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This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional) Lie group. We follow the variational approach to nonequilibrium thermodynamics…
Different methods to extract the temperature and density in heavy ion collisions are compared using a statistical model tailored to reproduce many experimental features at low excitation energy. The model assumes a sequential decay of an…
We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic…
We study the applicability of the finite temperature effective potential in the equation of motion of a homogeneous "misaligned" scalar condensate $\varphi$, and find important caveats that severely restrict its domain of validity: i:) the…
We provided a concise and self-contained introduction to molecular dynamics (MD) simulation, which involves a body of fundamentals needed for all MD users. The associated computer code, simulating a gas of classical particles interacting…
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the…
Complex systems produce high-dimensional signals that lack macroscopic variables analogous to entropy, temperature, or free energy. This work introduces a thermoinformational formulation that derives entropy, internal energy, temperature,…
The discontinuity, or imaginary part of a self-energy at finite temperature is proportional to the rate at which the corresponding particles are produced when very few of them are present, and also to the rate at which their phase space…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for…
The first-order general relativistic theory of a generic dissipative (heat-conducting, viscous, particle-creating) fluid is rediscussed from a unified covariant frame-independent point of view. By generalizing some previous works in the…
This paper considers one-dimensional heat transfer in a media with temperature-dependent thermal conductivity. To model the transient behavior of the system, we solve numerically the one-dimensional unsteady heat conduction equation with…
Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…
We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where {\it all the particles are different} (APD). The equilibrium properties of this APD system were studied in our earlier work…
We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…
We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan (1964) minimizes the residuum of…
This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers…
One of the key objectives in investigating small stochastic systems is the development of micrometer-sized engines and the understanding of their thermodynamics. However, the primary mathematical tool used for this purpose, the overdamped…
In this paper we investigate the asymptotic behavior and decay of the solution of the discrete in time $N$-dimensional heat equation. We give a convergence rate with which the solution tends to the discrete fundamental solution, and the…