Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

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.

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.

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

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Tunneling among rotation tori

We consider an integrable Hamiltonian system generated by the resonant normal form in order to study a particular mechanism of tunneling. We isolated near doublets of energy corresponding to rotation tori of the classical dynamics counterpart and the degeneracies breakdown is attributed to rotation-rotation tunneling. (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.

Effect of enzymatic pretreatment and increasing the organic loading rate of lipid-rich wastewater treated in a hybrid UASB reactor

This study aimed at evaluating the effect of increasing organic loading rates and of enzyme pretreatment on the stability and efficiency of a hybrid upflow anaerobic sludge blanket reactor (UASBh) treating dairy effluent. The UASBh was submitted to the following average organic loading rates (OLR) 0.98 Kg.m(-3).d(-1), 4.58 Kg.m(-3).d(-1), 8.89 Kg.m(-3).d(-1) and 15.73 Kg.m(-3).d(-1), and with the higher value, the reactor was fed with effluent with and without an enzymatic pretreatment to hydrolyze fats. The hydraulic detention time was 24 h, and the temperature was 30 +/- 2 degrees C. The reactor was equipped with a superior foam bed and showed good efficiency and stability until an OLR of 8.89 Kg.m(-3).d(-1). The foam bed was efficient for solid retention and residual volatile acid concentration consumption. The enzymatic pretreatment did not contribute to the process stability, propitiating loss in both biomass and system efficiency. Specific methanogenic activity tests indicated the presence of inhibition after the sludge had been submitted to the pretreated effluent It was concluded that continuous exposure to the hydrolysis products or to the enzyme caused a dramatic drop in the efficiency and stability of the process, and the single exposure of the biomass to this condition did not inhibit methane formation. (C) 2011 Elsevier B.V. All rights reserved.

Effects of Synthesis Conditions on the Nanostructure of Hybrid Sols Produced by the Hydrolytic Condensation of (3-Methacryloxypropyl)trimethoxysilane

Polysilsesquioxanes containing methacrylate pendant groups were prepared by the sol-gel process through hydrolysis and condensation of (3-methacryloxypropyl)trimethoxysilane (MPTS) dissolved in a methanol/methyl methacrylate (MMA) mixture. The effects of different water, MMA, and methanol contents, as well as of pH, on the nanoscopic and local structures of the system, at advanced stages of the condensation reaction, were studied by small-angle X-ray scattering (SAXS) and (29)Si nuclear magnetic resonance (NMR) spectroscopy, respectively. SAXS results indicate that the nanoscopic features of the hybrid sol could be described by a hierarchical model composed of two levels, namely (i) silsesquioxane (SSQO) nanoparticles Surrounded by the methacrylate pendant groups and the methanol/MMA mixture. and (ii) aggregation zones or islands containing correlated SSQO nanoparticles, embedded in the liquid medium. The (29)Si NMR results Show that the inner Structures of SSQO nanoparticles produced at pH 1 and 3 were built Up of polyhedral structures. mainly cagelike octamers and small linear oligomers, respectively. Irrespective of MMA and methanol contents, for a [H(2)O]/[MPTS] ratio higher than or equal to 1, the SSQO nailoparticles produced at pH I exhibit an average condensation degree (CD approximate to 69-87%) and average radius of gyration (R(g) approximate to 2.5 angstrom) larger than those produced at pH 3 (CD approximate to 48-67% and R(g) approximate to 1.5 angstrom). Methanol appears to act as a redispersion agent, by decreasing the number of particles inside the aggregation zones, while the addition of MMA induces a swelling of the aggregation zones.

Hybrid reflections in InGaP/GaAs(001) by synchrotron radiation multiple diffraction

Hybrid reflections (HRs) involving substrate and layer planes (SL type) [Morelhao et al., Appl. Phys. Len. 73 (15), 2194 (1998)] observed in Chemical Beam Epitaxy (CBE) grown InGaP/GaAs(001) structures were used as a three-dimensional probe to analyze structural properties of epitaxial layers. A set of (002) rocking curves (omega-scan) measured for each 15 degrees in the azimuthal plane was arranged in a pole diagram in phi for two samples with different layer thicknesses (#A -58 nm and #B - 370 nm) and this allowed us to infer the azimuthal epilayer homogeneity in both samples. Also, it was shown the occurrence of (1 (1) over bar3) HR detected even in the thinner layer sample. Mappings of the HR diffraction condition (omega:phi) allowed to observe the crystal truncation rod through the elongation of HR shape along the substrate secondary reflection streak which can indicate in-plane match of layer/substrate lattice parameters. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Dynamical noncommutativity

The model of dynamical noncommutativity is proposed. The system consists of two interrelated parts. The first of them describes the physical degrees of freedom with the coordinates q(1) and q(2), and the second corresponds to the noncommutativity eta which has a proper dynamics. After quantization, the commutator of two physical coordinates is proportional to the function of eta. The interesting feature of our model is the dependence of nonlocality on the energy of the system. The more the energy, the more the nonlocality. The leading contribution is due to the mode of noncommutativity; however, the physical degrees of freedom also contribute in nonlocality in higher orders in theta .

Oxygen-mediated electron transport through hybrid silicon-organic interfaces

We investigate from first principles the electronic and transport properties of hybrid organic/silicon interfaces of relevance to molecular electronics. We focus on conjugated molecules bonded to hydrogenated Si through hydroxyl or thiol groups. The electronic structure of the systems is addressed within density functional theory, and the electron transport across the interface is directly evaluated within the Landauer approach. The microscopic effects of molecule-substrate bonding on the transport efficiency are explicitly analyzed, and the oxygen-bonded interface is identified as a candidate system when preferential hole transfer is needed.

A general treatment of geometric phases and dynamical invariants

Based only on the parallel-transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee`s non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non- Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature. Copyright (c) EPLA, 2008.