Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Competitive evaporation in arrays of droplets

We consider the evaporation of periodic arrays of initially equal droplets in two-dimensional systems with open (absorbing) boundaries. Our study is based on the numerical solution of the Cahn-Hilliard equation. We show that due to cooperative effects the droplets which are further from the boundary may evaporate earlier than those in the boundary¿s vicinity. The time evolution of the overall amount of matter in the system is also studied.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Breathers and thermal relaxation in Fermi-Pasta-Ulam arrays

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi¿Pasta¿Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters

Kinetic resolution: a powerful tool for the synthesis of planar-chiral ferrocenes

Since the serendipitous discovery of ferrocene by Pauson and Kealy in 1951, it has become one of the most important structures in Organic Chemistry. Lately, kinetic resolution has emerged as a useful tool for the synthesis of planar chiral ferrocenes. This review aims to cover and discuss the development of this topic.

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.

Contact force transitions in regrasp tasks of planar objects

This paper presents a simple and fast solution to the problem of finding the time variations of the forces that keep the object equilibrium when a finger is removed from a three contact point grasp or a finger is added to a two contact point grasp, assuming the existence of an external perturbation force (that can be the object weight itself). The procedure returns force set points for the control system of a manipulator device in a regrasping action. The approach was implemented and a numerical example is included in the paper to illustrate how it works.

A Write-Based Solver for SAT Modulo the Theory of Arrays

The extensional theory of arrays is one of the most important ones for applications of SAT Modulo Theories (SMT) to hardware and software verification. Here we present a new T-solver for arrays in the context of the DPLL(T) approach to SMT. The main characteristics of our solver are: (i) no translation of writes into reads is needed, (ii) there is no axiom instantiation, and (iii) the T-solver interacts with the Boolean engine by asking to split on equality literals between indices. As far as we know, this is the first accurate description of an array solver integrated in a state-of-the-art SMT solver and, unlike most state-of-the-art solvers, it is not based on a lazy instantiation of the array axioms. Moreover, it is very competitive in practice, specially on problems that require heavy reasoning on array literals

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, . . . , n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

L'albedo lunar i els satèl·lits: Recerca sobre els efectes de l'albedo lunar en les plaques solars d'un satèl·lit artificial que orbita al voltant de la Lluna

Treball de recerca realitzat per una alumna d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. L’albedo lunar i els satèl•lits és un treball que relaciona l’enginyeria aeroespacial amb l’astronomia. El seu objectiu principal investigar si l’albedo lunar, els rajos de sol reflectits a la superfície lunar, pot modificar significativament la temperatura de les plaques solars d’un satèl•lit artificial que orbiti la Lluna i, en conseqüència, afectar-ne el rendiment. El segon objectiu del treball és calcular si seria possible fer un mapa d’albedo lunar, a partir de la temperatura d’un satèl•lit en òrbita al voltant de la Lluna, que permetria conèixer amb més precisió la composició de la superfície lunar. Després d’adquirir els fonaments teòrics necessaris per a realitzar el treball, del procés per a trobar la manera de dur a terme els càlculs i d’efectuar els càlculs en si, les conclusions del treball són que l’albedo lunar causa un augment de temperatura en els satèl•lits prou significatiu per afectar-ne el rendiment; i que amb les temperatures enregistrades per un satèl•lit en òrbita al voltant de la Lluna es podria crear un mapa d’albedo. Aquesta recerca ha estat feta per suggeriment i sota la supervisió del CTAE (Centre de Tecnologia Aeroespacial) per analitzar si els resultats són aplicables al satèl•lit que s’enviarà a la Lluna, Lunar Mission BW1.

Disseny, modelat i fabricació d'una antena "trap" per aplicacions WLAN

En aquest treball s’ha dissenyat i fabricat una antena monopol en estructura planar capaç de treballar correctament a les freqüències WLAN de 2,45-2,5 GHz (802.11b/g) i 4,9-5,875 GHz (802.11a/h/j). Per arribar a aquest objectiu primer s’ha presentat el model de línia de transmissió acabada en circuit obert per simular el comportament d’una antena. S’han comparat i verificat els resultats amb el model d’antena de fil. Seguidament, s’ha estudiat el comportament que introdueix el fet de carregar l’antena amb un ressonador LC. Finalment, s’ha passat del model d’antena de fil a una estructura planar. Aquesta geometria ha permès la realització del trap LC de forma distribuïda a través d’un ressonador CLL. El principi de disseny de l’antena està basat en la introducció d’aquest ressonador CLL amb freqüència de ressonància situada entre les dos bandes de treball i que junt amb l’ajust dels diversos paràmetres que defineixen l’antena han permès obtenir més 1 GHz d’ample de banda a la freqüència de 5 GHz.

Caracterización de materiales en banda W

Para medir los coeficientes de transmisión y reflexión, S21 y S11, de diferentes materiales o muestras planas, se usa un sistema de toma de medidas en espacio libre operando banda W (75 – 110 GHz). Usando estos parámetros, S21 y S11, podemos calcular la permitividad dieléctrica relativa compleja (Er ) y la permeabilidad magnética relativa compleja (μr) mediante un proceso llamado NRW (Nicolson-Ross-Weir). El sistema para medir consiste en dos antenas de bocina, una transmisora y otra receptora, dos espejos con los que obtenemos una onda plana para medir las propiedades del material y un ordenador o dispositivo que calcula los resultados. Este dispositivo requiere de calibración para la obtención de resultados óptimos. Dicho sistema se puede simular de manera ideal con un software llamado ADS (Assistance Design System) para el estudio y comparación de grosores, permitividades dieléctricas relativas y permeabilidades magnéticas relativas de los materiales en función de la frecuencia.