Matrix methods for radial Schr\"{o}dinger eigenproblems defined on a semi-infinite domain

In this paper, we discuss numerical approximation of the eigenvalues of the one-dimensional radial Schr\"{o}dinger equation posed on a semi-infinite interval. The original problem is first transformed to one defined on a finite domain by applying suitable change of the independent variable. The eigenvalue problem for the resulting differential operator is then approximated by a generalized algebraic eigenvalue problem arising after discretization of the analytical problem by the matrix method based on high order finite difference schemes. Numerical experiments illustrate the performance of the approach

Acoustic metamaterial models on the (2+1)D Schwarzschild plane

[EN] Recent developments in acoustic metamaterial engineering have led to the design and fabrication of devices with formidable properties, such as acoustic cloaking, superlenses and ultra-sound waves. Artificial materials of this type are generally absent in natural environments. In this work, we focus on feasible implementations of acoustic black holes on the 2D plane, that is, within (2+1)D spacetime. For an accurate description of planar black holes in transformation acoustics, we examine Schwarzschild-type models. After proposing an appropriate form for the Lorentzian metric of the underlying spacetime, we explore the geometric content and physical consequences of such models, which will turn out to have de Sitter and anti-de Sitter spacetime structure. For this purpose, we derive a general expression for its acoustic wave propagation. Next, a numerical simulation is carried out for prototype waves which probe these spacetime geometries. Finally, we discuss how to fine-tune the corresponding acoustic parameters for an implementation in the laboratory environment.M. M. T. acknowledges financial support by the Spanish Ministerio de Economia y Competitividad, the European Regional Development Fund under grant TIN2014-59294-P, and the Generalitat Valenciana (BEST2017). He also wishes to thank for the cordial reception and hospitality at the Institute for Analysis and Scientific Computing of the Vienna University of Technology where part of the present work was established.Tung, MM.; Weinmüller, EB. (2019). Acoustic metamaterial models on the (2+1)D Schwarzschild plane. Journal of Computational and Applied Mathematics. 346:162-170. https://doi.org/10.1016/j.cam.2018.07.009S16217034

Computational modeling and simulation to increase laser shooting accuracy of autonomous LEO trackers

In this paper, we introduce a computational procedure that enables autonomous LEO laser trackers endowed with INSs to increase the current accuracy when shooting at middle distant medium-size LEO debris targets. The code is designed for the trackers to throw the targets into the atmosphere by means of ablations. In case that the targets are eclipsed to the trackers by the Earth, the motions of the trackers and targets are modeled by equations that contain post-Newtonian terms accounting for the curvature of space. Otherwise, when the approaching targets become visible for the trackers, we additionally use more accurate equations, which allow to account for the local bending of the laser beams aimed at the targets. We observe that under certain circumstances the correct shooting configurations that allow to safely and efficiently shoot down the targets, differ from the current estimations by distances that may be larger than the size of many targets. In short, this procedure enables to estimate the optimal shooting instants for any middle distant medium-size LEO debris targe

Gravitational frequency shifts in transformation acoustics

In metamaterial acoustics, it is conceivable that any type of fine-tuned acoustic properties far beyond those found in nature may be transferred to an appropriate medium. Effective design and engineering of these modern acoustic metadevices poses one of the forefront challenges in this field. As a practical example of a new covariant approach for modelling acoustics on spacetime manifolds, we choose to implement the acoustic analogue of the frequency shift due to gravitational time dilation. In accordance with Einstein's equivalence principle, two different spacetimes, corresponding to uniform acceleration or uniform gravity, are considered. For wave propagation in a uniformly accelerating rigid frame, an acoustic event horizon arises. The discussion includes a detailed numerical analysis for both spacetime geometries. Copyright (c) EPLA, 2013MMT wishes to thank MARKUS SCHOBINGER for an introduction to the SBVP MATLAB solver and acknowledges partial support by the Universidad Politecnica de Valencia (PAID-00-12) and the International Office of the Vienna University of Technology.Tung, MM.; Weinmüller, EB. (2013). Gravitational frequency shifts in transformation acoustics. EPL. 101(5):54006-54011. https://doi.org/10.1209/0295-5075/101/54006S5400654011101

Discrete charging of metallic grains: Statistics of addition spectra

We analyze the statistics of electrostatic energies (and their differences) for a quantum dot system composed of a finite number $K$ of electron islands (metallic grains) with random capacitance-inductance matrix $C$, for which the total charge is discrete, $Q=Ne$ (where $e$ is the charge of an electron and $N$ is an integer). The analysis is based on a generalized charging model, where the electrons are distributed among the grains such that the electrostatic energy E(N) is minimal. Its second difference (inverse compressibility) $\chi_{N}=E(N+1)-2 E(N)+E(N-1)$ represents the spacing between adjacent Coulomb blockade peaks appearing when the conductance of the quantum dot is plotted against gate voltage. The statistics of this quantity has been the focus of experimental and theoretical investigations during the last two decades. We provide an algorithm for calculating the distribution function corresponding to $\chi_{N}$ and show that this function is piecewise polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract and Introduction

Relaxational study of poly(vinylpyrrolidone-co-butyl acrylate) membrane by dielectric and dynamic mechanical spectroscopy

[EN] A poly(vinylpyrrolidone-co-butyl acrylate) (60VP-40BA) membrane is synthesized as a tractable and hydrophilic material, obtaining a water-swelling percentage around 60%. An investigation of molecular mobility by means of differential scanning calorimetry, dynamic mechanical analysis and broadband dielectric relaxation spectroscopy (DRS) is fulfilled in the dry membrane. Dielectric and viscoelastic relaxation measurements are carried out on the 60VP-40BA sample at several frequencies between -150 and 150 degrees C. The dielectric spectrum shows several relaxation processes labelled gamma, beta and alpha in increasing order of temperature, whereas in the mechanical spectrum only the beta and alpha relaxation processes are completely defined. In the dielectric measurements, conductive contributions overlap the alpha-relaxation. The apparent activation energies have similar values for the beta-relaxation in both, the mechanical and the dielectric measurements. The beta process is a Johari-Golstein secondary relaxation and it is related to the local motions of the pyrrolidone group accompanied by the motion of the segments of the polymer backbone. The gamma process is connected with the butyl unit's motions, both located in the side chains of the polymer.BRF, MC, PO and MJS are grateful to CICYT for grant MAT2012-33483. FG and JMG thank the Spanish Ministerio de Economia y Competitividad-FEDER (MAT2011-22544) and the Consejeria de Educacion-Junta de Castilla y Leon (BU001A10-2).Redondo Foj, MB.; Carsí Rosique, M.; Ortiz Serna, MP.; Sanchis Sánchez, MJ.; García, FC.; García. José Miguel (2013). Relaxational study of poly(vinylpyrrolidone-co-butyl acrylate) membrane by dielectric and dynamic mechanical spectroscopy. JOURNAL OF PHYSICS D-APPLIED PHYSICS. 46(29):295304-1-295304-12. https://doi.org/10.1088/0022-3727/46/29/295304S295304-1295304-12462

The Convergence of Shooting Methods for Singular Boundary Value Problems

We investigate the convergence properties of single and multiple shooting when applied to singular boundary value problems. Particular attention is paid to the well-posedness of the process. It is shown that boundary value problems can be solved eciently when a high order integrator for the associated singular initial value problems is available. Moreover, convergence results for a perturbed Newton iteration are discussed