Protein-Ion Binding Process on Finite Macromolecular Concentration. A Poisson-Boltzmann and Monte Carlo Study

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics in dumbbell domains II. The limiting problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Regularization and singular perturbation techniques for non-smooth systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

LOSS of EXPONENTIAL STABILITY FOR A THERMOELASTIC SYSTEM WITH MEMORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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

Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture

Employing a time dependent mean-field-hydrodynamic model we study the generation of black solitons in a degenerate fermion-fermion mixture in a cigar-shaped geometry using variational and numerical solutions. The black soliton is found to be the first stationary vibrational excitation of the system and is considered to be a nonlinear continuation of the vibrational excitation of the harmonic oscillator state. We illustrate the stationary nature of the black soliton, by studying different perturbations on it after its formation.

Bound states of attractive Bose-Einstein condensates in shallow traps in two and three dimensions

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity), we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a localized exponentially screened radially symmetric harmonic potential well in two and three dimensions. We also consider an axially symmetric configuration with zero axial trap and a exponentially screened radial trap so that the resulting bound state can freely move along the axial direction like a soliton. The binding of the present states in shallow wells is mostly due to the nonlinear interaction with the trap playing a minor role. Hence, these BEC states are more suitable to study the effect of the nonlinear force on the dynamics. We illustrate the highly nonlinear nature of breathing oscillations of these states. Such bound states could be created in BECs and studied in the laboratory with present knowhow.

Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems

We associate to an arbitrary Z-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer-Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.

Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation

In this Letter we investigate Lie symmetries of a (2 + 1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1 + 1)-dimensional systems of partial differential equations in which one of them turns out to be a (1 + 1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation. (C) 2000 Published by Elsevier B.V. B.V.

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

Dissipative area-preserving one-dimensional Fermi accelerator model

The influence of dissipation on the simplified Fermi-Ulam accelerator model (SFUM) is investigated. The model is described in terms of a two-dimensional nonlinear mapping obtained from differential equations. It is shown that a dissipative SFUM possesses regions of phase space characterized by the property of area preservation.

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)