Related papers: Performance Assessment of Variational Integrators …
Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
We investigate the energy transfer dynamics in a donor-acceptor model by developing a time-local master equation technique based on a variational transformation of the underlying Hamiltonian. The variational transformation allows a…
This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference…
The paper studies the evolution of the thermomechanical and electric state of a thermoviscoelastic thermistor that is in frictional contact with a reactive foundation. The mechanical process is dynamic, while the electric process is…
We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together…
The dynamical motion of mechanical systems possesses underlying geometric structures, and preserving these structures in numerical integration improves the qualitative accuracy and reduces the long-time error of the simulation. For a single…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, named the perturbing and dissipative parameters, and it…
The goal of this paper is to develop energy-preserving variational integrators for time-dependent mechanical systems with forcing. We first present the Lagrange-d'Alembert principle in the extended Lagrangian mechanics framework and derive…
A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework…
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…
Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…
The purpose of this work is to analyze the mathematical model governing motion of $n$-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state…