Related papers: An integrable example of gradient flows based on o…
This work focuses on the numerical computation of defocusing action ground states for rotating nonlinear Schr\"odinger equations (RNLS) using a direct gradient flow (DGF) method. We address theoretical gaps in the existing literature…
For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean…
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from…
The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian…
In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a constructive method, alternating minimizing movements for the…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
Using the formalism of the Khalatnikov potential, we derive exact general formulae for the entropy flow dS/dy, where y is the rapidity, as a function of temperature for the (1+1) relativistic hydrodynamics of a perfect fluid. We study in…
We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation may admit a type change ranging from parabolic to elliptic…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical…
In this work, we study a fourth order exponential equation, $u_t=\Delta e^{-\Delta u},$ derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the…
We derive a new formulation of the $3D$ compressible Euler equations with dynamic entropy exhibiting remarkable null structures and regularity properties. Our results hold for an arbitrary equation of state (which yields the pressure in…
We develop a semi-discrete optimal transport scheme for the compressible semi-geostrophic equations, a system that plays an important role in modelling large-scale atmospheric dynamics and frontogenesis. Unlike the incompressible case, the…
We introduce an optimal transport topology on the space of probability measures over a fiber bundle, which penalizes the transport cost from one fiber to another. For simplicity, we illustrate our construction in the Euclidean case…
Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and non-conforming Finite Element, Mixed Finite Element and Finite…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
For addressing optimisation tasks on finite dimensional quantum systems, we give a comprehensive account of the foundations of gradient flows on Riemannian manifolds including new developments: we extend former results from Lie groups such…
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed…
This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…