On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.

Existence of secondary bifurcations or isolas for PDEs

In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines the Global Bifurcation Theorem, knowledge about the non-existence of nontrivial steady state solutions at the zero parameter value and explicit information about the coexistence of multiple nontrivial steady states at a positive parameter value. We apply the method to the two-dimensional Swift-Hohenberg equation. (C) 2011 Elsevier Ltd. All rights reserved.

Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system) causing spatial mode excitation Since the latter manifests as intermittent spikes this has been called a bubbling transition We present numerical evidences that this transition occurs due to the so called blowout bifurcation whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition (C) 2010 Elsevier B V All rights reserved

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Reversible and irreversible magnetization components behavior in Ni nanowires

Polycrystalline Ni nanowires were electrodeposited in nanoporous anodized alumina membranes with mean diameter of approximately 42 nm. Their magnetic properties were studied at 300 K, by measurements of recoil curves from demagnetized state and also from saturated state. M(rev) and M(irr) components were obtained and M(rev)(M(irr)) H curves were constructed from the experimental data. These curves showed a behavior that suggests a non-uniform reversal mode influenced by the presence of dipolar interactions in the system. A qualitative approach to this behavior is obtained using a Stoner-Wohlfarth model modified by a mean field term and local interaction fields. (C) 2008 Elsevier B.V. All rights reserved.

Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an in finite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.

Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies`s extension

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is the extended Skyrme-Faddeev model with a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled nonlinear partial differential equations in two variables by a successive over-relaxation method. We construct numerical solutions with the Hopf charge up to 4. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms.

Thermal dependence of the zero-bias conductance through a nanostructure

We show that the conductance of a quantum wire side-coupled to a quantum dot, with a gate potential favoring the formation of a dot magnetic moment, is a universal function of the temperature. Universality prevails even if the currents through the dot and the wire interfere. We apply this result to the experimental data of Sato et al. (Phys. Rev. Lett., 95 (2005) 066801). Copyright (C) EPLA, 2009

Structural stability and reversible unfolding of recombinant porcine S100A12

Porcine S100A12 is a member of the S100 proteins, family of small acidic calcium-binding proteins characterized by the presence of two EF-hand motifs. These proteins are involved in many cellular events such as the regulation of protein phosphorylation, enzymatic activity, protein-protein interaction, Ca(2+) homeostasis, inflammatory processes and intermediate filament polymerization. In addition, members of this family bind Zn(2+) or Ca(2+) with cooperative effect on binding. In this study, the gene sequence encoding porcine S100A12 was obtained by the synthetic gene approach using E. coli codon bias. Additionally, we report a thermodynamic study of the recombinant S100A12 using circular dichroism, fluorescence and isothermal titration calorimetry. The results of urea and temperature induced unfolding and refolding processes indicated a reversible two-state process. Also, the ANS fluorescence studies showed that in presence of divalent ions the protein exposes hydrophobic sites which could facilitate the interaction with other proteins and trigger the physiological responses. (c) 2008 Elsevier B.V. All rights reserved.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Jornalismo e interesses econômico-políticos : o caso das montadoras e o governo do PT em Zero Hora : 1999, o ano em que o jornal abandona o neoliberalismo e se torna "Keynesiano"

Este trabalho analisa a cobertura do jornal Zero Hora sobre o impasse entre o governo do Rio Grande do Sul e as montadoras de automóveis Ford e General Motors, no período de 16/03/1999 a 03/05/1999. É um estudo que procura, através do referencial da hermenêutica de profundidade, demonstrar como é construída a ideologia no jornalismo do grupo RBS – maior conglomerado de mídia da região Sul do Brasil –, com base no conceito proposto por Thompson de “sentido a serviço do poder”. A minuciosa pesquisa possibilitou perceber não só o agendamento de Zero Hora no caso envolvendo o governo do Partido dos Trabalhadores (PT) e as montadoras, mas a construção ideológica empreendida pelo jornal, legitimando o discurso das montadoras e da oposição, e desqualificando os argumentos do governo. O discurso neoliberal de redução das atribuições do Estado, hegemônico nas páginas de Zero Hora durante a década de 90, é trocado – nos primeiros meses do governo petista – por um discurso fragmentado, oportunista e descontextualizado do pensamento keynesiano, defendendo o papel importante do Estado na geração de emprego e renda, como propulsor do desenvolvimento através de investimentos e outras políticas de incentivos capazes de gerar um círculo virtuoso na economia. A cobertura tendenciosa de Zero Hora se tornaria um dos elementos constitutivos de um Cenário de Representação da Política (CR-P) desfavorável à candidatura petista na eleição para o governo do Rio Grande do Sul em 2002.