Méthodes rapides et efficaces pour la résolution numérique d'équations de type Hamilton-Jacobi avec application à la simulation de feux de forêt

Cette thèse est divisée en trois chapitres. Le premier explique comment utiliser la méthode «level-set» de manière rigoureuse pour faire la simulation de feux de forêt en utilisant comme modèle physique pour la propagation le modèle de l'ellipse de Richards. Le second présente un nouveau schéma semi-implicite avec une preuve de convergence pour la solution d'une équation de type Hamilton-Jacobi anisotrope. L'avantage principal de cette méthode est qu'elle permet de réutiliser des solutions à des problèmes «proches» pour accélérer le calcul. Une autre application de ce schéma est l'homogénéisation. Le troisième chapitre montre comment utiliser les méthodes numériques des deux premiers chapitres pour étudier l'influence de variations à petites échelles dans la vitesse du vent sur la propagation d'un feu de forêt à l'aide de la théorie de l'homogénéisation.

Une aventurière de haut vol, Lady Hamilton, ambassadrice d'Angleterre, et la révolution de Naples, d'après des documents inédits (1763-1815)

At head of title: Joseph Turquan et Jules d'Auriac.

D. Davidis Hamilton ... Tractatus duplex : prior de praxeos regulis, alter de febre miliari ; accesit febris miliaris historiarum fasciculus.

Davidis Hamiltoni ... Tractatus de febre miliari ..., p. [39]-176, con port. propia

Oeuvres complètes d'Hamilton.

Mode of access: Internet.

Escala Hamilton: estudo das características psicométricas em uma amostra do sul do Brasil

Objetivo Investigar as características psicométricas de uma versão traduzida da escala, propondo uma Versão Revisada que atenda aos critérios de adaptação transcultural para o contexto brasileiro. Métodos Este estudo incluiu 231 sujeitos – deprimidos (45,5%), bipolares (7,8%) e saudáveis (46,7%) – que participaram de uma pesquisa epidemiológica no sul do Brasil. A avaliação de transtornos mentais foi realizada por meio da Clinical Interview for DSM-IV (SCID) e uma versão traduzida da Escala de Avaliação de Depressão de Hamilton (HAM-D), que habitualmente vem sendo utilizada no país sem estudos de adaptação. Resultados Identificou-se o ponto de corte (9 pontos) para discriminar a presença ou não de sintomas de depressão pela análise da curva ROC, resultando em uma sensibilidade e especificidade de 90 e 91%, respectivamente. A validade interna foi investigada pela análise fatorial e consistência dos itens. Dos 17 itens originais, apenas o item que avalia a “consciência do transtorno” não apresentou carga fatorial satisfatória para avaliar depressão geral e foi eliminado; os 16 restantes agruparam-se em cinco dimensões, denominadas: Humor deprimido, Anorexia, Insônia, Somatização e Ansiedade, as quais, com exceção da última, mostraram homogeneidade nos seus construtos (coeficientes alfa entre 0,66 e 0,78). Na análise de conteúdo dos itens, cinco especialistas sugeriram alterações redacionais em sete itens. Conclusão O estudo determina um ponto de corte diferente do original e evidencia características psicométricas favoráveis para a utilização da escala no Brasil.

The Macropodoidea (Marsupialia) of the early Pliocene Hamilton local fauna, Victoria, Australia / Timothy F. Flannery --, et al.

n.s. no.25(1992)

Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

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.

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

A quantitative test of Hamilton's rule for the evolution of altruism.

The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb - c > 0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule). In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory.