Spacetime algebraic skeleton

The cosmological constant is shown to have an algebraic meaning: it is essentially an eigenvalue of a Casimir invariant of the Lorentz group acting on the spaces tangent to every spacetime. This is found in the context of de Sitter spacetimes, for which the Einstein equation is a relation between operators. Nevertheless, the result brings, to the foreground the skeleton algebraic structure underlying the geometry of general physical spacetimes. which differ from one another by the fleshening of that structure by different tetrad fields.

Solitons from dressing in an algebraic approach to the constrained KP hierarchy

The algebraic matrix hierarchy approach based on affine Lie sl(n) algebras leads to a variety of 1 + 1 soliton equations. By varying the rank of the underlying sl(n) algebra as well as its gradation in the affine setting, one encompasses the set of the soliton equations of the constrained KP hierarchy.The soliton solutions are then obtained as elements of the orbits of the dressing transformations constructed in terms of representations of the vertex operators of the affine sl(n) algebras realized in the unconventional gradations. Such soliton solutions exhibit non-trivial dependence on the KdV (odd) time flows and KP (odd and even) time Bows which distinguishes them From the conventional structure of the Darboux-Backlund-Wronskian solutions of the constrained KP hierarchy.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Superstring vertex operators in an AdS(5) x S-5 background

A quantizable action has recently been proposed for the superstring in an AdS(5) x S-5 background with Ramond-Ramond flux. In this paper we construct physical vertex operators corresponding to on-shell fluctuations around the AdS(5) x S-5 background. The structure of these AdS(5) x S-5 vertex operators closely resembles the structure of the massless vertex operators in a flat background. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Pure spinor vertex operators in Siegel gauge and loop amplitude regularization

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new proposal for the picture changing operators in the minimal pure spinor formalism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New class of spin projection operators for 3D models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)