Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Numerical study of the atmospheric flow over a coastal cliff

This work presents a numerical method suitable for the study of the development of internal boundary layers (IBL) and their characteristics for flows over various types of coastal cliffs. The IBL is an important meteorological occurrence for flows with surface roughness and topographical step changes. A two-dimensional flow program was used for this study. The governing equations were written using the vorticity-velocity formulation. The spatial derivatives were discretized by high-order compact finite differences schemes. The time integration was performed with a low storage fourth-order Runge-Kutta scheme. The coastal cliff (step) was specified through an immersed boundary method. The validation of the code was done by comparison of the results with experimental and observational data. The numerical simulations were carried out for different coastal cliff heights and inclinations. The results show that the predominant factors for the height of the IBL and its characteristics are the upstream velocity, and the height and form (inclination) of the coastal cliff. Copyright (C) 2010 John Wiley & Sons, Ltd.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.

SZNAJD MODEL AND PROPORTIONAL ELECTIONS: THE ROLE OF THE TOPOLOGY OF THE NETWORK

The Sznajd model (SM) has been employed with success in the last years to describe opinion propagation in a community. In particular, it has been claimed that its transient is able to reproduce some scale properties observed in data of proportional elections, in different countries, if the community structure (the network) is scale-free. In this work, we investigate the properties of the transient of a particular version of the SM, introduced by Bernardes and co-authors in 2002. We studied the behavior of the model in networks of different topologies through the time evolution of an order parameter known as interface density, and concluded that regular lattices with high dimensionality also leads to a power-law distribution of the number of candidates with v votes. Also, we show that the particular absorbing state achieved in the stationary state (or else, the winner candidate), is related to a particular feature of the model, that may not be realistic in all situations.

An inductor-free realization of the Chua`s circuit based on electronic analogy

Although literature presents several alternatives, an approach based on the electronic analogy was still not considered for the implementation of an inductor-free realization of the double scroll Chua`s circuit. This paper presents a new inductor-free configuration of the Chua`s circuit based on the electronic analogy. This proposal results in a versatile and functional inductorless implementation of the Chua`s circuit that offers new and interesting features for several applications. The analogous circuit is implemented and used to perform an experimental mapping of a large variety of attractors.

The effect of the negative coupling parameter on the spectrum of a trapped Bose gas

The interest in attractive Bose-Einstein Condensates arises due to the chemical instabilities generate when the number of trapped atoms is above a critical number. In this case, recombination process promotes the collapse of the cloud. This behavior is normally geometry dependent. Within the context of the mean field approximation, the system is described by the Gross-Pitaevskii equation. We have considered the attractive Bose-Einstein condensate, confined in a nonspherical trap, investigating numerically and analytically the solutions, using controlled perturbation and self-similar approximation methods. This approximation is valid in all interval of the negative coupling parameter allowing interpolation between weak-coupling and strong-coupling limits. When using the self-similar approximation methods, accurate analytical formulas were derived. These obtained expressions are discussed for several different traps and may contribute to the understanding of experimental observations.

Application of abrupt cut-off models in the analysis of the capacitance spectra of conjugated polymer devices

In this paper, a detailed study of the capacitance spectra obtained from Au/doped-polyaniline/Al structures in the frequency domain (0.05 Hz-10 MHz), and at different temperatures (150-340 K) is carried out. The capacitance spectra behavior in semiconductors can be appropriately described by using abrupt cut-off models, since they assume that the electronic gap states that can follow the ac modulation have response times varying rapidly with a certain abscissa, which is dependent on both temperature and frequency. Two models based on the abrupt cut-off concept, formerly developed to describe inorganic semiconductor devices, have been used to analyze the capacitance spectra of devices based on doped polyaniline (PANI), which is a well-known polymeric semiconductor with innumerous potential technological applications. The application of these models allowed the determination of significant parameters, such as Debye length (approximate to 20 nm), position of bulk Fermi level (approximate to 320 meV) and associated density of states (approximate to 2x10(18) eV(-1) cm(-3)), width of the space charge region (approximate to 70 nm), built-in potential (approximate to 780 meV), and the gap states` distribution.

The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: (i) when each oscillator is coupled to its own reservoir, and (ii) when both oscillators are coupled to a common reservoir. After deriving and solving the master equation for each case, we analyze the decoherence process of particular entanglements in the positional space of both oscillators. To analyze the decoherence mechanism we have derived a general decay function, for the off-diagonal peaks of the density matrix, which applies both to common and separate reservoirs. We have also identified the expected interaction between the two dissipative oscillators induced by their common reservoir. Such a reservoir-induced interaction, which gives rise to interesting collective damping effects, such as the emergence of relaxation- and decoherence-free subspaces, is shown to be blurred by the high-temperature regime considered in this study. However, we find that different interactions between the dissipative oscillators, described by rotating or counter-rotating terms, result in different decay rates for the interference terms of the density matrix. (C) 2010 Elsevier B.V. All rights reserved.

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, in particular, are important for the construction of improved density functionals. Here we investigate one such universal property-the Lieb-Oxford lower bound-for ionic and molecular systems. In recent work [J Chem Phys 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals. (C) 2008 Wiley Periodicals Inc.

Molecular Basis of the Thermostability and Thermophilicity of Laminarinases: X-ray Structure of the Hyperthermostable Laminarinase from Rhodothermus marinus and Molecular Dynamics Simulations

Glycosyl hydrolases are enzymes capable of breaking the glycosidic linkage of polysaccharides and have considerable industrial and biotechnological applications. Driven by the later applications, it is frequently desirable that glycosyl hydrolases display stability and activity under extreme environment conditions, such as high temperatures and extreme pHs. Here, we present X-ray structure of the hyperthermophilic laminarinase from Rhodothermus marinus (RmLamR) determined at 1.95 angstrom resolution and molecular dynamics simulation studies aimed to comprehend the molecular basis, for the thermal stability of this class of enzymes. As most thermostable proteins, RmLamR contains a relatively large number of salt bridges, which are not randomly distributed on the structure. On the contrary, they form clusters interconnecting beta-sheets of the catalytic domain. Not all salt bridges, however, are beneficial for the protein thermostability: the existence of charge-charge interactions permeating the hydrophobic core of the enzymes actually contributes to destabilize the structure by facilitating water penetration into hydrophobic cavities, as can be seen in the case of mesophilic enzymes. Furthermore, we demonstrate that the mobility of the side-chains is perturbed differently in each class of enzymes. The side-chains of loop residues surrounding the catalytic cleft in the mesophilic laminarinase gain mobility and obstruct the active site at high temperature. By contrast, thermophilic laminarinases preserve their active site flexibility, and the active-site cleft remains accessible for recognition of polysaccharide substrates even at high temperatures. The present results provide structural insights into the role played by salt-bridges and active site flexibility on protein thermal stability and may be relevant for other classes of proteins, particularly glycosyl hydrolases.

Is the unfolding of the group discussion off-pattern? Improving coordination support in educational forums using mobile devices

A forum is a valuable tool to foster reflection in an in-depth discussion; however, it forces the course mediator to continually pay close attention in order to coordinate learners` activities. Moreover, monitoring a forum is time consuming given that it is impossible to know in advance when new messages are going to be posted. Additionally, a forum may be inactive for a long period and suddenly receive a burst of messages forcing forum mediators to frequently log on in order to know how the discussion is unfolding to intervene whenever it is necessary. Mediators also need to deal with a large amount of messages to identify off-pattern situations. This work presents a piece of action research that investigates how to improve coordination support in a forum using mobile devices for mitigating mediator`s difficulties in following the status of a forum. Based on summarized information extracted from message meta-data, mediators consult visual information summaries on PDAs and receive textual notifications in their mobile phone. This investigation revealed that mediators used the mobile-based coordination support to keep informed on what is taking place within the forum without the need to log on their desktop computer. (C) 2009 Elsevier Ltd. All rights reserved.