Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By seperating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described

Forced oscillation assessment of respiratory mechanics in ventilated patients

The forced oscillation technique (FOT) is a method for non-invasively assessing respiratory mechanics that is applicable both in paralysed and non-paralysed patients. As the FOT requires a minimal modification of the conventional ventilation setting and does not interfere with the ventilation protocol, the technique is potentially useful to monitor patient mechanics during invasive and noninvasive ventilation. FOT allows the assessment of the respiratory system linearity by measuring resistance and reactance at different lung volumes or end-expiratory pressures. Moreover, FOT allows the physician to track the changes in patient mechanics along the ventilation cycle. Applying FOT at different frequencies may allow the physician to interpret patient mechanics in terms of models with pathophysiological interest. The current methodological and technical experience make possible the implementation of portable and compact computerised FOT systems specifically addressed to its application in the mechanical ventilation setting.

Statistical mechanics in the extended Gaussian ensemble

The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 66, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle. The probability of each microstate depends on two parameters ß and ¿ which allow one to fix, independently, the mean energy of the system and the energy fluctuations, respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the q-exponential distribution. As an example, an application to a system with few independent spins is presented.

Interaccion among systems of finite size in predictive relativistic mechanics I. General framework

We derive a Hamiltonian formulation for the three-dimensional formalism of predictive relativistic mechanics. This Hamiltonian structure is used to derive a set of dynamical equations describing the interaction among systems in perturbation theory.

Interaccion among systems of finite size in predictive relativistic mechanics -II. Electromagnetic and gravitational interactions

We explicitly construct a closed system of differential equations describing the electromagnetic and gravitational interactions among bodies to first order in the coupling constants, retaining terms up to order c-2. The Breit and Barker and O'Connell Hamiltonians are recovered by means of a coordinate transformation. The method used throws light on the meaning of these coordinates.

Interactions among systems of finite size en predictive relativistic mechanics III. Short-range interaction and second-order terms

We compute up to and including all the c-2 terms in the dynamical equations for extended bodies interacting through electromagnetic, gravitational, or short-range fields. We show that these equations can be reduced to those of point particles with intrinsic angular momentum assuming spherical symmetry.

General Interaction Picture from Action Principle for Mechanics

In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Disseny i desenvolupament de videojocs

Estudi i implementació d’una plataforma de prototipatge de videojocs mitjançant la qual es pot crear un videojoc elemental, descartant aspectes decoratius o accessoris. Aquesta eina pretén millorar l’etapa de disseny d’un videojoc avançant el moment en que aquest es podrà jugar. Això permetrà prendre decisions importants en base a proves i experiències mesurables. S’ha implementat un sistema programable en llenguatge de script que estalvia a l’usuari treballar en els aspectes tecnològics i li permet centrar-se en crear la mecànica del joc que vol ser provat.

Dinàmica de sistemes mesoscòpics amb correlacions quàntiques mitjançant la formulació de de Broglie-Bohm

Per a determinar la dinàmica espai-temporal completa d’un sistema quàntic tridimensional de N partícules cal integrar l’equació d’Schrödinger en 3N dimensions. La capacitat dels ordinadors actuals permet fer-ho com a molt en 3 dimensions. Amb l’objectiu de disminuir el temps de càlcul necessari per a integrar l’equació d’Schrödinger multidimensional, es realitzen usualment una sèrie d’aproximacions, com l’aproximació de Born–Oppenheimer o la de camp mig. En general, el preu que es paga en realitzar aquestes aproximacions és la pèrdua de les correlacions quàntiques (o entrellaçament). Per tant, és necessari desenvolupar mètodes numèrics que permetin integrar i estudiar la dinàmica de sistemes mesoscòpics (sistemes d’entre tres i unes deu partícules) i en els que es tinguin en compte, encara que sigui de forma aproximada, les correlacions quàntiques entre partícules. Recentment, en el context de la propagació d’electrons per efecte túnel en materials semiconductors, X. Oriols ha desenvolupat un nou mètode [Phys. Rev. Lett. 98, 066803 (2007)] per al tractament de les correlacions quàntiques en sistemes mesoscòpics. Aquesta nova proposta es fonamenta en la formulació de la mecànica quàntica de de Broglie– Bohm. Així, volem fer notar que l’enfoc del problema que realitza X. Oriols i que pretenem aquí seguir no es realitza a fi de comptar amb una eina interpretativa, sinó per a obtenir una eina de càlcul numèric amb la que integrar de manera més eficient l’equació d’Schrödinger corresponent a sistemes quàntics de poques partícules. En el marc del present projecte de tesi doctoral es pretén estendre els algorismes desenvolupats per X. Oriols a sistemes quàntics constituïts tant per fermions com per bosons, i aplicar aquests algorismes a diferents sistemes quàntics mesoscòpics on les correlacions quàntiques juguen un paper important. De forma específica, els problemes a estudiar són els següents: (i) Fotoionització de l’àtom d’heli i de l’àtom de liti mitjançant un làser intens. (ii) Estudi de la relació entre la formulació de X. Oriols amb la aproximació de Born–Oppenheimer. (iii) Estudi de les correlacions quàntiques en sistemes bi- i tripartits en l’espai de configuració de les partícules mitjançant la formulació de de Broglie–Bohm.

Análisis morfométrico de la extremidad anterior en Carnivora

Durante los cuatro años de disfrute de la beca (2006 – 2009) se ha consolidado una base de datos de medidas osteológicas del esqueleto apendicular de numerosas especies del O. Carnivora. Concretamente, se han medido 364 individuos de 126 especies. Los ejemplares pertenecían a las colecciones del Phyletisches Museum (Jena, Alemania), el Museum für Naturkunde (Berlín, Alemania), el Museu de Ciències Naturals de la Ciutadella (Barcelona, España), el Múseum National d'Histoire Naturelle (París, Francia), y el Museo Nacional de Ciencias Naturales (Madrid, España). Asimismo, con estos datos se han estado preparando tres artículos sobre la morfología de ciertos elementos del esqueleto apendicular en carnívoros, dos de los cuales se encuentran actualmente en estado de revisión para su publicación científica. Dos de ellos, "Scapula, habitat and locomotion in Carnivora" y "Size and shape in the carnivore scapula", relacionan la morfología escapular con factores como el tamaño del animal, el tipo de locomoción que presenta y el hábitat en el que se encuentra; el primero mediante metodología multivariante (análisis funcional) y el segundo bajo las nuevas técnicas de morfometría geométrica. El tercer artículo, "Scaling and mechanics in the carnivore calcaneus: A comparison of natural and artificial selection", evalúa el efecto de diferentes tipos de selección, natural frente a artificial, sobre la morfología del calcáneo y su influencia en la biomecánica de este hueso. Finalmente, también se ha desarrollado un estudio experimental sobre la búsqueda de estabilidad durante la locomoción arbórea, cuyos resultados han dado lugar al artículo "The search for stability on narrow supports: An experimental study in cats and dogs", que también se halla bajo revisión actualmente.