Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Hamiltonian and Lagrangian constraints of the bosonic string

We study the Hamiltonian and Lagrangian constraints of the Polyakov string. The gauge fixing at the Hamiltonian and Lagrangian level is also studied.

Ordered structures in rotating ultracold Bose gases

Two-dimentional systems of trapped samples of few cold bosonic atoms submitted to strong rotation around the perpendicular axis may be realized in optical lattices and microtraps. We investigate theoretically the evolution of ground state structures of such systems as the rotational frequency Omega increases. Various kinds of ordered structures are observed. In some cases, hidden interference patterns exhibit themselves only in the pair correlation function; in some other cases explicit broken-symmetry structures appear that modulate the density. For N < 10 atoms, the standard scenario, valid for large sytems is absent, and is only gradually recovered as N increases. On the one hand, the Laughlin state in the strong rotational regime contains ordered structures much more similar to a Wigner molecule than to a fermionic quantum liquid. On the other hand, in the weak rotational regime, the possibility to obtain equilibrium states, whose density reveals an array of vortices, is restricted to the vicinity of some critical values of the rotational frequency Omega.

Equivalence Between the Lagrangian and Hamiltonian Formalisms for Constrained Systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL-projectable.

Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces

A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the first reduce method is emphasized. One of the main results is the relation between the propagator obtained la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out. 1995 American Institute of Physics.

Topographic forcing of flow partition and flow structures at river bifurcations

This paper presents the predicted flow dynamics from the application of a Reynolds-averaged NavierStokes model to a series of bifurcation geometries with morphologies measured during previous flume experiments. The topography of the bifurcations consists of either plane or bedform-dominated beds which may or may not possess discordance between the two bifurcation distributaries. Numerical predictions are compared with experimental results to assess the ability of the numerical model to reproduce the division of flow into the bifurcation distributaries. The hydrodynamic model predicts: (1) diverting fluxes in the upstream channel which direct water into the distributaries; (2) super-elevation of the free surface induced at the bifurcation edge by pressure differences; and (3) counter-rotating secondary circulation cells which develop upstream of the apex of the bifurcation and move into the downstream channels, with water converging at the surface and diverging at the bed. When bedforms are not present, weak transversal fluxes characterize the upstream channel for almost its entire length, associated with clearly distinguishable secondary circulation cells, although these may be under-estimated by the turbulence model used in the solution. In the bedform dominated case, the same hydrodynamic conditions were not observed, with the bifurcation influence restricted and depth scale secondary circulation cells not forming. The results also demonstrate the dominant effect bed discordance has upon flow division between the two distributaries. Finally, results indicate that in bedform dominated rivers. Consequently, we suggest that sand-bed river bifurcations are more likely to have an influence that extends much further upstream and have a greater impact upon water distribution. This may contribute to observed morphological differences between sand-bedded and gravel-bedded braided river networks. Copyright (C) 2012 John Wiley & Sons, Ltd.

Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional (3D) islands on top of the wetting layer in the Stranski-Krastanov mode of growth is considered in a model in 1 + 1 dimensions accounting for the anharmonicity and nonconvexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than expanded overlayers beyond a critical lattice misfit. In expanded overlayers the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. This explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after the corresponding critical sizes have been exceeded. The rearrangements are initiated by nucleation events, each one needing to overcome a lower energetic barrier than the one before. The model is in good qualitative agreement with available experimental observations.

Long-range-interactions induced ordered structures in deposition processes

We present a new model of sequential adsorption in which the adsorbing particles experience dipolar interactions. We show that in the presence of these long-range interactions, highly ordered structures in the adsorbed layer may be induced at low temperatures. The new phenomenology is manifest through significant variations of the pair correlation function and the jamming limit, with respect to the case of noninteracting particles. Our study could be relevant in understanding the adsorption of magnetic colloidal particles in the presence of a magnetic field.

Coherent stochastic resonance

We consider Brownian motion on a line terminated by two trapping points. A bias term in the form of a telegraph signal is applied to this system. It is shown that the first two moments of survival time exhibit a minimum at the same resonant frequency.

Flow structures at an idealized bifurcation : a numerical experiment

River bifurcations are key nodes within braided river systems controlling the flow and sediment partitioning and therefore the dynamics of the river braiding process. Recent research has shown that certain geometrical configurations induce instabilities that lead to downstream mid-channel bar formation and the formation of bifurcations. However, we currently have a poor understanding of the flow division process within bifurcations and the flow dynamics in the downstream bifurcates, both of which are needed to understand bifurcation stability. This paper presents results of a numerical sensitivity experiment undertaken using computational fluid dynamics (CFD) with the purpose of understanding the flow dynamics of a series of idealized bifurcations. A geometric sensitivity analysis is undertaken for a range of channel slopes (0.005 to 0.03), bifurcation angles (22 degrees to 42 degrees) and a restricted set of inflow conditions based upon simulating flow through meander bends with different curvature on the flow field dynamics through the bifurcation. The results demonstrate that the overall slope of the bifurcation affects the velocity of flow through the bifurcation and when slope asymmetry is introduced, the flow structures in the bifurcation are modified. In terms of bifurcation evolution the most important observation appears to be that once slope asymmetry is greater than 0.2 the flow within the steep bifurcate shows potential instability and the potential for alternate channel bar formation. Bifurcation angle also defines the flow structures within the bifurcation with an increase in bifurcation angle increasing the flow velocity down both bifurcates. However, redistributive effects of secondary circulation caused by upstream curvature can very easily counter the effects of local bifurcation characteristics. Copyright (C) 2011 John Wiley & Sons, Ltd.

Apprentissage automatique de la morphologie : le cas des structures racine-schème

RÉSUMÉ Cette thèse porte sur le développement de méthodes algorithmiques pour découvrir automatiquement la structure morphologique des mots d'un corpus. On considère en particulier le cas des langues s'approchant du type introflexionnel, comme l'arabe ou l'hébreu. La tradition linguistique décrit la morphologie de ces langues en termes d'unités discontinues : les racines consonantiques et les schèmes vocaliques. Ce genre de structure constitue un défi pour les systèmes actuels d'apprentissage automatique, qui opèrent généralement avec des unités continues. La stratégie adoptée ici consiste à traiter le problème comme une séquence de deux sous-problèmes. Le premier est d'ordre phonologique : il s'agit de diviser les symboles (phonèmes, lettres) du corpus en deux groupes correspondant autant que possible aux consonnes et voyelles phonétiques. Le second est de nature morphologique et repose sur les résultats du premier : il s'agit d'établir l'inventaire des racines et schèmes du corpus et de déterminer leurs règles de combinaison. On examine la portée et les limites d'une approche basée sur deux hypothèses : (i) la distinction entre consonnes et voyelles peut être inférée sur la base de leur tendance à alterner dans la chaîne parlée; (ii) les racines et les schèmes peuvent être identifiés respectivement aux séquences de consonnes et voyelles découvertes précédemment. L'algorithme proposé utilise une méthode purement distributionnelle pour partitionner les symboles du corpus. Puis il applique des principes analogiques pour identifier un ensemble de candidats sérieux au titre de racine ou de schème, et pour élargir progressivement cet ensemble. Cette extension est soumise à une procédure d'évaluation basée sur le principe de la longueur de description minimale, dans- l'esprit de LINGUISTICA (Goldsmith, 2001). L'algorithme est implémenté sous la forme d'un programme informatique nommé ARABICA, et évalué sur un corpus de noms arabes, du point de vue de sa capacité à décrire le système du pluriel. Cette étude montre que des structures linguistiques complexes peuvent être découvertes en ne faisant qu'un minimum d'hypothèses a priori sur les phénomènes considérés. Elle illustre la synergie possible entre des mécanismes d'apprentissage portant sur des niveaux de description linguistique distincts, et cherche à déterminer quand et pourquoi cette coopération échoue. Elle conclut que la tension entre l'universalité de la distinction consonnes-voyelles et la spécificité de la structuration racine-schème est cruciale pour expliquer les forces et les faiblesses d'une telle approche. ABSTRACT This dissertation is concerned with the development of algorithmic methods for the unsupervised learning of natural language morphology, using a symbolically transcribed wordlist. It focuses on the case of languages approaching the introflectional type, such as Arabic or Hebrew. The morphology of such languages is traditionally described in terms of discontinuous units: consonantal roots and vocalic patterns. Inferring this kind of structure is a challenging task for current unsupervised learning systems, which generally operate with continuous units. In this study, the problem of learning root-and-pattern morphology is divided into a phonological and a morphological subproblem. The phonological component of the analysis seeks to partition the symbols of a corpus (phonemes, letters) into two subsets that correspond well with the phonetic definition of consonants and vowels; building around this result, the morphological component attempts to establish the list of roots and patterns in the corpus, and to infer the rules that govern their combinations. We assess the extent to which this can be done on the basis of two hypotheses: (i) the distinction between consonants and vowels can be learned by observing their tendency to alternate in speech; (ii) roots and patterns can be identified as sequences of the previously discovered consonants and vowels respectively. The proposed algorithm uses a purely distributional method for partitioning symbols. Then it applies analogical principles to identify a preliminary set of reliable roots and patterns, and gradually enlarge it. This extension process is guided by an evaluation procedure based on the minimum description length principle, in line with the approach to morphological learning embodied in LINGUISTICA (Goldsmith, 2001). The algorithm is implemented as a computer program named ARABICA; it is evaluated with regard to its ability to account for the system of plural formation in a corpus of Arabic nouns. This thesis shows that complex linguistic structures can be discovered without recourse to a rich set of a priori hypotheses about the phenomena under consideration. It illustrates the possible synergy between learning mechanisms operating at distinct levels of linguistic description, and attempts to determine where and why such a cooperation fails. It concludes that the tension between the universality of the consonant-vowel distinction and the specificity of root-and-pattern structure is crucial for understanding the advantages and weaknesses of this approach.