Antonio Capella

Universidad Nacional Autónoma de México | UNAM · Institute of Mathematics

We provide quantitative inner and outer bounds for the symmetric quasiconvex hull Qe(U)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q^e({\mathcal {U}})$$\end{documen...

We introduce a Bayesian sequential data assimilation and forecasting method for non-autonomous dynamical systems. We applied this method to the current COVID-19 pandemic. It is assumed that suitable transmission, epidemic and observation models are available and previously validated. The transmission and epidemic models are coded into a dynamical s...

We study some particular cases of the n-well problem in two-dimensional linear elasticity. Assuming that every well in U⊂Rsym2×2 belong to the same two-dimensional affine subspace, we characterize the symmetric lamination convex hull Le(U) for any number of wells in terms of the symmetric lamination convex hull of all three-well subsets contained i...

We introduce a Bayesian sequential data assimilation method for COVID-19 forecasting. It is assumed that suitable transmission, epidemic and observation models are available and previously validated and the transmission and epidemic models are coded into a dynamical system. The observation model depends on the dynamical system state variables and p...

We present a forecasting model aim to predict hospital occupancy in metropolitan areas during the current COVID-19 pandemic. Our SEIRD type model features asymptomatic and symptomatic infections with detailed hospital dynamics. We model explicitly branching probabilities and non-exponential residence times in each latent and infected compartments....

We study some particular cases of the $n$-well problem in two-dimensional linear elasticity. Assuming that all wells in $\mathcal{U}\subset\mathbb{R}^{2\times 2}_\text{sym}$ belong to the same affine subspace, we characterize the symmetric lamination convex hull $L^e(\mathcal{U})$ for any number of wells in terms of the symmetric lamination convex...

We propose an efficient Bayesian approach to infer a fault displacement from geodetic data in a slow slip event. Our physical model of the slip process reduces to a multiple linear regression subject to constraints. Assuming a Gaussian model for the geodetic data and considering a truncated multivariate normal prior distribution for the unknown fau...

We give quantitative estimates for the quasiconvex hull $Q^e(\mathcal{U})$ on linear strains generated by a three well set $\mathcal{U}$ in the space of $2\times 2$ symmetric matrices $\mathbb{R}^{2\times2}_{sym}$. In our study, we consider all possible compatible configurations for the three wells and prove that if there exist two matrices in $\ma...

The effective reproduction number $R_t$ measures an infectious disease's transmissibility as the number of secondary infections in one reproduction time in a population having both susceptible and non-susceptible hosts. Current approaches do not quantify the uncertainty correctly in estimating $R_t$, as expected by the observed variability in conta...

We present a forecasting model aim to predict hospital occupancy in metropolitan areas during the current COVID-19 pandemic. Our SEIRD type model features asymptomatic and symptomatic infections with detailed hospital dynamics. We model explicitly branching probabilities and non-exponential residence times in each latent and infected compartments....

We present a compartmental SEIRD model aimed at forecasting hospital occupancy in metropolitan areas during the current COVID-19 outbreak. The model features asymptomatic and symptomatic infections with detailed hospital dynamics. We model explicitly branching probabilities and non exponential residence times in each latent and infected compartment...

The main objective of this work is to demonstrate that non-local terms of the structure variable and shear-stress is a sufficient condition to predict multiple bands in rheologically complex fluids, i.e., shear-thickening fluids. Here, shear bands are considered as dissipative structures arising from spatial instabilities (Turing patterns) rather t...

This paper presents the principles and application of a super-resolution (SR) technique aimed to obtain high resolution spectra obtained from the optogalvanic effect in Neon and Argon discharges over the 413-423 nm wavelength range. By applying the super-resolution algorithm to the experimental data, a surprising 70-fold reduction of the linewidth...

A mathematical description of transformation processes in magnetic shape memory alloys (MSMA) under applied stresses and external magnetic fields needs a combination of micromagnetics and continuum elasticity theory. In this note, we discuss the so-called constrained theories, i.e., models where the state described by the pair (linear strain, magne...

We are interested in the cubic-to-tetragonal phase transition in a shape memory alloy. We consider geometrically linear elasticity. In this framework, Dolzmann and Müller have shown that the only stress-free configurations are (locally) twins (i.e. laminates of just two of the three martensitic variants). However, configurations with arbitrarily sm...

We investigate stable solutions of elliptic equations of the type where n ≥ 2, s ∈ (0, 1), λ ≥0 and f is any smooth positive superlinear function. The operator (− Δ) stands for the fractional Laplacian, a pseudo-differential operator of order 2s. According to the value of λ, we study the existence and regularity of weak solutions u.

Whenever in a classical accretion disk the thin disk approximation fails interior to a certain radius, a transition from Keplerian to radial infalling trajectories should occur. We show that this transition is actually expected to occur interior to a certain critical radius, provided surface density profiles are steeper than $\Sigma(R) \propto R^{-...

We consider the nonlinear and nonlocal problem $$ A_{1/2}u=|u|^{2^\sharp-2}u\ \text{in \Omega, \quad u=0 \text{on} \partial\Omega $$where $A_{1/2}$ represents the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions, $\Omega$ is a bounded smooth domain in $\R^n$, $n\ge 2$ and $2^{\sharp}=2n/(n-1)$ is the critical...

We investigate stable solutions of elliptic equations of the type \begin{equation*} \left \{ \begin{aligned} (-\Delta)^s u&=\lambda f(u) \qquad {\mbox{ in $B_1 \subset \R^{n}$}} \\ u&= 0 \qquad{\mbox{ on $\partial B_1$,}}\end{aligned}\right . \end{equation*} where $n\ge2$, $s \in (0,1)$, $\lambda \geq 0$ and $f$ is any smooth positive superlinear f...

We study a three-dimensional model for alloys that undergo a cubic-to-tetragonal phase transition in the martensitic phase. Any pair of the three martensitic variants can form a stress-free laminate. However, this laminate is only compatible on average with the remaining variant. The resulting local stresses favor a microstructure if all three vari...

We consider semi-stable, radially symmetric, and decreasing solutions of a reaction equation involving the p-Laplacian, where the reaction term is a locally Lipschitz function, and the domain is the unit ball. For this class of radial solutions, which includes local minimizers, we establish pointwise and Sobolev estimates which are optimal and do n...

We consider semi-stable, radially symmetric, and decreasing solutions of − Δp u = g(u) in the unit ball of \({\mathbb{R}^n}\) , where p > 1, Δp is the p-Laplace operator, and g is a locally Lipschitz function. For this class of radial solutions, which includes local minimizers, we establish pointwise, L q , and W 1,q estimates which are optimal and...

In certain regimes and for relative small applied fields, magnetic domain walls behave as mechanical particles in a viscous fluid. By analogy their dynamic can be described with an evolution equation of the form where M and are the effective wall mass and wall mobility, and H is an applied forcing. These effective parameters depend on the particul...

The cross-tie domain wall structure in micrometre and sub-micrometre wide patterned elements of NiFe, and a thickness range of 30 to 70nm, has been studied by Lorentz microscopy. Whilst the basic geometry of the cross-tie repeat units remains unchanged, their density increases when the cross-tie length is constrained to be smaller than the value as...

We investigate the magnetization dynamics in soft ferromagnetic films with small damping. In this case, the gyrotropic nature of Landau–Lifshitz–Gilbert dynamics and the shape anisotropy effects from stray-field interactions effectively lead to a wave-type dynamics for the in-plane magnetization. We apply this result to study the motion of Néel wal...

We discuss regularity issues for minimizers of three nonlinear ellip-tic problems. They concern minimal cones, minimizing harmonic maps into a hemisphere, and radial local minimizers of semilinear elliptic equa-tions. We describe the strong analogies among the three regularity the-ories. They all use a method originated in a paper of J. Simons on t...

We consider a special class of radial solutions of semilinear equations −Δu=g(u) in the unit ball of Rn. It is the class of semi-stable solutions, which includes local minimizers, minimal solutions, and extremal solutions. We establish sharp pointwise, Lq, and Wk,q estimates for semi-stable radial solutions. Our regularity results do not depend on...

The use of 4 power-limited, variable-specific-impulse propulsion system to transfer a vehicle from the smaller primary to an arbitrary circular restricted three-body trajectory and the subsequent guidance along all phases of the complete trajectory is investigated. As a practical application, the transfer of a spacecraft with a finite-burn propulsi...

We establish that every nonconstant bounded radial solution u of -Deltau = f(u) in all of R-n is unstable if n less than or equal to 10. The result applies to every C-1 nonlinearity f satisfying a generic nondegeneracy condition. In particular, it applies to every analytic and every power-like nonlinearity. We also give an example of a nonconstant...

It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential opera...

In ferromagnetic materials, the gyrotropic nature of Landau-Lifshitz-Gilbert dynamics and anisotropic effects from stray-field interaction lead in certain regimes effectively to a wave-type dynamic equation. In the case of soft thin films and small Gilbert damping, we investigate the motion of Néel walls and prove the existence of traveling wave so...

We establish that every nonconstant bounded radial solution u of −?u = f (u) in all of Rn is unstable if n ? 10. The result applies to every C1 nonlinearity f satisfying a generic nondegeneracy condition. In particular, it applies to every analytic and every power-like nonlinearity. We also give an example of a nonconstant bounded radial solution u...

En este artículo primero se desarrolla un esquema en diferencias finitas de segundo orden, tanto en la discretización espacial como temporal, para la resolución de la versión lineal de la ecuación de Korteweg–de Vries (KdV) en dominios acotados. Seguidamente, y basándose en el esquema descrito anteriormente, se presenta un modelo numérico para impl...