arXiv subjects

J. A. de la Torre

Publications and source records attributed to J. A. de la Torre.

6 recordsLinked to original sources

arXiv2026

Self-averaging parameter estimation for coarse-grained particle models

We introduce a parameter estimation method that utilizes microscopic data, specifically averages and correlations of selected microscopic observables, to determine the parameters of a stochastic differential equation governing coarse-grained degrees of freedom. The method is not limited to static parameters found in the reversible part of the coarse-grained dynamics, such as those in the free energy function or potential of mean force, but also extends to dynamic parameters, including friction coefficients. The method couples the stochastic differential equation with free parameters to dynamic equations for the parameters. The coupled system self-averages, according to Anosov-Kifer's theorem, in such a way that the final state of the parameters gives coincidence between the microscopic and mesoscopic averages and correlations of selected observables. The method is validated in two examples: a Brownian particle in a harmonic potential, and a set of Brownian particles interacting hydrodynamically with the Rotne-Prager-Yamakawa mobility tensor. This latter case illustrates how the method can be used not only to determine coefficients but also state dependent transport properties - in this case, the position dependent form of the mobility tensor. The parameter estimation for these two models yields excellent results. Subsequently we use the methodology to study a bimodal-mass Lennard-Jones fluid for which we infer both the potential of mean force between the heavy particles and its hydrodynamic mobility tensor.

cond-mat.stat-mech↗

arXiv2026

Unraveling Internal Friction in a Coarse-Grained Protein Model

Understanding 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 arises 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 coarse-grained (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.

cond-mat.soft↗

arXiv2024

Stochastic Dissipative Euler's equations for a free body

Intrinsic 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, 105184 (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 principal axis 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 framework.

cond-mat.stat-mech↗

arXiv2023

Internal dissipation in the tennis racket effect

The phenomenon known as the tennis racket effect is observed when a rigid body experiences unstable rotation around its intermediate axis. In free space, this leads to the Dzhanibekov effect, where triaxial objects like a spinning wing bolt may continuously flip their rotational axis. 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 tennis racket effect. Euler's equations for a rigid body effectively describe the tennis racket effect, but cannot account for the precession relaxation effect. A recent theory has put forward a generalization of Euler's equations that includes dissipation in a thermodynamically consistent way. The theory displays two dissipative mechanisms: orientational diffusion and viscoelasticity. Here we show that orientational diffusion, rather than viscoelasticity, primarily drives precession relaxation and effectively suppresses the tennis racket effect.

physics.class-ph↗

arXiv2023

The role of thermal fluctuations in the motion of a free body

The 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.

cond-mat.stat-mech↗

arXiv2015

Finite element discretization of non-linear diffusion equations with thermal fluctuations

We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure of the continuum equation. Specifically, it conserves the total number of particles and fulfills an H-theorem as the original partial differential equation. Guided by the Theory of Coarse-Graining, we discuss the inclusion of thermal fluctuations in the non-linear diffusion equation. This sheds light on the meaning of such a fluctuating hydrodynamics equation and to the limitations of the approximations involved. The methodology proposed for the introduction of thermal fluctuations in finite element methods is general and valid for both regular and irregular grids in arbitrary dimensions. We focus here on simulations of the Ginzburg-Landau free energy functional using both regular and irregular 1D grids. Convergence of the numerical results is obtained for the static and dynamic structure factors as the resolution of the grid is increased.

cond-mat.stat-mech↗