Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

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.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Chaotic phase synchronization and desynchronization in an oscillator network for object selection

Object selection refers to the mechanism of extracting objects of interest while ignoring other objects and background in a given visual scene. It is a fundamental issue for many computer vision and image analysis techniques and it is still a challenging task to artificial Visual systems. Chaotic phase synchronization takes place in cases involving almost identical dynamical systems and it means that the phase difference between the systems is kept bounded over the time, while their amplitudes remain chaotic and may be uncorrelated. Instead of complete synchronization, phase synchronization is believed to be a mechanism for neural integration in brain. In this paper, an object selection model is proposed. Oscillators in the network representing the salient object in a given scene are phase synchronized, while no phase synchronization occurs for background objects. In this way, the salient object can be extracted. In this model, a shift mechanism is also introduced to change attention from one object to another. Computer simulations show that the model produces some results similar to those observed in natural vision systems.

Dust and smoke transport from Africa to South America: Lidar profiling over Cape Verde and the Amazon rainforest

Quasi-simultaneous vertically resolved multiwavelength aerosol Raman lidar observations were conducted in the near field (Praia, Cape Verde, 15 degrees N, 23.5 degrees W) and in the far field (Manaus, Amazon basin, Brazil, 2.5 degrees S, 60 degrees W) of the long-range transport regime between West Africa and South America. Based on a unique data set (case study) of spectrally resolved backscatter and extinction coefficients, and of the depolarization ratio a detailed characterization of aerosol properties, vertical stratification, mixing, and aging behavior during the long-distance travel in February 2008 (dry season in western Africa, wet season in the Amazon basin) is presented. While highly stratified aerosol layers of dust and smoke up to 5.5 km height were found close to Africa, the aerosol over Manaus was almost well-mixed, reached up to 3.5 km, and mainly consisted of aged biomass burning smoke. Citation: Ansmann, A., H. Baars, M. Tesche, D. Muller, D. Althausen, R. Engelmann, T. Pauliquevis, and P. Artaxo (2009), Dust and smoke transport from Africa to South America: Lidar profiling over Cape Verde and the Amazon rainforest, Geophys. Res. Lett., 36, L11802, doi: 10.1029/2009GL037923.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen: (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes. (C) 2011 Elsevier B.V. All rights reserved.

Ab initio study of SO2 molecules interacting with pristine and transition metal covered fullerenes as a possible route for nanofilters

In this work, a systematic study of SO2 molecules interacting with pristine and transition metal (TM) covered C-60 is presented by means of first principles calculations. It is observed that the SO2 molecule interacts weakly with the pristine C-60 fullerene, although the resulting interaction is largely increased when the C-60 structure is covered with Fe, Mn, or Ti atoms and the SO2 Molecules are bounded through the TM atoms. The number of bounded SO2 molecules per TM atoms, in addition to the elevated binding energies per molecules, allows us to conclude that such composites can be used as a template for efficient devices to remove SO2 molecules or, alternatively, as SO2 gas sensor.

Third-order nonlinearity of Er(3+)-doped lead phosphate glass

The third-order optical susceptibility and dispersion of the linear refractive index of Er(3+)-doped lead phosphate glass were measured in the wavelength range between 400 and 1940 nm by using the spectrally resolved femtosecond Maker fringes technique. The nonlinear refractive index obtained from the third-order susceptibility was found to be five times higher than that of silica, indicating that Er(3+)-doped lead phosphate glass is a potential candidate to be used as the base component for the fabrication of photonic devices. For comparison purposes, the Z-scan technique was also employed to obtain the values of the nonlinear refractive index of Er(3+)-doped lead phosphate glass at several wavelengths, and the values obtained using the two techniques agree to within 15%.

The Cariris Velhos tectonic event in Northeast Brazil

The Borborema Province in northeastern South America is a typical Brasiliano-Pan-African branching system of Neoproterozoic orogens that forms part of the Western Gondwana assembly. The province is positioned between the Sao Luis-West Africa craton to the north and the Sao Francisco (Congo-Kasai) craton to the south. For this province the main characteristics are (a) its subdivision into five major tectonic domains, bounded mostly by long shear zones, as follows: Medio Coreau, Ceara Central, Rio Grande do Norte, Transversal, and Southern; (b) the alternation of supracrustal belts with reworked basement inliers (Archean nuclei + Paleoproterozoic belts); and (c) the diversity of granitic plutonism, from Neoproterozoic to Early Cambrian ages, that affect supracrustal rocks as well as basement inliers. Recently, orogenic rock assemblages of early Tonian (1000-920 Ma) orogenic evolution have been recognized, which are restricted to the Transversal and Southern domains of the Province. Within the Transversal Zone, the Alto Pajeu terrane locally includes some remnants of oceanic crust along with island arc and continental arc rock assemblages, but the dominant supracrustal rocks are mature and immature pelitic metasedimentary and metavolcaniclastic rocks. Contiguous and parallel to the Alto Pajeu terrane, the Riacho Gravata subterrane consists mainly of low-grade metamorphic successions of metarhythmites, some of which are clearly turbiditic in origin, metaconglomerates, and sporadic marbles, along with interbedded metarhyolitic and metadacitic volcanic or metavolcaniclastic rocks. Both terrane and subterrane are cut by syn-contractional intrusive sheets of dominantly peraluminous high-K calc-alkaline, granititic to granodioritic metaplutonic rocks. The geochemical patterns of both supracrustal and intrusive rocks show similarities with associations of mature continental arc volcano-sedimentary sequences, but some subordinate intra-plate characteristics are also found. In both the Alto Pajeu and Riacho Gravata terranes, TIMS and SHRIMP U-Pb isotopic data from zircons from both metavolcanic and metaplutonic rocks yield ages between 1.0 and 0.92 Ga, which define the time span for an event of orogenic character, the Cariris Velhos event. Less extensive occurrences of rocks of Cariris Velhos age are recognized mainly in the southernmost domains of the Province, as for example in the Polo Redondo-Maranco terrane, where arc-affinity migmatite-granitic and meta-volcano-sedimentary rocks show U-Pb ages (SHRIMP data) around 0.98-0.97 Ga. For all these domains, Sm-Nd data exhibit Tom model ages between 1.9 and 1.1 Ga with corresponding slightly negative to slightly positive epsilon(Nd)(t) values. These domains, along with the Borborema Province as a whole, were significantly affected by tectonic and magmatic events of the Brasiliano Cycle (0.7-0.5 Ga), so that it is possible that there are some other early Tonian rock assemblages which were completely masked and hidden by these later Brasiliano events. Cariris Velhos processes are younger than the majority of orogenic systems at the end of Mesoproterozoic Era and beginning of Neoproterozoic throughout the world, e.g. Irumide belt, Kibaride belt and Namaqua-Natal belt, and considerably younger than those of the youngest orogenic process (Ottawan) in the Grenvillian System. Therefore, they were probably not associated with the proposed assembly of Rodinia. We suggest, instead, that Cariris Velhos magmatism and tectonism could have been related to a continental margin magmatic arc, with possible back-arc associations, and that this margin may have been a short-lived (<100 m.y.) leading edge of the newly assembled Rodinia supercontinent. (C) 2009 Elsevier Ltd. All rights reserved.

Quaternary tectonics in a passive margin: Marajo Island, northern Brazil

Marajo Island is located in a passive continental margin that evolved from rifting associated with the opening of the Equatorial South Atlantic Ocean in the Late Jurassic/Early Cretaceous period. This study, based on remote sensing integrated with sedimentology, as well as subsurface and seismographic data available from the literature, allows discussion of the significance of tectonics during the Quaternary history of marginal basins. Results show that eastern Marajo Island contains channels with evidence of tectonic control. Mapping of straight channels defined four main groups of lineaments (i.e. NNE-SSW, NE-SW, NW-SE and E-W) that parallel main normal and strike-slip fault zones recorded for the Amazon region. Additionally, sedimentological studies of late Quaternary and Holocene deposits indicate numerous ductile and brittle structures within stratigraphic horizons bounded by undeformed strata, related to seismogenic deformation during or shortly after sediment deposition. This conclusion is consistent with subsurface Bouguer mapping suggestive of eastern Marajo Island being still part of the Marajo graben system, where important fault reactivation is recorded up to the Quaternary. Together with the recognition of several phases of fault reactivation, these data suggest that faults developed in association with rift basins might remain active in passive margins, imposing important control on development of depositional systems. Copyright (C) 2007 John Wiley & Sons, Ltd.