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This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Explicit quantification of uncertainty in engineering simulations is being increasingly used to inform robust and reliable design practices. In the aerospace industry, computationally-feasible analyses for design optimization purposes often…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
The unprecedented increase of commercial airlines and private jets over the next ten years presents a challenge for air traffic control. Precise flight trajectory prediction is of great significance in air transportation management, which…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
Autopilot is a system designed to guide a vehicle without aid. Due to increase in flight hours and complexity of modern day flight it has become imperative to equip the aircrafts with autopilot. Thus reliability and consistency of an…
In this paper, a quantitative risk assessment approach is discussed for the design of an obstacle detection function for low-speed freight trains with grade of automation (GoA)~4. In this 5-step approach, starting with single detection…
By including elements of the density matrix formalism, the semiclassical ensemble Monte Carlo method for carrier transport is extended to incorporate incoherent tunneling, known to play an important role in quantum cascade lasers (QCLs). In…
In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a…
Nonlinear control allocation is an important part of modern nonlinear dynamic inversion based flight control systems which require highly accurate model of aircraft aerodynamics. Generally, an accurately implemented onboard model determines…
We are concerned with a mixture of Boltzmann and McKean-Vlasov type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself,and driven by a Poisson point measure with the…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
We investigate the statistical properties of an over-damped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is…
We present a lattice Boltzmann algorithm for liquid crystal hydrodynamics. The coupling between the tensor order parameter and the flow is treated consistently allowing investigation of a wide range of non-Newtonian flow behavior. We…
Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters…
Automated synthesis of correct-by-construction controllers for autonomous systems is crucial for their deployment in safety-critical scenarios. Such autonomous systems are naturally modeled as stochastic dynamical models. The general…
Recent numerical analyses to optimize the design of microfluidic devices for more effective entrapment or segregation of surrogate circulating tumor cells (CTCs) from healthy cells have been reported in the literature without concurrently…