46 citations · 93 across the 17 of their papers we have counts for
17 papers
A matrix-based spectral method for the numerical approximation of the fractional Laplacian and the fractional -Laplacian of functions defined on
Loïc Constantin, Carlota M. Cuesta, Francisco de la Hoz
Given a function defined on , its fractional -Laplacian is given by $$(-Δ)_p^su(\vec x)=C_1(n,s,p)\int_{\mathbb R^n}\frac{|u(\vec x)-u(\vec y)|^{p-2}(u(\vec x)-…
A Non-Recursive, Dimension-Independent Schur-Decomposition Algorithm for -Dimensional Sylvester Tensor Equations
Carlota M. Cuesta, Francisco de la Hoz
In this paper we present a non-recursive direct solver, based on the Bartels-Stewart algorithm, for -dimensional Sylvester tensor equations. The method relies only on Schur deco…
A study of the reconnection of antiparallel vortices in the infinitely thin case and in the finite thickness case
Francisco de la Hoz, Sergei Iakunin
The simplest case is the reconnection of a pair of antiparallel line vortices, e.g., condensation trails of an aircraft. The vortices first undergo long wave deformation (Crow wave…
Regular Polygonal Vortex Filament Evolution and Exponential Sums
Fernando Chamizo, Francisco de la Hoz
In this paper, we give a rigorous proof for the expression of the angle between adjacent sides in the skew polygons appearing at rational times in the evolution of regular polygons…
Numerical Approximation of Riesz-Feller Operators on
Carlota M. Cuesta, Francisco de la Hoz, Ivan Girona
In this paper, we develop an accurate pseudospectral method to approximate numerically the Riesz-Feller operator on , where , and $|γ|\le\min\{α, 2 -…
Numerical computation of the half Laplacian by means of a fast convolution algorithm
Carlota M. Cuesta, Francisco de la Hoz, Ivan Girona
In this paper, we develop a fast and accurate pseudospectral method to approximate numerically the half Laplacian of a function on , which is equivalent to…
A fast convolution method for the fractional Laplacian in
Jorge Cayama, Carlota M. Cuesta, Francisco de la Hoz +1
In this article, we develop a new method to approximate numerically the fractional Laplacian of functions defined on , as well as some more general singular integrals. A…
Vortex Filament Equation for a regular polygon in the hyperbolic plane
Francisco de la Hoz, Sandeep Kumar, Luis Vega
The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean…
On the Relationship between the One-Corner Problem and the -Corner Problem for the Vortex Filament Equation
Francisco de la Hoz, Luis Vega
In this paper, we give evidence that the evolution of the Vortex Filament Equation for a regular -corner polygon as initial datum can be explained at infinitesimal times as the…
A pseudo-spectral method for a non-local KdV-Burgers equation posed on
Francisco de la Hoz, Carlota Maria Cuesta
In this paper, we present a new pseudo-spectral method to solve the initial value problem associated to a non-local KdV-Burgers equation involving a Caputo-type fractional derivati…
An analytical and numerical study of steady patches in the disc
Francisco de la Hoz, Zineb Hassainia, Taoufik Hmidi +1
In this paper, we prove the existence of -fold rotating patches for the Euler equations in the disc, for both simply-connected and doubly-connected cases. Compared to the planar…
Doubly connected V-states for the generalized surface quasi-geostrophic equations
Francisco de la Hoz, Zineb Hassainia, Taoufik Hmidi
In this paper, we prove the existence of doubly connected V-states for the generalized SQG equations with They can be described by countable branches bifurcating from…
Doubly connected V-states for the planar Euler equations
Taoufik Hmidi, Francisco de la Hoz, Joan Mateu +1
We prove existence of doubly connected V-states for the planar Euler equations which are not annuli. The proof proceeds by bifurcation from annuli at simple "eigenvalues". The bifu…
The vortex filament equation as a pseudorandom generator
Francisco de la Hoz, Luis Vega
In this paper, we consider the evolution of the so-called vortex filament equation (VFE), \begin{equation*} \mathbf X_t = \mathbf X_s\wedge\mathbf X_{ss}, \end{equation*} taking a…
Vortex Filament Equation for a Regular Polygon
Francisco de la Hoz, Luis Vega
In this paper, we study the evolution of the vortex filament equation (VFE), with being a regular planar poly…
Numerical study of a flow of regular planar curves that develop singularities at finite time
Francisco de la Hoz
In this paper, we will study the following geometric flow, obtained by Goldstein and Petrich while considering the evolution of a vortex patch in the plane under Euler's equations,…
A numerical study of the self-similar solutions of the Schroedinger Map
Francisco de la Hoz, Carlos Garcia-Cervera, Luis Vega
We present a numerical study of the self-similar solutions of the Localized Induction Approximation of a vortex filament. These self-similar solutions, which constitute a one-param…