Related papers: Metriplectic 4-bracket algorithm for constructing …
We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This…
Metriplectic dynamics is applied to compute equilibria of fluid dynamical systems. The result is a relaxation method in which Hamiltonian dynamics (symplectic structure) is combined with dissipative mechanisms (metric structure) that…
In this research, we introduce and investigate an approximation method that preserves the structural integrity of the non-isothermal Cahn-Hilliard-Navier-Stokes system. Our approach extends a previously proposed technique [1], which…
The development of machine learning sheds new light on the problem of statistical thermodynamics in multicomponent alloys. However, a data-driven approach to construct the effective Hamiltonian requires sufficiently large data sets, which…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated.…
We present a structure-preserving and thermodynamically consistent numerical scheme for classical magnetohydrodynamics, incorporating viscosity, magnetic resistivity, heat transfer, and thermoelectric effect. The governing equations are…
We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy,…
In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the…
We address the energy transfer in the differential system $$ \begin{cases} u_{ttt}+\alpha u_{tt} - \beta \Delta u_t - \gamma \Delta u = -\eta \Delta \theta \\ \theta_t - \kappa \Delta \theta =\eta \Delta u_{tt}+ \alpha\eta \Delta u_t…
The equations of reversible (inviscid, adiabatic) fluid dynamics have a well-known variational formulation based on Hamilton's principle and the Lagrangian, to which is associated a Hamiltonian formulation that involves a Poisson bracket…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
Technical components are usually well optimized. However, simply combining these optimized components in a technical system does not necessarily lead to optimal systems. Therefore, focusing on a system perspective reveals new potential for…
A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
We consider and compare four Hamiltonian formulations of thermostated mechanics, three of them kinetic, and the other one configurational. Though all four approaches ``work'' at equilibrium, their application to many-body nonequilibrium…
We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we describe a novel numerical algorithm - the convex hull algorithm (CHA) - in order to compute, both, entropy dissipative solutions…
Integral equations for thermodynamic quantities are derived in the framework of the non-crossing approximation (NCA). Entropy and specific heat of 4f contribution are calculated without numerical differentiations of thermodynamic potential.…
It is shown that the Fokker-Planck equation describing diffusion processes in noncanonical Hamiltonian systems exhibits a metriplectic structure, i.e. an algebraic bracket formalism that generates the equation in consistency with the…
This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more…