Manuel Solano | (Benemérita) Universidad Autónoma de Puebla (original) (raw)

Papers by Manuel Solano

An object falling in a fluid reaches a terminal velocity when the drag force and its weight are b... more An object falling in a fluid reaches a terminal velocity when the drag force and its weight are balanced. Contrastingly, an object impacting into a granular medium rapidly dissipates all its energy and comes to rest always at a shallow depth. Here we study, experimentally and theoretically, the penetration dynamics of a projectile in a very long silo filled with expanded polystyrene particles. We discovered that, above a critical mass, the projectile reaches a terminal velocity and, therefore, an endless penetration.

Center-location of a laser spot is a problem of interest when the laser is used for processing an... more Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

We determined the total system elastic Helmholtz free energy, under the constraints of constant t... more We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. “hard spheres”) embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.

Manual of the suite DensToolKit. Installation, usage, and scientific background.

Epstein and Plesset's seminal work on the rate of gas bubble dissolution and growth in a simple l... more Epstein and Plesset's seminal work on the rate of gas bubble dissolution and growth in a simple liquid is generalized to render it applicable to a gas bubble embedded in a soft elastic solid. Both the underlying diffusion equation and the expression for the gas bubble pressure were modified to allow for the non-zero shear modulus of the medium. The extension of the diffusion equation results in a trivial shift (by an additive constant) in the value of the diffusion coefficient, and does not change the form of the rate equations. But the use of a generalized Young–Laplace equation for the bubble pressure resulted in significant differences on the dynamics of bubble dissolution and growth, relative to an inviscid liquid medium. Depending on whether the salient parameters (solute concentration, initial bubble radius, surface tension, and shear modulus) lead to bubble growth or dissolution, the effect of allowing for a non-zero shear modulus in the generalized Young–Laplace equation is to speed up the rate of bubble growth, or to reduce the rate of bubble dissolution, respectively. The relation to previous work on visco-elastic materials is discussed, as is the connection of this work to the problem of Decompression Sickness (specifically, “the bends”). Examples of tissues to which our expressions can be applied are provided. Also, a new phenomenon is predicted whereby, for some parameter values, a bubble can be metastable and persist for long times, or it may grow, when embedded in a homogeneous under-saturated soft elastic medium.

We solved the Laplace equation for the radius of an arterial gas embolism (AGE), during and after... more We solved the Laplace equation for the radius of an arterial gas embolism (AGE), during and after breath-hold diving. We used a simple three-region diffusion model for the AGE, and applied our results to two types of breath-hold dives: single, very deep competitive-level dives and repetitive shallower breath-hold dives similar to those carried out by indigenous commercial pearl divers in the South Pacific. Because of the effect of surface tension, AGEs tend to dissolve in arterial blood when arteries remote from supersaturated tissue. However if, before fully dissolving, they reach the capillary beds that perfuse the brain and the inner ear, they may become inflated with inert gas that is transferred into them from these contiguous temporarily supersaturated tissues. By using simple kinetic models of cerebral and inner ear tissue, the nitrogen tissue partial pressures during and after the dive(s) were determined. These were used to theoretically calculate AGE growth and dissolution curves for AGEs lodged in capillaries of the brain and inner ear. From these curves it was found that both cerebral and inner ear decompression sickness are expected to occur occasionally in single competitive-level dives. It was also determined from these curves that for the commercial repetitive dives considered, the duration of the surface interval (the time interval separating individual repetitive dives from one another) was a key determinant, as to whether inner ear and/or cerebral decompression sickness arose. Our predictions both for single competitive-level and repetitive commercial breath-hold diving were consistent with what is known about the incidence of cerebral and inner ear decompression sickness in these forms of diving.

DensToolKit is a suite of cross-platform, optionally parallelized, programs for analyzing the mol... more DensToolKit is a suite of cross-platform, optionally parallelized, programs for analyzing the molecular electron density (ρ
) and several fields derived from it. Scalar and vector fields, such as the gradient of the electron density (∇ρ
), electron localization function (ELF) and its gradient, localized orbital locator (LOL), region of slow electrons (RoSE), reduced density gradient, localized electrons detector (LED), information entropy, molecular electrostatic potential, kinetic energy densities K
and G
, among others, can be evaluated on zero, one, two, and three dimensional grids. The suite includes a program for searching critical points and bond paths of the electron density, under the framework of Quantum Theory of Atoms in Molecules. DensToolKit also evaluates the momentum space electron density on spatial grids, and the reduced density matrix of order one along lines joining two arbitrary atoms of a molecule. The source code is distributed under the GNU-GPLv3 license, and we release the code with the intent of establishing an open-source collaborative project. The style of DensToolKit’s code follows some of the guidelines of an object-oriented program. This allows us to supply the user with a simple manner for easily implement new scalar or vector fields, provided they are derived from any of the fields already implemented in the code. In this paper, we present some of the most salient features of the programs contained in the suite, some examples of how to run them, and the mathematical definitions of the implemented fields along with hints of how we optimized their evaluation. We benchmarked our suite against both a freely-available program and a commercial package. Speed-ups of ∼2×, and up to 12× were obtained using a non-parallel compilation of DensToolKit for the evaluation of fields. DensToolKit takes similar times for finding critical points, compared to a commercial package. Finally, we present some perspectives for the future development and growth of the suite.

We prove that some basic aspects of gravity commonly attributed to the modern connection-based ap... more We prove that some basic aspects of gravity commonly attributed to the modern connection-based approaches, can be reached naturally within the usual Riemannian geometry-based approach, by assuming the independence between the metric and the connection of the background manifold. These aspects are: 1) the BF-like field theory structure of the Einstein–Hilbert action, of the cosmological term, and of the corresponding equations of motion; 2) the formulation of Maxwellian field theories using only the Riemannian connection and its corresponding curvature tensor, and the subsequent unification of gravity and gauge interactions in a four dimensional field theory; 3) the construction of four and three dimensional geometrical invariants in terms of the Riemann tensor and its traces, particularly the formulation of an anomalous Chern–Simons topological model where the action of diffeomorphisms is identified with the action of a gauge symmetry, close to Witten’s formulation of three-dimensional gravity as a Chern–Simon gauge theory. 4) Tordions as propagating and non-propagating fields are also formulated in this approach. This new formulation collapses to the usual one when the metric connection is invoked, and certain geometrical structures very known in the traditional literature can be identified as remanent structures in this collapse.

Manual of the suite DensToolKit. Installation, usage, and scientific background.