arXiv subjects

A. Durán

Publications and source records attributed to A. Durán.

18 recordsLinked to original sources

arXiv2026

The numerical solution of 2D Boussinesq/Boussinesq models for internal waves with spectral methods

The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of fluids with different densities and subjected to a Boussinesq physical regime in each layer. Well-posedness of the periodic initial-value problem (ivp) of the systems is first analized. Then, a discretization in space based on the spectral Fourier-Galerkin method is introduced and error estimates for the semidiscrete approximation are derived. Using an efficient time integrator, some numerical experiments to illustrate the performance of the discretization are presented.

math.NA↗

arXiv2025

A high-order method for the numerical approximation of fractional nonlinear Schrödinger equations

In this paper, the periodic initial-value problem for the fractional nonlinear Schrödinger (fNLS) equation is discretized in space by a Fourier spectral Galerkin method and in time by diagonally implicit, high-order Runge-Kutta schemes, based on the composition with the implicit midpoint rule (IMR). Some properties and error estimates for the semidiscretization in space and for the full discretization are proved. The convergence results and the general performance of the scheme are illustrated with several numerical experiments.

math.NA↗

arXiv2025

Outflow Interaction in Cep-E: Numerical Simulation and Observational Manifestation

There is clear observational evidence that the main Class 0/I stages of the star formation process are associated with powerful collimated outflows (jets), which sometimes propagate up to distances as large as $10^{4-5}$ au scales in molecular clouds. Additionally, intermediate high-mass and low-mass protostars have often been observed to form in crowded clusters, where the typical separation distance between any two cluster members is of the same order or smaller than the scale of the outflow length. Therefore, there must be an interaction between the molecular outflows of different protostars within the protostellar association. A good example of this is the case of Cepheus E-mm, which is a protostellar outflow extending over a few dozen au. At its core is a binary system consisting of two protostars, Cep E-A and Cep E-B, separated by about 1000 au. Both protostars eject molecular jets at velocities of ~100 km/s. The interaction between these molecular outflows provides an opportunity to study the effects of jet collisions in a clustered star-forming environment, as they may leave detectable imprints on the morphology of the main envelope of the system. Our work aims to study the effects of the collision of molecular jets associated with the components of the binary system Cep-A and Cep-E, analyzing the disruption or reduction of molecular emission in the main envelope of the system, which the molecular outflow { launched} by Cep-A presumably pushes. If we characterize the collision in this system, we can provide insights into the expected morphology and molecular emissions in collisions of molecular outflows { associated to star forming process.

astro-ph.SR↗

arXiv2024

Mathematical properties of Klein-Gordon-Boussinesq systems

The Klein-Gordon-Boussinesq (KGB) system is proposed in the literature as a model problem to study the validity of approximations in the long wave limit provided by simpler equations such as KdV, nonlinear Schrödinger or Whitham equations. In this paper, the KGB system is analyzed as a mathematical model in three specific points. The first one concerns well-posedness of the initial-value problem with the study of local existence and uniqueness of solution and the conditions under which the local solution is global or blows up at finite time. The second point is focused on traveling wave solutions of the KGB system. The existence of different types of solitary waves is derived from two classical approaches, while from their numerical generation several properties of the solitary wave profiles are studied. In addition, the validity of the KdV approximation is analyzed by computational means and from the corresponding KdV soliton solutions.

math.AP↗

arXiv2024

Long-term behaviour of symmetric partitioned linear multistep methods I. Global error and conservation of invariants

In this paper an asymptotic expansion of the global error on the stepsize for partitioned linear multistep methods is proved. This provides a tool to analyse the behaviour of these integrators with respect to error growth with time and conservation of invariants. In particular, symmetric partitioned linear multistep methods with no common roots in their first characteristic polynomials, except unity, appear as efficient methods to approximate non-separable Hamiltonian systems since they can be explicit and show good long term behaviour at the same time. As a case study, a thorough analysis is given for small oscillations of the double pendulum problem, which is illustrated by numerical experiments.

math.NA↗

arXiv2024

Notes on solitary-wave solutions of Rosenau-type equations

The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of three different forms are derived. The results depend on some conditions on the speed of the waves with respect to the parameters of the equations. They are discussed for several families of Rosenau equations present in the literature. The analysis is illustrated with a numerical study of generation of approximate solitary-wave profiles from a numerical procedure based on the Petviashvili iteration.

math.AP↗

arXiv2024

Solitary-wave solutions of the fractional nonlinear Schrödinger equation. I. Existence and numerical generation

The present paper is the first part of a project devoted to the fractional nonlinear Schrödinger (fNLS) equation. It is concerned with the existence and numerical generation of the solitary-wave solutions. For the first point, some conserved quantities of the problem are used to search for solitary-wave solutions as relative equilibria. From the relative equilibrium condition, a result of existence via the Concentration-Compactness theory is derived. Several properties of the waves, such as the regularity and the asymptotic decay in some cases, are derived from the existence result. Some other properties, such as the monotone behaviour and the speed-amplitude relation, will be explored computationally. To this end, a numerical procedure for the generation of the profiles is proposed. The method is based on a Fourier pseudospectral approximation of the differential system for the profiles and the use of Petviashvili's iteration with extrapolation.

math.AP↗

arXiv2023

FAUST VIII. The protostellar disk of VLA 1623-2417 W and its streamers imaged by ALMA

More than 50% of solar-mass stars form in multiple systems. It is therefore crucial to investigate how multiplicity affects the star and planet formation processes at the protostellar stage. We report continuum and C$^{18}$O (2-1) observations of the VLA 1623-2417 protostellar system at 50 au angular resolution as part of the ALMA Large Program FAUST. The 1.3 mm continuum probes the disks of VLA 1623A, B, and W, and the circumbinary disk of the A1+A2 binary. The C$^{18}$O emission reveals, for the first time, the gas in the disk-envelope of VLA 1623W. We estimate the dynamical mass of VLA 1623W, $M_{\rm dyn}=0.45\pm0.08$ M$_{\odot}$, and the mass of its disk, $M_{\rm disk}\sim6\times10^{-3}$ M$_{\odot}$. C$^{18}$O also reveals streamers that extend up to 1000 au, spatially and kinematically connecting the envelope and outflow cavities of the A1+A2+B system with the disk of VLA 1623W. The presence of the streamers, as well as the spatial ($\sim$1300 au) and velocity ($\sim$2.2 km/s) offset of VLA 1623W suggest that either sources W and A+B formed in different cores, interacting between them, or that source W has been ejected from the VLA 1623 multiple system during its formation. In the latter case, the streamers may funnel material from the envelope and cavities of VLA 1623AB onto VLA 1623W, thus concurring to set its final mass and chemical content.

astro-ph.SR↗

arXiv2022

FAUST VI. VLA 1623--2417 B: a new laboratory for astrochemistry around protostars on 50 au scale

The ALMA interferometer, with its unprecedented combination of high-sensitivity and high-angular resolution, allows for (sub-)mm wavelength mapping of protostellar systems at Solar System scales. Astrochemistry has benefited from imaging interstellar complex organic molecules in these jet-disk systems. Here we report the first detection of methanol (CH3OH) and methyl formate (HCOOCH3) emission towards the triple protostellar system VLA1623-2417 A1+A2+B, obtained in the context of the ALMA Large Program FAUST. Compact methanol emission is detected in lines from Eu = 45 K up to 61 K and 537 K towards components A1 and B, respectively. LVG analysis of the CH3OH lines towards VLA1623-2417 B indicates a size of 0.11-0.34 arcsec (14-45 au), a column density N(CH3OH) = 10^16-10^17 cm-2, kinetic temperature > 170 K, and volume density > 10^8 cm-3. An LTE approach is used for VLA1623-2417 A1, given the limited Eu range, and yields Trot < 135 K. The methanol emission around both VLA1623-2417 A1 and B shows velocity gradients along the main axis of each disk. Although the axial geometry of the two disks is similar, the observed velocity gradients are reversed. The CH3OH spectra from B shows two broad (4-5 km s-1) peaks, which are red- and blue-shifted by about 6-7 km s-1 from the systemic velocity. Assuming a chemically enriched ring within the accretion disk, close to the centrifugal barrier, its radius is calculated to be 33 au. The methanol spectra towards A1 are somewhat narrower (about 4 km s-1), implying a radius of 12-24 au.

astro-ph.GA↗

arXiv2022

Notes on the Boussinesq-Full dispersion systems for internal waves: Numerical solution and solitary waves

In this paper we study some theoretical and numerical issues of the Boussinesq/Full dispersion system. This is a a three-parameter system of pde's that models the propagation of internal waves along the interface of two-fluid layers with rigid lid condition for the upper layer, and under a Boussinesq regime for the upper layer and a full dispersion regime for the lower layer. We first discretize in space the periodic initial-value problem with a Fourier-Galerkin spectral method and prove error estimates for several ranges of values of the parameters. Solitary waves of the model systems are then studied numerically in several ways. The numerical generation is analyzed by approximating the ode system with periodic boundary conditions for the solitary-wave profiles with a Fourier spectral scheme, implemented in a collocation form, and solving iteratively the corresponding algebraic system in Fourier space with the Petviashvili method accelerated with the minimal polynomial extrapolation technique. Motivated by the numerical results, a new result of existence of solitary waves is proved. In the last part of the paper, the dynamics of these solitary waves is studied computationally, To this end, the semidiscrete systems obtained from the Fourier-Galerkin discretization in space are integrated numerically in time by a Runge-Kutta Composition method of order four. The fully discrete scheme is used to explore numerically the stability of solitary waves, their collisions, and the resolution of other initial conditions into solitary waves.

math.NA↗

arXiv2020

FAUST I. The hot corino at the heart of the prototypical Class I protostar L1551 IRS5

The study of hot corinos in Solar-like protostars has been so far mostly limited to the Class 0 phase, hampering our understanding of their origin and evolution. In addition, recent evidence suggests that planet formation starts already during Class I phase, which, therefore, represents a crucial step in the future planetary system chemical composition. Hence, the study of hot corinos in Class I protostars has become of paramount importance. Here we report the discovery of a hot corino towards the prototypical Class I protostar L1551 IRS5, obtained within the ALMA Large Program FAUST. We detected several lines from methanol and its isopotologues ($^{13}$CH$_{\rm 3}$OH and CH$_{\rm 2}$DOH), methyl formate and ethanol. Lines are bright toward the north component of the IRS5 binary system, and a possible second hot corino may be associated with the south component. The methanol lines non-LTE analysis constrains the gas temperature ($\sim$100 K), density ($\geq$1.5$\times$10$^{8}$ cm$^{-3}$), and emitting size ($\sim$10 au in radius). All CH$_{\rm 3}$OH and $^{13}$CH$_{\rm 3}$OH lines are optically thick, preventing a reliable measure of the deuteration. The methyl formate and ethanol relative abundances are compatible with those measured in Class 0 hot corinos. Thus, based on the present work, little chemical evolution from Class 0 to I hot corinos occurs.

astro-ph.SR↗

arXiv2020

An asymptotic model for internal capillary-gravity waves in deep water

Considered in this paper is a bi-directional model for the propagation of interfacial capillary-gravity waves in a two-layer system of fluids with rigid lid condition for the upper layer and lower layer with a much larger or infinite depth. The system is derived from a reformulation of the Euler equations for internal waves with nonnegligible surface tension effects in the interface and the corresponding asymptotic model under the Benjamin-Ono regime. Another unidirectional model, so-called regularized Benjamin equation, generalizing the Benjamin equation, is also introduced. Well-posedness of the new equations and existence of solitary wave solutions are discussed.

math.AP↗

arXiv2019

On a model for internal waves in rotating fluids

In this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the dispersion balance. The physical regime of validation is discussed and mathematical properties of the new system, concerning well-posedness, conservation laws and existence of solitary-wave solutions, are analyzed.

math.AP↗

arXiv2019

On nonparaxial nonlinear Schrödinger-type equations

In this paper the one-dimensional nonparaxial nonlinear Schrödinger equation is considered. This was proposed as an alternative to the classical nonlinear Schrödinger equation in those situations where the assumption of paraxiality may fail. The paper contributes to the mathematical properties of the equation in a two-fold way. First, some theoretical results on linear well-posedness, Hamiltonian and multi-symplectic formulations are derived. Then we propose to take into account these properties in order to deal with the numerical approximation. In this sense, different numerical procedures that preserve the Hamiltonian and multi-symplectic structures are discussed and illustrated with numerical experiments.

math.AP↗

arXiv2018

Reversal magnetization, spin reorientation and exchange bias in YCrO$_3$ doped with praseodymium

Crystal structure, thermal and magnetic properties were systematically studied in the Y$_{1-x}$Pr$_x$CrO$_3$ with $0 \leq x \leq 0.3$ compositions. Magnetic susceptibility and specific heat measurements show an increase of the antiferromagnetic transition temperature ($T_N$) as Pr is substituted in the Y sites and notable magnetic features are observed below $T_N$. Strong coupling between magnetic and crystalline parameters is observed in a small range of Pr compositions. A small perturbation in the lattice parameters by Pr ion is sufficient to induce a spin reorientation transition followed by magnetization reversal, to finally induce exchange bias effect. The spin reorientation temperature ($T_{SR}$) is increased from 35 K to 149 K for $0.025 \leq x \leq 0.1$ compositions. It is found that the Cr spins sublattice rotates continuously from $T_{SR}$ to a new spin configuration a lower temperature. In addition, magnetization reversal is observed at $T^* \sim 35$ K for x= 0.05 up to $T^* \sim 63$ K for x = 0.20 composition. The $M-H$ curves show negative exchange bias effect induced by Pr ions, which are observed below of 100 K and being more intense at 5 K. At 10 K, the magnetic contribution of the specific heat, as well as the ZFC magnetization, show the rise of a peak with increasing Pr content. The magnetic anomaly could be associated with the freezing of the Pr magnetic moment randomly distributed at the 4c crystallographic site. A clear correspondence between spin reorientation, magnetization reversal and exchange bias anisotropy with the tilting and octahedral distortion is also discussed.

cond-mat.mtrl-sci↗

arXiv2017

Nonlinear Bloch modes, optical switching and Bragg solitons in tightly coupled micro-ring resonator chains

We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady state nonlinear Bloch modes are derived. The switching behavior of the transmission system is addressed numerically and the results are explained in the light of this analytical result. We also present a numerical study on the spontaneous generation of Bragg solitons from a continuous-wave input.

nlin.PS↗

arXiv2017

Cross-diffusion systems for image processing: II. The nonlinear case

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a numerical point of view, a computational study of the performance of the models is carried out, suggesting their diversity and potentialities to treat image filtering problems. The present paper is a continuation of a previous work of the same authors, devoted to linear cross-diffusion models. \keywords{Cross-diffusion \and Complex diffusion \and Image restoration}

math.AP↗

arXiv2012

Mechanism of small-polaron formation in the biferroic YCrO3 doped with calcium

The effects of Ca substitutions on the structure, magnetism and electrical properties of YCrO3 ceramics are investigated by X-ray diffraction, magnetic susceptibility and electrical conductivity measurements. The cell volume decrease occurs through the change from Cr(III) to Cr(IV) as a result of the charge compensation of the Ca doping. No changes are observed in the antiferromagnetic transition temperature while strong changes are observed in the transport measurements due to Ca content. The increase of the electrical conductivity as well as the decrease of the activation energy are caused by the formation of the small-polarons localized in the O-Cr-O lattice distortion. The origin of small-polarons in the undoped sample is different in nature from the calcium doped. "Local non-centrosymetry" is the source of the small-polaron formation in undoped sample, while the change from Cr(III) to Cr(IV) through the charge compensation of Ca(II) in the Y(III) site is the source of small-polarons formations. The decrease of the average bond length Cr-O as well as effective moments in the paramagnetic state and the increase of the electrical conductivity are clear evidence that the Ca doping induces localized polarons, which in turn, these quasiparticles move from site to site by a thermally activated process in the doped YCrO3 compound. Here, we also discuss a possible mechanism of small-polaron injections in YCrO3 matrix.

cond-mat.mtrl-sci↗