Departamento de Matemática Aplicadahttps://hdl.handle.net/10481/313612024-07-25T11:01:53Z2024-07-25T11:01:53ZENO and WENO cubic quasi-interpolating splines in Bernstein–Bézier formAràndiga, F.Barrera Rosillo, DomingoEddargani, Salahhttps://hdl.handle.net/10481/934682024-07-25T09:51:55ZENO and WENO cubic quasi-interpolating splines in Bernstein–Bézier form
Aràndiga, F.; Barrera Rosillo, Domingo; Eddargani, Salah
In this paper we propose the use of 𝐶������1-continuous cubic quasi-interpolation schemes expressed
in Bernstein–Bézier form to approximate functions with jumps. The construction of these
schemes is explicit and consists of directly attaching the Bernstein–Bézier coefficients to
appropriate combinations of the given data values. This construction can lead to quasiinterpolation
schemes with free parameters. This allows to write these schemes of optimal
convergence order as a non-negative convex combination of certain quasi-interpolation schemes
of lower convergence order. The idea behind that, is to divide the data set used to define a quasiinterpolant
of optimal order into subsets, and then define the associated quasi-interpolants.
The free parameters facilitate the choice of the convex combination weights. We then apply
the WENO approach to the weights to eliminate the Gibbs phenomenon that occurs when we
approximate in a non-smooth region. The proposed schemes are of optimal order in the smooth
regions and near optimal order is achieved in the neighboring region of discontinuity.
Quantum revivals in HgTe/CdTe quantum wells and topological phase transitionsMayorgas Reyes, AlbertoCalixto Molina, ManuelCordero, Nicolás A.Romera Gutiérrez, ElviraCastaños Garza, Octavio Héctorhttps://hdl.handle.net/10481/934462024-07-24T10:29:45ZQuantum revivals in HgTe/CdTe quantum wells and topological phase transitions
Mayorgas Reyes, Alberto; Calixto Molina, Manuel; Cordero, Nicolás A.; Romera Gutiérrez, Elvira; Castaños Garza, Octavio Héctor
The time evolution of a wave packet is a tool to detect topological phase transitions in
two-dimensional Dirac materials, such as graphene and silicene. Here we extend the
analysis to HgTe/CdTe quantum wells and study the evolution of their electron current
wave packet, using 2D effective Dirac Hamiltonians and different layer thicknesses. We
show that the two different periodicities that appear in this temporal evolution reach
a minimum near the critical thickness, where the system goes from normal to inverted
regime. Moreover, the maximum of the electron current amplitude changes with the
layer thickness, identifying that current maxima reach their higher value at the critical
thickness. Thus, we can characterize the topological phase transitions in terms of the
periodicity and amplitude of the electron currents.
New methods for quasi-interpolation approximations: Resolution of odd-degree singularitiesBuhmann, MartinJäger, JaninJódar, JoaquínRodríguez González, Miguel Luishttps://hdl.handle.net/10481/931602024-07-16T13:55:59ZNew methods for quasi-interpolation approximations: Resolution of odd-degree singularities
Buhmann, Martin; Jäger, Janin; Jódar, Joaquín; Rodríguez González, Miguel Luis
In this paper, we study functional approximations where we choose the so-called radial
basis function method and more specifically, quasi-interpolation. From the various available
approaches to the latter, we form new quasi-Lagrange functions when the orders of the
singularities of the radial function’s Fourier transforms at zero do not match the parity of the
dimension of the space, and therefore new expansions and coefficients are needed to overcome
this problem. We develop explicit constructions of infinite Fourier expansions that provide these
coefficients and make an extensive comparison of the approximation qualities and – with a
particular focus – polynomial reproduction and uniform approximation order of the various
formulae. One of the interesting observations concerns the link between algebraic conditions of
expansion coefficients and analytic properties of localness and convergence.
HICODY_01_DMP_V1.0_WP1Poyato Sánchez, Jesús Davidhttps://hdl.handle.net/10481/931492024-07-17T07:35:13ZHICODY_01_DMP_V1.0_WP1
Poyato Sánchez, Jesús David
This material has been created for pedagogical purposes to serve as guide for the management of scientific data for different users such as undergraduate students, master and phD students, and post-doctoral researchers. In particular, this report describes the initial Data Management Plan (DMP) for the project HICODY (101064402), which is funded by the European Commission through the Marie Skłodowska-Curie Actions (MSCA) as part of the Postdoctoral Fellowships Programme (HORIZON-MSCA-2021-PF-01). The coordinator of this DMP, who is also the researcher associated to the funded fellowship, is Dr. David Poyato from the Department of Applied Mathematics at the University of Granada (UGR), Spain (the beneficiary institution). The purpose of this DMP is to provide a detailed description of the procedures of the datasets generated during the lifetime of the project. This DMP will describe the main data management principles in terms of data standards and metadata, sharing, archiving, preservation, and security. This is an alive document that will be updated at regular intervals during the lifetime of the project and be allocated in the institutional repository of the UGR, DIGIBUG.
Iterative schemes for linear equations of the second kind and related inverse problemsBerenguer Maldonado, María IsabelRuiz Galán, Manuelhttps://hdl.handle.net/10481/929172024-07-02T09:29:26ZIterative schemes for linear equations of the second kind and related inverse problems
Berenguer Maldonado, María Isabel; Ruiz Galán, Manuel
This paper consists of two parts. The first one deals with the generation of an iterative algorithm to obtain an approximate solution of a linear equation of the second kind in a Banach space. This generation is based on a perturbed version of the geometric series theorem which, in particular, allows us to find a family of unisolvent linear Fredholm integral equations of the second kind, even when the associated linear operator has norm greater than or equal to 1. When we consider Fredholm equations of this type and linear Volterra integral equations of second kind, the numerical schemes obtained when appropriate Schauder bases are also introduced in the spaces where the equations operate, enable us to approximate their respective solutions iteratively. The second part of this work focuses on the design of a numerical method for solving an inverse problem associated with a linear equation of the second kind in a Banach space, a method which we apply to problems of parameter estimation related to the two classes of integral equations mentioned above.