Persona: Torre Rodríguez, Jaime Arturo de la
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Torre Rodríguez
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Jaime Arturo de la
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Publicación The role of thermal fluctuations in the motion of a free body(ELSEVIER, 2024) Español Garrigos, José; Thachuk, Mark E.; Torre Rodríguez, Jaime Arturo de laThe motion of a rigid body is described in Classical Mechanics with the venerable Euler’s equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however, cannot satisfy this property, as a consequence of thermal fluctuations. We generalize Euler’s equations for a free body in order to describe dissipative and thermal fluctuation effects in a thermodynamically consistent way. The origin of these effects is internal, i.e. not due to an external thermal bath. The stochastic differential equations governing the orientation and central moments of the body are derived from first principles through the theory of coarse-graining. Within this theory, Euler’s equations emerge as the reversible part of the dynamics. For the irreversible part, we identify two distinct dissipative mechanisms; one associated with diffusion of the orientation, whose origin lies in the difference between the spin velocity and the angular velocity, and one associated with the damping of dilations, i.e. inelasticity. We show that a deformable body with zero angular momentum will explore uniformly, through thermal fluctuations, all possible orientations. When the body spins, the equations describe the evolution towards the alignment of the body’s major principal axis with the angular momentum vector. In this alignment process, the body increases its temperature. We demonstrate that the origin of the alignment process is not inelasticity but rather orientational diffusion. The theory also predicts the equilibrium shape of a spinning body.Publicación Top-down and Bottom-up Approaches to Discrete Diffusion Models(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias. Departamento de Física Fundamental, 2015) Torre Rodríguez, Jaime Arturo de la; Español Garrigos, JoséPublicación Coarse-graining Brownian motion : from particles to a discrete diffusion equation(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2010-10-13) Torre Rodríguez, Jaime Arturo de la; Español Garrigos, JoséWe consider a recently obtained coarse-grained discrete equation for the diffusion of Brownian particles. The detailed level of description is governed by a Brownian dynamics of non-interacting particles. The coarse-level is described by discrete concentration variables defined in terms of the Delaunay cell. These coarse variables obey a stochastic differential equation that can be understood as a discrete version of a diffusion equation. The diffusion equation contains two basic building blocks which are the entropy function and the friction matrix. The entropy function is shown to be non-additive due to the overlapping of cells in the Delaunay construction. The friction matrix is state dependent in principle, but for near-equilibrium situations it is shown that it may safely evaluated at the equilibrium value of the density field