transport emerges due to an interplay of nonlinear response and
viscoelastic effects for fractional Brownian motion in periodic potentials with
broken space-inversion symmetry and driven by a time-periodic field. The
anomalous transport becomes optimal for a subthreshold driving when the driving
period matches a characteristic time scale of interwell transitions. It can
also be optimized by varying temperature, amplitude of periodic potential and
driving strength. The useful work done against a load shows a parabolic
dependence on the load strength. It grows sublinearly with time and the
corresponding thermodynamic efficiency decays algebraically in time because the
energy supplied by the driving field scales with time linearly. However, it
compares well with the efficiency of normal diffusion rocking ratchets on an
appreciably long time scale
Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations
Based on recently derived exact stochastic Liouville-von Neumann equations,
several strategies for the efficient simulation of open quantum systems are
developed and tested on the spin-boson model. The accuracy and efficiency of
these simulations is verified for several test cases including both coherent
and incoherent dynamics, involving timescales differing by several orders of
magnitude. Using simulations with a time-dependent field, the time evolution of
coherences in the reduced density matrix is investigated. Even in the case of
weak damping, pronounced preparation effects are found. These indicate hidden
coherence in the interacting system which can only be indirectly observed in
the basis of the reduced quantum dynamics.Comment: 25 pages, 7 figures; to be published in Chemical Physic
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