Search results for " Fisica Matematica"

Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains

2022

AbstractWe have theoretically investigated the phenomenon of Eckhaus instability of stationary patterns arising in hyperbolic reaction–diffusion models on large finite domains, in both supercritical and subcritical regime. Adopting multiple-scale weakly-nonlinear analysis, we have deduced the cubic and cubic–quintic real Ginzburg–Landau equations ruling the evolution of pattern amplitude close to criticality. Starting from these envelope equations, we have provided the explicit expressions of the most relevant dynamical features characterizing primary and secondary quantized branches of any order: stationary amplitude, existence and stability thresholds and linear growth rate. Particular em…

Toward a formalization of a two traders market with information exchange

2014

This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here {models a two traders system with information exchange with the help of four fundamental operators: cash and share operators; a portfolio operator and an operator reflecting the loss of information. An information Hamiltonian is considered and an additional Hamiltonian is presented which reflects the dynamics of selling/buying shares between traders. An important result of the paper is that when the information Hamiltonian is zero, portfolio operators commute with the Hamiltonian and this suggests that the dy…

Lagrangian dynamics and possible isochronous behavior in several classes of non-linear second order oscillators via the use of Jacobi last multiplier

2015

Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane–Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler–Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical result…

Approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom

1999

We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling prop…

Nonlinear Kelvin waves on a quantized vortex line in superfluid helium

2013

In this paper we show an exact solution (Kelvin wave) of an approximated dynamical equation for a quantized vortex line in helium superfluid at finite temperature. It is shown that the applied heat flux interacts with the vortex line, and the amplitude of the Kelvin wave can grow (the so-called Donnelly instability) or decrease according with the mutual direction between heat flux and wave vector.

On modeling the immune competition with Darwinian dynamics

Mathematical and computational models are increasingly used in this century to help modeling of living systems. Mathematical modeling presents many methods for studying and analyzing the behavior of biological systems, in particular, cellular systems. As Bellomo (2008), Bellouquid and Delitala (2006), suggest " The modeling of living systems is not an easy task, it requests technically complex mathematical methods to deal with the inner complexity of biological systems which exhibit features and behaviors very different from those of inert matter". The mathematical approach used in this dissertation is based on the Kinetic Theory of Active Particles (KTAP), that has been specifically develo…

Nonlocal model of Superfluid Turbulence: Constitutive Theory

2014

In this paper, the constitutive restrictions for the fluxes in a nonlocal model of superfluid turbulence are deduced from the entropy principle, using the Liu method of Lagrange multipliers. The proposed model chooses as fundamental fields the density, the velocity, the energy density, the heat flux, and the averaged vortex line length per unit volume. The onstitutive quantities are assumed to depend on the fundamental fields and on their first derivative.

Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators

2016

When modelling systems with a dispersed phase involving elliptic operators, as is the case of the Stokes or Navier-Stokes problem or the heat equation in a bounded domain, the geometrical structure of the space occupied by the dispersed phase enters in the homogenization process through its capacity, a quantity which can be used to define the equivalence classes in \(H^1\). We shall review the relationship between capacity and homogenization terms in the limit when the number of inclusions becomes large, focusing in particular on the situation where the distribution of inclusions is not necessarily too regular (i.e. it is not periodic).

The Heisenberg dynamics of spin systems: A quasi*‐algebras approach

1996

The problem of the existence of the thermodynamical limit of the algebraic dynamics for a class of spin systems is considered in the framework of a generalized algebraic approach in terms of a special class of quasi*-algebras, called CQ*-algebras. Physical applications to (almost) mean-field models and to bubble models are discussed. © 1996 American Institute of Physics.

Discrete KP Equation and Momentum Mapping of Toda System

2003

Abstract A new approach to discrete KP equation is considered, starting from the Gelfand-Zakhharevich theory for the research of Casimir function for Toda Poisson pencil. The link between the usual approach through the use of discrete Lax operators, is emphasized. We show that these two different formulations of the discrete KP equation are equivalent and they are different representations of the same equations. The relation between the two approaches to the KP equation is obtained by a change of frame in the space of upper truncated Laurent series and translated into the space of shift operators.