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 fieldPublicación Internal dissipation in the Dzhanibekov effect(Elsevier, 0001-08-20) Torre Rodríguez, Jaime Arturo de la; Español Garrigos, JoséThe Dzhanibekov effect is the phenomenon by which triaxial objects like a spinning wing bolt may continuously flip their rotational axis when initially spinning around the intermediate axis of inertia. This effect is closely related to the Tennis Racket theorem that establishes that the intermediate axis of inertia is unstable. Over time, however, dissipation ensures that a torque free spinning body will eventually rotate around its major axis, in a process called precession relaxation, which counteracts the Dzhanibekov effect. Euler’s equations for a rigid body effectively describe the Dzhanibekov effect, but cannot account for the precession relaxation effect. A dissipative generalization of Euler’s equations displays two dissipative mechanisms: orientational diffusion and viscoelasticity. Here we show through numerical simulations of the dissipative Euler’s equations that orientational diffusion, rather than viscoelasticity, primarily drives precession relaxation and effectively suppresses the Dzhanibekov effect.Publicación Stochastic Dissipative Euler’s equations for a free body(De Gruyter Brill, 2024-11-05) Torre Rodríguez, Jaime Arturo de la; Sánchez Rodríguez, Jesús; Español Garrigos, JoséIntrinsic thermal fluctuations within a real solid challenge the rigid body assumption that is central to Euler’s equations for the motion of a free body. Recently, we have introduced a dissipative and stochastic version of Euler’s equations in a thermodynamically consistent way (European Journal of Mechanics – A/Solids 103, 105,184 (2024)). This framework describes the evolution of both orientation and shape of a free body, incorporating internal thermal fluctuations and their concomitant dissipative mechanisms. In the present work, we demonstrate that, in the absence of angular momentum, the theory predicts that the principal axes unit vectors of a body undergo an anisotropic Brownian motion on the unit sphere, with the anisotropy arising from the body’s varying moments of inertia. The resulting equilibrium time correlation function of the principal eigenvectors decays exponentially. This theoretical prediction is confirmed in molecular dynamics simulations of small bodies. The comparison of theory and equilibrium MD simulations allow us to measure the orientational diffusion tensor. We then use this information in the Stochastic Dissipative Euler’s Equations, to describe a non-equilibrium situation of a body spinning around the unstable intermediate axis. The agreement between theory and simulations is excellent, offering a validation of the theoretical frameworkPublicación Unraveling internal friction in a coarse-grained protein model(AIP Publishing, 2025-03-19) Monago Díaz, Carlos Sebastián; Torre Rodríguez, Jaime Arturo de la; Delgado-Buscalioni, RafaelUnderstanding the dynamic behavior of complex biomolecules requires simplified models that not only make computations feasible but also reveal fundamental mechanisms. Coarse-graining (CG) achieves this by grouping atoms into beads, whose stochastic dynamics can be derived using the Mori–Zwanzig formalism, capturing both reversible and irreversible interactions. In liquid, the dissipative bead–bead interactions have so far been restricted to hydrodynamic couplings. However, friction does not only arise from the solvent but, notably, from the internal degrees of freedom missing in the CG beads. This leads to an additional “internal friction” whose relevance is studied in this contribution. By comparing with all-atom molecular dynamics (MD), we neatly show that in order to accurately reproduce the dynamics of a globular protein in water using a CG model, not only a precise determination of elastic couplings and the Stokesian self-friction of each bead is required. Critically, the inclusion of internal friction between beads is also necessary for a faithful representation of protein dynamics. We propose to optimize the parameters of the CG model through a self-averaging method that integrates the CG dynamics with an evolution equation for the CG parameters. This approach ensures that selected quantities, such as the radial distribution function and the time correlation of bead velocities, match the corresponding MD values.