Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Experimental Assessment of the Sensitiveness of an Electrochemical Oscillator towards Chemical Perturbations

In this study we address the problem of the response of a (electro)chemical oscillator towards chemical perturbations of different magnitudes. The chemical perturbation was achieved by addition of distinct amounts of trifluoromethanesulfonate (TFMSA), a rather stable and non-specifically adsorbing anion, and the system under investigation was the methanol electro-oxidation reaction under both stationary and oscillatory regimes. Increasing the anion concentration resulted in a decrease in the reaction rates of methanol oxidation and a general decrease in the parameter window where oscillations occurred. Furthermore, the addition of TFMSA was found to decrease the induction period and the total duration of oscillations. The mechanism underlying these observations was derived mathematically and revealed that inhibition in the methanol oxidation through blockage of active sites was found to further accelerate the intrinsic non-stationarity of the unperturbed system. Altogether, the presented results are among the few concerning the experimental assessment of the sensitiveness of an oscillator towards chemical perturbations. The universal nature of the complex chemical oscillator investigated here might be used for reference when studying the dynamics of other less accessible perturbed networks of (bio)chemical reactions.

Detection of gait perturbations based on proprioceptive information. Application to Limit Cycle Walkers

Walking on irregular surfaces and in the presence of unexpected events is a challenging problem for bipedal machines. Up to date, their ability to cope with gait disturbances is far less successful than humans': Neither trajectory controlled robots, nor dynamic walking machines (Limit CycleWalkers) are able to handle them satisfactorily. On the contrary, humans reject gait perturbations naturally and efficiently relying on their sensory organs that, if needed, elicit a recovery action. A similar approach may be envisioned for bipedal robots and exoskeletons: An algorithm continuously observes the state of the walker and, if an unexpected event happens, triggers an adequate reaction. This paper presents a monitoring algorithm that provides immediate detection of any type of perturbation based solely on a phase representation of the normal walking of the robot. The proposed method was evaluated in a Limit Cycle Walker prototype that suffered push and trip perturbations at different moments of the gait cycle, providing 100% successful detections for the current experimental apparatus and adequately tuned parameters, with no false positives when the robot is walking unperturbed.

Tidal perturbations of the rotation of the moon: the creep tide approach

In this communication we report results from the application to the study of the rotation of the Moon of the creeping tide theory just proposed (Ferraz-Mello, Cel. Mech. Dyn. Astron., submitted. ArXiv astro-ph 1204.3957). The choice of the Moon for the first application of this new theory is motivated by the fact that the Moon is one of the best observed celestial bodies and the comparison of the theoretical predictions of the theory with observations i may validate the theory or point out the need of further improvements. Particularly, the tidal perturbations of the rotation of the Moon - the physical libration of the Moon - have been detected in the Lunar Laser Ranging measurements (Williams et al. JGR 106, 27933, 2001). The major difficulty in this application comes from the fact that tidal torques in a planet-satellite system are very sensitive to the distance between the two-bodies, which is strongly affected by Solar perturbations. In the case of the Moon, the main solar perturbations - the Evection and the Variation - are more important than most of the Keplerian oscillations, being smaller only than the first Keplerian harmonic (equation of the centre). Besides, two of the three components of the Moon's libration in longitude whose tidal contributions were determined by LLR are related to these perturbations. The results may allow us to determine the main parameter of a possible Moon's creeping tide. The preliminary results point to a relaxation factor (gamma) 2 to 4 times smaller than the one predicted from the often cited values of thr Moon's quality factor Q (between 30 and 40), and points to larger Q values.

Tank experiments with borehole self-potential data

Despite their importance in the evaluation of petroleum and gas reservoirs, measurements of self-potential data under borehole conditions (well-logging) have found only minor applications in aquifer and waste-site characterization. This can be attributed to lower signals from the diffusion fronts in near-surface environments because measurements are made long after the drilling of the well, when concentration fronts are already disappearing. Proportionally higher signals arise from streaming potentials that prevent using simple interpretation models that assume signals from diffusion only. Our laboratory experiments found that dual-source self-potential signals can be described by a simple linear model, and that contributions (from diffusion and streaming potentials) can be isolated by slightly perturbing the borehole conditions. Perturbations are applied either by changing the concentration of the borehole-filling solution or its column height. Parameters useful for formation evaluation can be estimated from data measured during perturbations, namely, pore water resistivity, pressure drop across the borehole wall, and electrokinetic coupling parameter. These are important parameters to assess, respectively, water quality, aquifer lateral continuity, and interfacial properties of permeable formations.

Effect of pH and temperature on the global compactness, structure, and activity of cellobiohydrolase Cel7A from Trichoderma harzianum

Due to its elevated cellulolytic activity, the filamentous fungus Trichoderma harzianum (T. harzianum) has considerable potential in biomass hydrolysis application. Cellulases from Trichoderma reesei have been widely used in studies of cellulose breakdown. However, cellulases from T. harzianum are less-studied enzymes that have not been characterized biophysically and biochemically as yet. Here, we examined the effects of pH and temperature on the secondary and tertiary structures, compactness, and enzymatic activity of cellobiohydrolase Cel7A from T. harzianum (Th Cel7A) using a number of biophysical and biochemical techniques. Our results show that pH and temperature perturbations affect Th Cel7A stability by two different mechanisms. Variations in pH modify protonation of the enzyme residues, directly affecting its activity, while leading to structural destabilization only at extreme pH limits. Temperature, on the other hand, has direct influence on mobility, fold, and compactness of the enzyme, causing unfolding of Th Cel7A just above the optimum temperature limit. Finally, we demonstrated that incubation with cellobiose, the product of the reaction and a competitive inhibitor, significantly increased the thermal stability of Th Cel7A. Our studies might provide insights into understanding, at a molecular level, the interplay between structure and activity of Th Cel7A at different pH and temperature conditions.

Wormholes in de Sitter branes

In this work, we present a class of geometries which describes wormholes in a Randall-Sundrum brane model, focusing on de Sitter backgrounds. Maximal extensions of the solutions are constructed and their causal structures are discussed. A perturbative analysis is developed, where matter and gravitational perturbations are studied. Analytical results for the quasinormal spectra are obtained and an extensive numerical survey is conducted. Our results indicate that the wormhole geometries presented are stable.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

Influence Assessment in an Heteroscedastic Errors-in-Variables Model

The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

Postural adjustment after an unexpected perturbation in children with haemophilia

. Children with haemophilia often bleed inside joints and muscles, which may impair postural adjustments. These postural adjustments are necessary to control postural balance during daily activities. The inability to quickly recover postural balance could elevate the risk of bleeding. To determine whether children with haemophilia have impaired postural adjustment after an unexpected perturbation compared with healthy children. Twenty children with haemophilia comprised the haemophilic group (HG), and 20 healthy, age-paired children comprised the control group (CG). Subjects stood on a force plate, and 4% of the subjects body weight was applied via a pulley system to a belt around the subjects trunks. The centre of pressure (COP) displacement was measured after the weight was unexpectedly released to produce a controlled postural perturbation followed by postural adjustment to recover balance. The subjects postural adjustments in eight subsequent intervals of 1 s (t1t8), beginning with the moment of weight removal, were compared among intervals and between groups. The applied perturbation magnitudes were the same for both groups, and no difference was observed between the groups in t1. However, the COP displacement in t2 in the HG was significantly higher than in the CG. No differences were observed between the groups in the other intervals. Within-group analysis showed that the COP was higher in t2 than in t4 (P = 0.016), t5 (P = 0.001) and t8 (P = 0.050) in the HG. No differences were observed among intervals in the CG. Children with haemophilia demonstrated differences in postural adjustment while undergoing unexpected balance perturbations when compared with healthily children.

Progress in the mathematical theory of quantum disordered systems

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition, including some joint work with Marchetti, the (quantum and classical) Edwards-Anderson (EA) spin-glass model and return to equilibrium for a class of spin-glass models, which includes the EA model initially in a very large transverse magnetic field. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770066]

Coupling Between GABA(A)-R Ligand-Binding Activity and Membrane Organization in beta-Cyclodextrin-Treated Synaptosomal Membranes from Bovine Brain Cortex: New Insights from EPR Experiments

Correlations between GABA(A) receptor (GABA(A)-R) activity and molecular organization of synaptosomal membranes (SM) were studied along the protocol for cholesterol (Cho) extraction with beta-cyclodextrin (beta-CD). The mere pre-incubation (PI) at 37A degrees C accompanying the beta-CD treatment was an underlying source of perturbations increasing [H-3]-FNZ maximal binding (70%) and K (d) (38%), plus a stiffening of SMs' hydrocarbon core region. The latter was inferred from an increased compressibility modulus (K) of SM-derived Langmuir films, a blue-shifted DPH fluorescence emission spectrum and the hysteresis in DPH fluorescence anisotropy (A (DPH)) in SMs submitted to a heating-cooling cycle (4-37-4A degrees C) with A (DPH,heating) < A (DPH,cooling). Compared with PI samples, the beta-CD treatment reduced B (max) by 5% which correlated with a 45%-decrement in the relative Cho content of SM, a decrease in K and in the order parameter in the EPR spectrum of a lipid spin probe labeled at C5 (5-SASL), and significantly increased A (TMA-DPH). PI, but not beta-CD treatment, could affect the binding affinity. EPR spectra of 5-SASL complexes with beta-CD-, SM-partitioned, and free in solution showed that, contrary to what is usually assumed, beta-CD is not completely eliminated from the system through centrifugation washings. It was concluded that beta-CD treatment involves effects of at least three different types of events affecting membrane organization: (a) effect of PI on membrane annealing, (b) effect of residual beta-CD on SM organization, and (c) Cho depletion. Consequently, molecular stiffness increases within the membrane core and decreases near the polar head groups, leading to a net increase in GABA(A)-R density, relative to untreated samples.

New cosmic accelerating scenario without dark energy

We propose an alternative, nonsingular, cosmic scenario based on gravitationally induced particle production. The model is an attempt to evade the coincidence and cosmological constant problems of the standard model (Lambda CDM) and also to connect the early and late time accelerating stages of the Universe. Our space-time emerges from a pure initial de Sitter stage thereby providing a natural solution to the horizon problem. Subsequently, due to an instability provoked by the production of massless particles, the Universe evolves smoothly to the standard radiation dominated era thereby ending the production of radiation as required by the conformal invariance. Next, the radiation becomes subdominant with the Universe entering in the cold dark matter dominated era. Finally, the negative pressure associated with the creation of cold dark matter (CCDM model) particles accelerates the expansion and drives the Universe to a final de Sitter stage. The late time cosmic expansion history of the CCDM model is exactly like in the standard Lambda CDM model; however, there is no dark energy. The model evolves between two limiting (early and late time) de Sitter regimes. All the stages are also discussed in terms of a scalar field description. This complete scenario is fully determined by two extreme energy densities, or equivalently, the associated de Sitter Hubble scales connected by rho(I)/rho(f) = (H-I/H-f)(2) similar to 10(122), a result that has no correlation with the cosmological constant problem. We also study the linear growth of matter perturbations at the final accelerating stage. It is found that the CCDM growth index can be written as a function of the Lambda growth index, gamma(Lambda) similar or equal to 6/11. In this framework, we also compare the observed growth rate of clustering with that predicted by the current CCDM model. Performing a chi(2) statistical test we show that the CCDM model provides growth rates that match sufficiently well with the observed growth rate of structure.

Signature of the scattering between dark sectors in large scale cosmic microwave background anisotropies

We study the interaction between dark sectors by considering the momentum transfer caused by the dark matter scattering elastically within the dark energy fluid. Describing the dark scattering analogy to the Thomson scattering which couples baryons and photons, we examine the impact of the dark scattering in CMB observations. Performing global fitting with the latest observational data, we find that for a dark energy equation of state w < -1, the CMB gives tight constraints on dark matter-dark energy elastic scattering. Assuming a dark matter particle of proton mass, we derive an elastic scattering cross section of sigma(D) < 3.295 x 10(-10)sigma(T) where sigma(T) is the cross section of Thomson scattering. For w > -1, however, the constraints are poor. For w = -1, sigma(D) can formally take any value.