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Related papers: Parametrization of stochastic multiscale triads

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We introduce a new dynamical picture, referred to as correlation picture,' which connects a correlated state to its uncorrelated counterpart. Using this picture allows us to derive an exact dynamical equation for a general open-system…

Quantum Physics · Physics 2020-11-10 S. Alipour , A. T. Rezakhani , A. P. Babu , K. Mølmer , M. Möttönen , T. Ala-Nissila

We propose a thermodynamically consistent minimal model to study synchronization which is made of driven and interacting three-state units. This system exhibits at the mean-field level two bifurcations separating three dynamical phases: a…

Statistical Mechanics · Physics 2018-09-12 Tim Herpich , Juzar Thingna , Massimiliano Esposito

In this paper, we investigate the open-loop and weak closed-loop solvabilities of stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. Interestingly, these two solvabilities are…

Probability · Mathematics 2019-09-17 Jiaqiang Wen , Xun Li , Jie Xiong

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…

Condensed Matter · Physics 2009-11-07 Gregor Diezemann , Gerald Hinze , Hans Sillescu

We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies…

Analysis of PDEs · Mathematics 2017-02-09 Arthur J. Vromans , A. A. F. van de Ven , Adrian Muntean

We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to…

Statistics Theory · Mathematics 2016-01-07 Nick Whiteley , Anthony Lee

We study a class of weakly coupled systems of Hamilton{Jacobi equations at the critical level. We associate to it a family of scalar discounted equation. Using control{theoretic tech- niques we construct an algorithm which allows obtaining…

Analysis of PDEs · Mathematics 2017-01-31 Antonio Siconolfi , Sahar Zabad

We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values…

Quantum Physics · Physics 2009-11-10 J. Piilo , S. Maniscalco , A. Messina , F. Petruccione

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

Data Analysis, Statistics and Probability · Physics 2012-04-11 Lewis Mitchell , Georg A. Gottwald

This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…

Dynamical Systems · Mathematics 2014-09-30 Gary Froyland , Georg A. Gottwald , Andy Hammerlindl

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

Chaotic Dynamics · Physics 2024-05-14 Ludovico Theo Giorgini , Andre N. Souza , Peter J. Schmid

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…

Systems and Control · Electrical Eng. & Systems 2023-01-02 Lars A. L. Janssen , Bart Besselink , Rob H. B. Fey , Nathan van de Wouw

This paper introduces a new approach of treating platoon systems using mean-variance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain.…

Optimization and Control · Mathematics 2014-01-22 Zhixin Yang , G. Yin , Le Yi Wang , Hongwei Zhang

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…

Numerical Analysis · Mathematics 2013-07-17 M. Kovács , S. Larsson , F. Lindgren

We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment…

Quantum Physics · Physics 2016-11-29 Philipp Strasberg , Gernot Schaller , Neill Lambert , Tobias Brandes

We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the…

Systems and Control · Electrical Eng. & Systems 2022-10-04 Hancheng Min , Enrique Mallada

We solve a weakly supervised regression problem. Under "weakly" we understand that for some training points the labels are known, for some unknown, and for others uncertain due to the presence of random noise or other reasons such as lack…

Machine Learning · Computer Science 2021-04-15 Vladimir Berikov , Alexander Litvinenko

This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…

Numerical Analysis · Mathematics 2025-02-13 Liang Chen , Yaru Chen , Qiuqi Li , Tao Zhou

In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…

Systems and Control · Computer Science 2015-11-13 Kooktae Lee , Raktim Bhattacharya

This paper presents the modal truncation and singular value decomposition (SVD) technique as two main algorithms for dynamic model reduction of the power system. The significance and accuracy of the proposed methods are investigated with…

Systems and Control · Electrical Eng. & Systems 2020-04-17 Mohammad Khatibi , Fatemeh Rahmani , Tanushree Agarwal