Related papers: Variational principle for a damped, quadratically …
Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While a remarkable progress has been witnessed in recent…
Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based…
In modeling relativistic thermodynamics, we frequently regard the particle number as a conserved quantity. The number conservation law, which comes from the requirement that the pull-back construction from fluid-matter 3-space has the same…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
We show that a noncollapsing solution below r_c can be constructed for the dynamics of randomly forced particle interacting with a dissipative boundary. The scaling analysis predicts a divergent collision rate at the boundary for the…
An infinite irregular harmonic chain of particles is considered. We assume that some particles (``defects'') in the chain have masses and force constants of interaction different from the masses and the interaction constants of the other…
We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with one and more than one independent variable, of first…
In this paper we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we…
A relation between variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It is shown that for a system of differential equations in Eulerian variables corresponding Lagrangian…
In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the…
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…
The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a…
We introduce a model of chemically active particles of a multi-component fluid that can change their interactions with other particles depending on their state. Since such switching of interactions can only be maintained by the input of…
We theoretically investigate the flow of the atomic excitations in a driven chiral-coupled atomic chain with nonreciprocal decay channels. This one-dimensional system allows infinite-range dipole-dipole interaction, and enables directional…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
In this work, we give a variation of parameters formula for nonautonomous linear impulsive differential equations with piecewise constant arguments of generalized type. We cover several cases of differential equations with deviated…
One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule…