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Microscopic swimming particles, which dissipate energy to execute persistent directed motion, are a classic example of a non-equilibrium system. We investigate the non-interacting Ornstein--Uhlenbeck Particle (OUP), which is propelled…
Several hydrodynamic models the atomic Bose-Einstein condensate beyond the mean-field approximation are discussed together from one point of view. All these models are derived from microscopic quantum description. The derivation is made…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
Upcoming experimental programs will look for signatures of a possible critical point in the QCD phase diagram in fluctuation observables. To understand and predict these signatures, one must account for the fact that the dynamics of any…
We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a given sub-critical speed. The speed of the…
Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been…
We derive the transient-time correlation function (TTCF) expression for the computation of phase variables of inhomogenous confined atomistic fluids undergoing boundary-driven planar shear (Couette) flow at constant pressure. Using…
This paper introduces a novel mathematical framework for examining the regularity and energy dissipation properties of solutions to the stochastic Navier-Stokes equations. By integrating Sobolev-Besov hybrid spaces, fractional differential…
In this paper, we study higher-order-accurate-in-time minimizing movements schemes for Wasserstein gradient flows. We introduce a novel accelerated second-order scheme, leveraging the differential structure of the Wasserstein space in both…
This paper provides results on Wasserstein gradient flows between measures on the real line. Utilizing the isometric embedding of the Wasserstein space $\mathcal P_2(\mathbb R)$ into the Hilbert space $L_2((0,1))$, Wasserstein gradient…
We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of…
In this paper, we start from a very natural system of cross-diffusion equations, which can be seen as a gradient flow for the Wasserstein distance of a certain functional. Unfortunately, the cross-diffusion system is not well-posed, as a…
This paper presents a novel distribution-agnostic Wasserstein distance-based estimation framework. The goal is to determine an optimal map combining prior estimate with measurement likelihood such that posterior estimation error optimally…
High-pressure transcritical fluid flows are central to modern energy and propulsion systems. A key challenge arises in confined configurations, where optimizing performance requires a detailed understanding of the coupled hydrodynamic and…
Wasserstein-GANs have been introduced to address the deficiencies of generative adversarial networks (GANs) regarding the problems of vanishing gradients and mode collapse during the training, leading to improved convergence behaviour and…
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems $(X^\varepsilon_t(x))_{t\geqslant 0}$ with $\varepsilon$-small additive L\'evy noise and initial…
We use the quantum Fisher information (QFI) to diagnose a dynamical phase transition (DPT) in a closed quantum system, which is usually defined in terms of non-analytic behaviour of a time-averaged order parameter. Employing the…
A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we…
Driven-dissipative open quantum many-body systems exhibit rich phases that are characterized by the steady states in the long-time dynamics. However, lossy open systems inevitably decay to the vacuum, making their transient evolution the…
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions.…