Related papers: Discretized sum-product type problems: Energy vari…
In this paper, we consider energy decay estimates for the following nonlinear evolution problem $$\begin{split} [P(u_t(t))]_t + A u(t) + B(t , x , u_t(t)) =0,\quad t\in J=(0,\infty), \end{split}$$ under suitable assumptions on the…
A new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and…
The composite CBS-QB3 method is widely used to obtain accurate energies of molecules and radicals although its use in the case of singlet diradicals gives rise to some difficulties. The problem is related to the parameterized correction…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
We present an energy conserving space discretisation of the rotating shallow water equations using compatible finite elements. It is based on an energy and enstrophy conserving Hamiltonian formulation as described in McRae and Cotter…
We study $p$-energies on post critically finite (p.c.f.) self-similar sets for $1<p<\infty$, as limits of discrete $p$-energies on approximation graphs, extending the construction of Dirichlet forms, the $p=2$ setting. By suitably enlarging…
Let G be any additive abelian group with cyclic torsion subgroup, and let A, B and C be finite subsets of G with cardinality n>0. We show that there is a numbering {a_i}_{i=1}^n of the elements of A, a numbering {b_i}_{i=1}^n of the…
A shell-type model of an inviscid fluid, previously considered in the literature, is investigated in absence of external force. Energy dissipation of positive solutions is proved and decay of energy like $t^{-2}$ is established.…
We shall introduce and study certain truncated sums of Hecke eigenvalues of $GL_2$-automorphic forms along quadratic polynomials. A power saving estimate is established and new applications to moments of critical $L$-values associated to…
We generalize Bourgain's discretized sum-product theorem to matrix algebras.
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
Comparing the result of inserting a complete set of physical states in a time ordered product of $b$ decay currents with the operator product expansion gives a class of zero recoil sum rules. They sum over physical states with excitation…
We study long-time properties of reversible reaction-diffusion systems of type A + B <-> C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the…
The rare $B_c \to D_{s,d}^{*} l^+ l^-$ decays are investigated in the framework of the three point QCD sum rules approach. Considering the gluon condensate corrections to the correlation function, the form factors relevant to these…
In this review we discuss the weak KPZ universality conjecture for a class of 1-d systems whose dynamics conserves one or more quantities. As a prototype example for the former case, we will focus on weakly asymmetric simple exclusion…
To help the difficult determination of the angle $\gamma$ of the unitarity triangle, Aleksan, Dunietz and Kayser have proposed the modes of the type $K^-D^+_s$, common to $B_s$ and $\bar{B}_s$. We point out that it is possible to gain in…
The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity…
We consider the drift-diffusion equation $$ u_t-\varepsilon \Delta u+\nabla\cdot(u\nabla K\star u)=0 $$ in the whole space with global-in-time bounded solutions. Mass concentration phenomena for radially symmetric solutions of this equation…