Related papers: Uncertainty Quantification And Analysis Of Dynamic…
In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
An uncertainty quantification framework is developed for Eulerian-Lagrangian models of particle-laden flows, where the fluid is modeled through a system of partial differential equations in the Eulerian frame and inertial particles are…
This paper considers a stochastic control framework, in which the residual model uncertainty of the dynamical system is learned using a Gaussian Process (GP). In the proposed formulation, the residual model uncertainty consists of a…
Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…
Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises,…
We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
Parameters of the mathematical model describing many practical dynamical systems are prone to vary due to aging or renewal, wear and tear, as well as changes in environmental or service conditions. These variabilities will adversely affect…
A system with two correlated Gaussian white noises is analysed. This system can describe both stochastic localization and long tails in the stationary distribution. Correlations between the noises can lead to a nonmonotonic behaviour of the…
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability…
We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After…
We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it…
Quantum measurements and the associated state changes are properly described in the language of instruments. We investigate the properties of a time continuous family of instruments associated with the recently introduced family of general…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…