Related papers: Modeling and Simulation of Non-equilibrium Flows w…
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…
We consider traffic flow models at different scales of observation. Starting from the well known hierarchy between microscopic, kinetic and macroscopic scales, we will investigate the propagation of uncertainties through the models using…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and…
We consider kinetic vehicular traffic flow models of BGK type. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic…
The main subject of this thesis rests on the study ---at different levels of description--- of instabilities in systems which are driven, i.e., maintained far from equilibrium by an external forcing. We focus here on two main classes,…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or…
The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the…
This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics of weakly compressible fluids. The mathematical model is…
Natural gas consumption by users of pipeline networks is subject to increasing uncertainty that originates from the intermittent nature of electric power loads serviced by gas-fired generators. To enable computationally efficient…
We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction…
Many systems such as autonomous vehicles and quadrotors are subject to parametric uncertainties and external disturbances. These uncertainties can lead to undesired performance degradation and safety issues. Therefore, it is important to…
This work suggests several methods of uncertainty treatment in multiscale modelling and describes their application to a system of coupled turbulent transport simulations of a tokamak plasma. We propose a method to quantify the usually…
By analogy with the kinetic theory of gases, most turbulence modeling strate- gies rely on an eddy viscosity to model the unresolved turbulent fluctuations. How- ever, the ratio of unresolved to resolved scales - very much like a degree of…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
We analyze the phenomenon of spontaneous stochasticity in fluid dynamics formulated as the nonuniqueness of solutions resulting from viscosity at infinitesimal scales acting through intermediate on large scales of the flow. We study the…
The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic…
This work aims at identifying and quantifying uncertainties related to elastic and viscoelastic parameters, which characterize the arterial wall behavior, in one-dimensional modeling of the human arterial hemodynamics. The chosen uncertain…