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Rafael Lopez

Publications and source records attributed to Rafael Lopez.

17 recordsLinked to original sources
arXiv2026

Serially Improved GTOs for Molecular Applications (SIGMA): basis sets from monovalent ions

A new family of ionic basis sets, denoted i{\sigma}XZ1, is presented for molecular calculations on systems containing monovalent ions. The basis sets extend the SIGMA family by explicitly accounting for the different electronic structure of cations and anions. Auxiliary basis sets for resolution-of-the-identity calculations are also developed for the Coulomb term. The performance of the proposed basis sets is assessed for alkali-halide clusters. Compared with conventional basis sets, i{\sigma}XZ1 provides an accurate description of structural, energetic, and electronic properties while showing remarkable robustness against near-linear dependencies, allowing stable calculations on systems containing up to 792 NaCl units. These features make the i{\sigma}XZ1 family a reliable and efficient alternative for large-scale calculations on ionic systems.

physics.chem-ph↗
arXiv2026

Some minimum principles for a class of nonlinear elliptic problems in divergence form

In this paper we study a general class of nonlinear elliptic problems in divergence form. First, we prove that the solutions to these problems satisfy a convexity property when the given domain is strictly convex. Then, making use of this convexity property, we develop some minimum principles for an appropriate $P$-function, in the sense of L.~E.~Payne. Finally, this new minimum principle is applied to find a priori estimates for the solutions, in terms of the mean curvature of the boundary of the underlying domain.

math.AP↗
arXiv2024

Conformal trajectories in 3-dimensional space form

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds $M^3$. Given a conformal vector field $V\in\mathfrak{X}(M^3)$, a conformal trajectory of $V$ is a regular curve $γ$ in $M^3$ satisfying $\nabla_{γ'}γ'=q\, V\timesγ'$, for some fixed non-zero constant $q\in {\mathbb{R}}$. In this paper, we study conformal trajectories in the space forms ${\mathbb{R}}^3$, ${\mathbb{S}}^3$ and ${\mathbb{H}}^3$. For (non-Killing) conformal vector fields in ${\mathbb{S}}^3$ (respectively in ${\mathbb{H}}^3$), we prove that conformal trajectories have constant curvature and its torsion is a linear combination of trigonometric (respectively hyperbolic) functions on the arc-length parameter. In the case of Euclidean space ${\mathbb{R}}^3$, we obtain the same result for the radial vector field and characterising all conformal trajectories.

math.DG↗
arXiv2023

Classification of separable hypersurfaces with constant sectional curvature

In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean $n$-space $\mathbb{R}^n$. In dimension $n=3$, this classification was solved by Hasanis and López [Manuscripta Math. 166, 403-417 (2021)]. When $n>3$, we prove that the separable hypersurfaces of null sectional curvature are three particular families of such hypersurfaces. Finally, we prove that hyperspheres are the only separable hypersurfaces with nonzero constant sectional curvature.

math.DG↗
arXiv2022

Robotic Maintenance of Road Infrastructures: The HERON Project

Of all public assets, road infrastructure tops the list. Roads are crucial for economic development and growth, providing access to education, health, and employment. The maintenance, repair, and upgrade of roads are therefore vital to road users' health and safety as well as to a well-functioning and prosperous modern economy. The EU-funded HERON project will develop an integrated automated system to adequately maintain road infrastructure. In turn, this will reduce accidents, lower maintenance costs, and increase road network capacity and efficiency. To coordinate maintenance works, the project will design an autonomous ground robotic vehicle that will be supported by autonomous drones. Sensors and scanners for 3D mapping will be used in addition to artificial intelligence toolkits to help coordinate road maintenance and upgrade workflows.

cs.RO↗
arXiv2021

Translating solitons of translation and homothetical types

We prove that if a translating soliton can be expressed as the sum of two curves and one of these curves is planar, then the other curve is also planar and consequently the surface must be a plane or a grim reaper. We also investigate translating solitons that can be locally written as the product of two functions of one variable. We extend the results in Lorentz-Minkowski space.

math.DG↗
arXiv2021

Ruled translating solitons in Minkowski 3-space

We characterize all ruled translating solitons in Minkowski 3-space. In contrast to the Euclidean space, we find ruled translating solitons that are not cylindrical. These surfaces appear when the vector field that defines the rulings, viewed as a curve, is a lightlike straight line. We also classify all cylindrical translating solitons, obtaining surfaces that can be considered as analogous to the grim reapers of Euclidean space, but also other surfaces which have no a counterpart in the Euclidean space.

math.DG↗
arXiv2020

Multi-Iteration Stochastic Optimizers

We introduce Multi-Iteration Stochastic Optimizers, a novel class of first-order stochastic methods that control the relative $L^2$ error using successive control variates along the iteration path. By exploiting correlations between iterates, these control variates reduce the estimator's variance, making an accurate mean gradient estimation computationally affordable. Our approach centers on the Multi-Iteration stochastiC Estimator (MICE), which can be seamlessly coupled with any first-order stochastic optimizer due to its non-intrusive design. The algorithm adaptively selects which iterates to include in its index set. We provide both an error analysis of MICE and a convergence analysis for Multi-Iteration Stochastic Optimizers across various problem classes, including some non-convex cases. In the smooth, strongly convex setting, we demonstrate that to approximate a minimizer within a tolerance $tol$, SGD-MICE requires, on average, $O(tol^{-1})$ stochastic gradient evaluations, compared to $O(tol^{-1}\log(tol^{-1}))$ for SGD with adaptive batch sizes. In numerical experiments, SGD-MICE achieved the desired tolerance with fewer than 3\% of the gradient evaluations required by adaptive batch SGD. Additionally, MICE offers a straightforward stopping criterion based on the gradient norm, validated through consistency tests. To assess its efficiency, we present examples using both SGD-MICE and Adam-MICE, including a stochastic adaptation of the Rosenbrock function and logistic regression on various datasets. Compared to SGD, SAG, SAGA, SVRG, and SARAH, our approach consistently reduces the gradient sampling cost without the need for extensive parameter tuning.

math.OC↗
arXiv2016

Remarks on the boundary curve of a constant mean curvature topological disc

We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature of the boundary curve, and a condition for the surface to be totally umbilic in terms of the normal curvature.

math.DG↗
arXiv2009

Constant angle surfaces in Minkowski space

A constant angle surface in Minkowski space is a spacelike surface whose unit normal vector field makes a constant hyperbolic angle with a fixed timelike vector. In this work we study and classify these surfaces. In particular, we show that they are flat. Next we prove that a tangent developable surface (resp. cylinder, cone) is a constant angle surface if and only if the generating curve is a helix (resp. a straight-line, a circle).

math.DG↗
arXiv2006

Rotational linear Weingarten surfaces of hyperbolic type

A linear Weingarten surface in Euclidean space ${\bf R}^3$ is a surface whose mean curvature $H$ and Gaussian curvature $K$ satisfy a relation of the form $aH+bK=c$, where $a,b,c\in {\bf R}$. Such a surface is said to be hyperbolic when $a^2+4bc<0$. In this paper we classify all rotational linear Weingarten surfaces of hyperbolic type. As a consequence, we obtain a family of complete hyperbolic linear Weingarten surfaces in ${\bf R}^3$ that consists into periodic surfaces with self-intersections.

math.DG↗
arXiv2005

Stationary liquid drops in Lorentz-Minkowski space

This paper analyzes the configurations of shapes that shows a spacelike liquid drop in Minkowski space deposited over a spacelike plane $Π$. We assume the presence of a uniform gravity field directed toward $Π$ and that the volume of the drop is prescribed. Our interest are the liquid drops that are critical points of the energy of the corresponding mechanical system and we will say then that the liquid drop is stationary. In such case, the liquid-air interface is determined by the condition that the mean curvature is a linear function of distance from $Π$ and that the drop makes a constant hyperbolic angle of contact with the plate $Π$. As first result, we shall prove that the liquid drop must be rotational symmetric with respect to an axis orthogonal to $Π$. Then we prove the existence and uniqueness of symmetric solutions for a given angle of contact with $Π$. Finally, we shall study the shapes that a liquid drop can adopt in terms of its size. So, we shall derive estimates of its height, volume and area of the wetted surface on $Π$.

math-ph↗
arXiv2005

Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space

In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space $ł^3$ and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational symmetric surfaces are the only compact spacelike surfaces in $ł^3$ of constant mean curvature bounded by two concentric circles in parallel planes. As conclusion, we characterize spacelike surfaces of revolution with constant mean curvature as the only that either i) are the solutions of the exterior Dirichlet problem for constant boundary data or ii) have an isolated conical-type singularity.

math.DG↗