arXiv subjects

C. Núñez

Publications and source records attributed to C. Núñez.

11 recordsLinked to original sources

arXiv2025

Symplectic Hamiltonian Hybridizable Discontinuous Galerkin Methods for Linearized Shallow Water Equations

This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an equivalent formulation of the equations by introducing an auxiliary variable. Then, we discretize the space variables using HDG methods, resulting in a semi-discrete scheme that preserves a discrete version of the Hamiltonian structure. The use of an alternative formulation with the auxiliary variable is crucial for developing the HDG scheme that preserves this Hamiltonian structure. The resulting system is subsequently discretized in time using symplectic integrators, ensuring the energy conservation of the fully discrete scheme. We present numerical experiments that demonstrate optimal convergence rates for all variables and showcase the conservation of total energy, as well as the evolution of other physical quantities.

math.NA↗

arXiv2022

Generalized Pitchfork Bifurcations in D-Concave Nonautonomous Scalar Ordinary Differential Equations

The global bifurcation diagrams for two different one-parametric perturbations ($+λx$ and $+λx^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant solution, that $f$ is recurrent in $t$, and that its first derivative with respect to $x$ is a strictly concave function. The use of the skewproduct formalism allows us to identify bifurcations with changes in the number of minimal sets and in the shape of the global attractor. In the case of perturbation $+λx$, a so-called global generalized pitchfork bifurcation may arise, with the particularity of lack of an analogue in autonomous dynamics. This new bifurcation pattern is extensively investigated in this work.

math.DS↗

arXiv2022

Bifurcation Theory of Attractors and Minimal Sets in D-Concave Nonautonomous Scalar Ordinary Differential Equations

Two one-parametric bifurcation problems for scalar nonautonomous ordinary differential equations are analyzed assuming the coercivity of the time-dependent function determining the equation and the concavity of its derivative with respect to the state variable. The skewproduct formalism leads to the analysis of the number and properties of the minimal sets and of the shape of the global attractor, whose abrupt variations determine the occurrence of local saddle-node, local transcritical and global pitchfork bifurcation points of minimal sets and of discontinuity points of the global attractor.

math.DS↗

arXiv2017

Spin-polarized electric current in silicene nanoribbons induced by atomic adsorption

We investigate the nonequilibrium transport properties of a silicene armchair nanoribbon with a random distribution of adsorbed atoms in apex positions. A ferromagnetic insulator grown below the nanoribbon splits spin-up and spin-down electron bands and gives rise to a spin polarization of the conductance. The conductance vanishes when the Fermi energy matches the adatom levels due to the coupling of adatom localized states with the continuum spectra of the nanoribbon. This is the well-known Fano effect, resulting in a spin-dependent antiresonance in the conductance. The different antiresonance energies of spin-up and spin-down electrons give rise to a full spin polarization of the conductance in a broad energy window. This spin-dependent Fano effect opens the possibility to using it in spintronics as a tuneable source of polarized electrons.

cond-mat.mes-hall↗

arXiv1998

Bogomol'nyi Bounds and the Supersymmetric Born-Infeld Theory

We study N=2 supersymmetric Born-Infeld-Higgs theory in 3 dimensions and derive Bogomol'nyi relations in its bosonic sector. A peculiar coupling between the Higgs and the gauge field (with dynamics determined by the Born-Infeld action) is forced by supersymmetry. The resulting equations coincide with those arising in the Maxwell-Higgs model. Concerning Bogomol'nyi bounds for the vortex energy, they are derived from the N=2 supersymmetry algebra.

hep-th↗

arXiv1997

Loop Corrections and Bosonization Formulae

We study the functional integrals that appear in a path integral bosonization procedure for more than two spacetime dimensions. Since they are not in general exactly solvable, their evaluation by a suitable loop expansion would be a natural procedure, even if the exact fermionic determinant were known. The outcome of our study is that we can consistently ignore loop corrections in the functional integral defining the bosonized action, if the same is done for the functional integral corresponding to the bosonic representation of the generating functional. If contributions up to some order $l$ in the number of loops are included in both integrals, all but the lowest terms cancel out in the final result for the generating functional.

hep-th↗

arXiv1996

Current Algebra and Bosonization in Three Dimensions

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.

hep-th↗

arXiv1995

An Alternative Dimensional Reduction Prescription

We propose an alternative dimensional reduction prescription which in respect with Green functions corresponds to drop the extra spatial coordinate. From this, we construct the dimensionally reduced Lagrangians both for scalars and fermions, discussing bosonization and supersymmetry in the particular 2-dimensional case. We argue that our proposal is in some situations more physical, in the sense that it mantains the form of the interactions between particles, thus preserving the dynamics corresponding to the higher dimensional space.

hep-th↗

arXiv1995

QUANTUM CORRECTIONS AND EXTREMAL BLACK HOLES

We consider static solutions of two dimensional dilaton gravity models as toy laboratories to address the question of the final fate of black holes. A non perturbative correction to the CGHS potential term is shown to lead classically to an extremal black hole geometry, thus providing a plausible solution to Hawking evaporation paradox. However, the full quantum theory does not admit an extremal solution.

hep-th↗

arXiv1993

Strings in Plane Wave Backgrounds Revisited

String theory in an exact plane wave background is explored. A new example of singularity in the sense of string theory for nonsingular spacetime metric is presented. The 4-tachyon scattering amplitude is constructed. The spectrum of states found from the poles in the factorization turns out to be equivalent to that of the theory in flat space-time. The massless vertex operator is obtained from the residue of the first order pole.

hep-th↗

arXiv1993

Nondiagonal $CP_m$ Coset Models and their PoincarÉ Polynomials

$N=2$ coset models of the type $SU(m+1)/SU(m)\times U(1)$ with nondiagonal modular invariants for both $SU(m+1)$ and $SU(m)$ are considered. Poincaré polynomials of the corresponding chiral rings of these algebras are constructed. They are used to compute the number of chiral generations of the associated string compactifications. Moddings by discrete symmetries are also discussed.

hep-th↗