Related papers: Functional inequalities: nonlinear flows and entro…
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to…
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: Firstly, as building blocks in the subcell flux…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics…
In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…
Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many…
Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an…
Since their introduction in the early sixties, the R\'enyi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
We study weighted inequalities of Hardy and Hardy-Poincar\'e type and find necessary and sufficient conditions on the weights so that the considered inequalities hold. Examples with the optimal constants are shown. Such inequalities are…
This work studies the effects of a through-flow on two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid confined between two plane plates, as a model problem to further our understanding of the fluid mechanics in the…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
We study optimal functions in a family of Caffarelli-Kohn-Nirenberg inequalities with a power-law weight, in a regime for which standard symmetrization techniques fail. We establish the existence of optimal functions, study their properties…
The statistical-mechanical study of the equilibrium properties of fluids, starting from the knowledge of the interparticle interaction potential, is essential to understand the role that microscopic interaction between individual particles…