Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. © 2010 Elsevier B.V. All rights reserved.

Quantum entanglement and information: The effect of entropy revisited

In non-extensive statistical mechanics [14], it is a nonsense statement to say that the entropy of a system is extensive (or not), without mentioning a law of composition of its elements. In this theory quantum correlations might be perceived through quantum information process. This article, that is an extension of recent work [4], is a comparative study between the entropies of Von Neumann and of Tsallis, with some implementations of the effect of entropy in quantum entanglement, important as a process for transmission of quantum information. We consider two factorized (Fock number) states, which interact through a beam splitter bilinear Hamiltonian with two entries. This comparison showed us that the entropies of Tsallis and Von Neumann behave differently depending on the reflectance of the beam splitter. © 2011 Academic Publications.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ. © 2011 Elsevier B.V. All rights reserved.

Dipolar droplet bound in a trapped Bose-Einstein condensate

We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164Dy droplet bound in a trapped nondipolar 87Rb BEC with a variable number of 164Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a 164Dy droplet by relaxing the trap on the 164Dy BEC in a trapped binary 87Rb-164Dy mixture. © 2013 American Physical Society.

Fractal dimension and Shannon's entropy analyses of the architectural complexity caused by the inflammatory reactions induced by highly crystalline polyvinyl alcohol) microspheres implanted in subcutaneous tissues of the Wistar rats

The results of the histopathological analyses after the implantation of highly crystalline PVA microspheres in subcutaneous tissues of Wistar rats are here in reported. Three different groups of PVA microparticles were systematically studied: highly crystalline, amorphous, and commercial ones. In addition to these experiments, complementary analyses of architectural complexity were performed using fractal dimension (FD), and Shannon's entropy (SE) concepts. The highly crystalline microspheres induced inflammatory reactions similar to the ones observed for the commercial ones, while the inflammatory reactions caused by the amorphous ones were less intense. Statistical analyses of the subcutaneous tissues of Wistar rats implanted with the highly crystalline microspheres resulted in FD and SE values significantly higher than the statistical parameters observed for the amorphous ones. The FD and SE parameters obtained for the subcutaneous tissues of Wistar rats implanted with crystalline and commercial microparticles were statistically similar. Briefly, the results indicated that the new highly crystalline microspheres had biocompatible behavior comparable to the commercial ones. In addition, statistical tools such as FD and SE analyses when combined with histopathological analyses can be useful tools to investigate the architectural complexity tissues caused by complex inflammatory reactions. © 2012 WILEY PERIODICALS, INC.

Identifying financial crises in real time

Following the thermodynamic formulation of a multifractal measure that was shown to enable the detection of large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crises in real time. We calculate the partition function from which we can obtain thermodynamic quantities analogous to the free energy and specific heat. The index is defined as the normalized energy variation and it can be used to study the behavior of stochastic time series, such as financial market daily data. Famous financial market crashes-Black Thursday (1929), Black Monday (1987) and the subprime crisis (2008)-are identified with clear and robust results. The method is also applied to the market fluctuations of 2011. From these results it appears as if the apparent crisis of 2011 is of a different nature to the other three. We also show that the analysis has forecasting capabilities. © 2012 Elsevier B.V. All rights reserved.

Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too. © 2012 Elsevier B.V. All rights reserved.

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity. © 2013 American Physical Society.

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Chaotic thermalization in classical gauge theories

We explore the idea that chaos concepts might be useful for understanding the thermalization in gauge theories. The SU(2) Higgs model is discussed as a prototype of system with gauge fields coupled to matter fields. Through the numerical solution of the equations of motion, we are able to characterize chaotic behavior via the corresponding Lyapunov exponent. Then it is demonstrated that the system's approach to equilibrium can be understood through direct application of the principles of Statistical Mechanics. © 2013 AIP Publishing LLC.

Stability of trapped degenerate dipolar Bose and Fermi gases

Trapped degenerate dipolar Bose and Fermi gases of the cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose-Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using a variational approximation and a numerical solution of a mean-field model. In the disc shape, with the polarization vector perpendicular to the plane of the disc, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disc-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree-Fock exchange and Brueckner-Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in the BEC and degenerate Fermi gas are given. © 2013 IOP Publishing Ltd.

Dynamics characterization of modified Gross-Pitaevskii equation

The dynamics of dissipative and coherent N-body systems, such as a Bose-Einstein condensate, which can be described by an extended Gross-Pitaevskii formalism, is investigated. In order to analyze chaotic and unstable regimes, two approaches are considered: a metric one, based on calculations of Lyapunov exponents, and an algorithmic one, based on the Lempel-Ziv criterion. The consistency of both approaches is established, with the Lempel-Ziv algorithmic found as an efficient complementary approach to the metric one for the fast characterization of dynamical behaviors obtained from finite sequences. © 2013 Elsevier B.V. All rights reserved.

Thermal phase transition for some spin-boson models

In this work we study two different spin-boson models. Such models are generalizations of the Dicke model, it means they describe systems of N identical two-level atoms coupled to a single-mode quantized bosonic field, assuming the rotating wave approximation. In the first model, we consider the wavelength of the bosonic field to be of the order of the linear dimension of the material composed of the atoms, therefore we consider the spatial sinusoidal form of the bosonic field. The second model is the Thompson model, where we consider the presence of phonons in the material composed of the atoms. We study finite temperature properties of the models using the path integral approach and functional methods. In the thermodynamic limit, N→∞, the systems exhibit phase transitions from normal to superradiant phase at some critical values of temperature and coupling constant. We find the asymptotic behavior of the partition functions and the collective spectrums of the systems in the normal and the superradiant phases. We observe that the collective spectrums have zero energy values in the superradiant phases, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the models. Our analysis and results are valid in the limit of zero temperature β→∞, where the models exhibit quantum phase transitions. © 2013 Elsevier B.V. All rights reserved.

Hot Brownian carriers in the Langevin picture: Application to a simple model for the Gunn effect in GaAs

We consider a charged Brownian gas under the influence of external, static and uniform electric and magnetic fields, immersed in a uniform bath temperature. We obtain the solution for the associated Langevin equation, and thereafter the evolution of the nonequilibrium temperature towards a nonequilibrium (hot) steady state. We apply our results to a simple yet relevant Brownian model for carrier transport in GaAs. We obtain a negative differential conductivity regime (Gunn effect) and discuss and compare our results with the experimental results. © 2013.