Computation of an integral basis of quartic number field

"Vegeu el resum a l'inici del document del fitxer ajunt."

A functional equation related to the product in a quadratic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Extensional flow of nematic liquid crystal under electric field gradient

Systematic asymptotic methods are used to formulate a model for the extensional flow of a thin sheet of nematic liquid crystal. With no external body forces applied, the model is found to be equivalent to the so-called Trouton model for Newtonian sheets (and fi bers), albeit with a modi fied "Trouton ratio". However, with a symmetry-breaking electric field gradient applied, behavior deviates from the Newtonian case, and the sheet can undergo fi nite-time breakup if a suitable destabilizing field is applied. Some simple exact solutions are presented to illustrate the results in certain idealized limits, as well as sample numerical results to the full model equations.

Estudi amb georadar del jaciment arqueològic de Lady Field (Woolston Manor Farm, Somerset, Gran Bretanya)

Projecte de recerca elaborat a partir d’una estada al University of Bristol, Gran Bretanya, durant agost i setembre del 2007. Els objectius del projecte d’estudi del jaciment de Lady Field (Woolston Manor Farm, Somerset, Gran Bretanya) eren, bàsicament, tres: en primer lloc, posar en pràctica els coneixements teòrics assolits durant la formació en prospecció geofísica; en segon lloc, aportar informació complementària a la aportada per la prospecció tradicional i el sondeig amb gradiòmetre magnètic efectuades prèviament per l’equip investigador del centre, arribant a definir millor les estructures poc definides per l’altre sistema i, finalment, obtenir un cas d’estudi sobre un jaciment medieval a Gran Bretanya, on les condicions geològiques i climàtiques, que afecten els resultats de la prospecció, són diferents a les del nostre país. Aquests objectius s’han assolit, ja que s’ha pogut portar a terme una prospecció de camp amb el sistema de georadar, processar les dades i obtenir-ne dades de qualitat i obtenir informació útil i rellevant de cara a la definició de les restes detectades, una vegada feta la interpretació. Els resultats mostren l’aparició en el subsòl del jaciment de quatre possibles fases d’ocupació, entre les que destaquen un moment amb possibles restes d’una antiga xarxa urbana, treballs agrícoles o un sistema de drenatge del terreny. Finalment l’estudi ha pogut constatar que la prospecció amb GPR en aquestes condicions geològiques és possible, tot i que les climàtiques –essencialment la pluja i la humitat del sòl- suposen complicacions a l’hora d’adquirir dades de forma segura per la maquinària i per la qualitat de les dades.

WMR navigation using local potential field corridors and narrow local occupancy grid perception

Path planning and control strategies applied to autonomous mobile robots should fulfil safety rules as well as achieve final goals. Trajectory planning applications should be fast and flexible to allow real time implementations as well as environment interactions. The methodology presented uses the on robot information as the meaningful data necessary to plan a narrow passage by using a corridor based on attraction potential fields that approaches the mobile robot to the final desired configuration. It employs local and dense occupancy grid perception to avoid collisions. The key goals of this research project are computational simplicity as well as the possibility of integrating this method with other methods reported by the research community. Another important aspect of this work consist in testing the proposed method by using a mobile robot with a perception system composed of a monocular camera and odometers placed on the two wheels of the differential driven motion system. Hence, visual data are used as a local horizon of perception in which trajectories without collisions are computed by satisfying final goal approaches and safety criteria

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed atdifferent points in time. Inherently, then, a compositional time series is a multivariatetime series with important constraints on the variables observed at any instance in time.Although this type of data frequently occurs in situations of real practical interest, atrawl through the statistical literature reveals that research in the field is very much in itsinfancy and that many theoretical and empirical issues still remain to be addressed. Anyappropriate statistical methodology for the analysis of compositional time series musttake into account the constraints which are not allowed for by the usual statisticaltechniques available for analysing multivariate time series. One general approach toanalyzing compositional time series consists in the application of an initial transform tobreak the positive and unit sum constraints, followed by the analysis of the transformedtime series using multivariate ARIMA models. In this paper we discuss the use of theadditive log-ratio, centred log-ratio and isometric log-ratio transforms. We also presentresults from an empirical study designed to explore how the selection of the initialtransform affects subsequent multivariate ARIMA modelling as well as the quality ofthe forecasts

Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,one can mimick the presymplectic constraint algorithm to obtain a constraint algorithmthat can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations offield theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.

Desenvolupament d'algorismes biològicament inspirats basats en Support Vector Machines

L'objectiu d'aquest projecte ha estat el desenvolupament d'algorismes biològicament inspirats per a l'olfacció artificial. Per a assolir-lo ens hem basat en el paradigma de les màquines amb suport vectorial. Hem construit algoritmes que imitaven els processos computacionals dels diferents sistemes que formen el sistema olfactiu dels insectes, especialment de la llagosta Schistocerca gregaria. Ens hem centrat en el lòbuls de les antenes, i en el cos fungiforme. El primer està considerat un dispositiu de codificació de les olors, que a partir de la resposta temporal dels receptors olfactius a les antenes genera un patró d'activació espaial i temporal. Quant al cos fungiforme es considera que la seva funció és la d'una memòria per als olors, així com un centre per a la integració multi-sensorial. El primer pas ha estat la construcció de models detallats dels dos sistemes. A continuació, hem utilitzat aquests models per a processar diferents tipus de senyals amb l'objectiu de abstraure els principis computacionals subjacents. Finalment, hem avaluat les capacitats d'aquests models abstractes, i els hem utilitzat per al processat de dades provinents de sensors de gasos. Els resultats mostren que el models abstractes tenen millor comportament front el soroll i més capacitat d'emmagatzematge de records que altres models més clàssics, com ara les memòries associatives de Hopfield o fins i tot en determinades circumstàncies que les mateixes Support Vector Machines.

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

From MuSIASEM theory to practice: report and reflections from field research in Kampot province, Cambodia

This document contains a report and summary of the field research activities in a rural community of rice farmers in Kampot province, Cambodia in 2011, which I conducted within the context of my PhD research at ICTA-UAB (Institute of Environmental Science and Technology, Autonomous University of Barcelona, Spain). The purpose of the field research was to gather data for a MuSIASEM analysis (Multi-Scale Integrated Analysis of Societal and Ecosystem Metabolism) at the village and household level, in order to analyze the multidimensional challenges that small farmers may face nowadays within the context of global rural change and declining access to land. While the literature on MuSIASEM offers a great variety of theoretical explanations and practical applications, there is little information available for students regarding the practical steps required for doing a MuSIASEM analysis at the local level. Within this context, this report offers not only a documentation of the field research design and data collection methods, but further provides a general overview on some organizational and preparative aspects, including some personal reflections, that one may face when preparing and conducting field research for MuSIASEM analysis. In summary, this document thus serves three objectives: (i) to assure methodological transparency for the future work, based on the collected data during field research, (ii) to share my personal experience on the preparative and practical steps required for field research and data collection for a MuSIASEM analysis at the local level, and (iii) to make available for the further interested reader some more detailed background information on the case study village.

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

A new efficient approach to the direct restricted active space self-consistent field method

An implicitly parallel method for integral-block driven restricted active space self-consistent field (RASSCF) algorithms is presented. The approach is based on a model space representation of the RAS active orbitals with an efficient expansion of the model subspaces. The applicability of the method is demonstrated with a RASSCF investigation of the first two excited states of indole

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence