Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Analysis of energy dissipation in stirred suspension polymerisation reactors using computational fluid dynamics

This work evaluates the spatial distribution of normalised rates of droplet breakage and droplet coalescence in liquidliquid dispersions maintained in agitated tanks at operation conditions normally used to perform suspension polymerisation reactions. Particularly, simulations are performed with multiphase computational fluid dynamics (CFD) models to represent the flow field in liquidliquid styrene suspension polymerisation reactors for the first time. CFD tools are used first to compute the spatial distribution of the turbulent energy dissipation rates (e) inside the reaction vessel; afterwards, normalised rates of droplet breakage and particle coalescence are computed as functions of e. Surprisingly, multiphase simulations showed that the rates of energy dissipation can be very high near the free vortex surfaces, which has been completely neglected in previous works. The obtained results indicate the existence of extremely large energy dissipation gradients inside the vessel, so that particle breakage occurs primarily in very small regions that surround the impeller and the free vortex surface, while particle coalescence takes place in the liquid bulk. As a consequence, particle breakage should be regarded as an independent source term or a boundary phenomenon. Based on the obtained results, it can be very difficult to justify the use of isotropic assumptions to formulate particle population balances in similar systems, even when multiple compartment models are used to describe the fluid dynamic behaviour of the agitated vessel. (C) 2011 Canadian Society for Chemical Engineering

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

The behavior of the average energy for an ensemble of non-interacting particles is studied using scaling arguments in a dissipative time-dependent stadium-like billiard. The dynamics of the system is described by a four dimensional nonlinear mapping. The dissipation is introduced via inelastic collisions between the particles and the moving boundary. For different combinations of initial velocities and damping coefficients, the long time dynamics of the particles leads them to reach different states of final energy and to visit different attractors, which change as the dissipation is varied. The decay of the average energy of the particles, which is observed for a large range of restitution coefficients and different initial velocities, is described using scaling arguments. Since this system exhibits unlimited energy growth in the absence of dissipation, our results for the dissipative case give support to the principle that Fermi acceleration seems not to be a robust phenomenon. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3699465]

Maternal Melatonin Programs the Daily Pattern of Energy Metabolism in Adult Offspring

Background: Shift work was recently described as a factor that increases the risk of Type 2 diabetes mellitus. In addition, rats born to mothers subjected to a phase shift throughout pregnancy are glucose intolerant. However, the mechanism by which a phase shift transmits metabolic information to the offspring has not been determined. Among several endocrine secretions, phase shifts in the light/dark cycle were described as altering the circadian profile of melatonin production by the pineal gland. The present study addresses the importance of maternal melatonin for the metabolic programming of the offspring. Methodology/Principal Findings: Female Wistar rats were submitted to SHAM surgery or pinealectomy (PINX). The PINX rats were divided into two groups and received either melatonin (PM) or vehicle. The SHAM, the PINX vehicle and the PM females were housed with male Wistar rats. Rats were allowed to mate and after weaning, the male and female offspring were subjected to a glucose tolerance test (GTT), a pyruvate tolerance test (PTT) and an insulin tolerance test (ITT). Pancreatic islets were isolated for insulin secretion, and insulin signaling was assessed in the liver and in the skeletal muscle by western blots. We found that male and female rats born to PINX mothers display glucose intolerance at the end of the light phase of the light/dark cycle, but not at the beginning. We further demonstrate that impaired glucose-stimulated insulin secretion and hepatic insulin resistance are mechanisms that may contribute to glucose intolerance in the offspring of PINX mothers. The metabolic programming described here occurs due to an absence of maternal melatonin because the offspring born to PINX mothers treated with melatonin were not glucose intolerant. Conclusions/Significance: The present results support the novel concept that maternal melatonin is responsible for the programming of the daily pattern of energy metabolism in their offspring.

A search for anisotropy in the arrival directions of ultra high energy cosmic rays recorded at the Pierre Auger Observatory

Observations of cosmic rays arrival directions made with the Pierre Auger Observatory have previously provided evidence of anisotropy at the 99% CL using the correlation of ultra high energy cosmic rays (UHECRs) with objects drawn from the Veron-Cetty Veron catalog. In this paper we report on the use of three catalog independent methods to search for anisotropy. The 2pt-L, 2pt+ and 3pt methods, each giving a different measure of self-clustering in arrival directions, were tested on mock cosmic ray data sets to study the impacts of sample size and magnetic smearing on their results, accounting for both angular and energy resolutions. If the sources of UHECRs follow the same large scale structure as ordinary galaxies in the local Universe and if UHECRs are deflected no more than a few degrees, a study of mock maps suggests that these three method can efficiently respond to the resulting anisotropy with a P-value = 1.0% or smaller with data sets as few as 100 events. using data taken from January 1, 2004 to July 31, 2010 we examined the 20, 30, ... , 110 highest energy events with a corresponding minimum energy threshold of about 49.3 EeV. The minimum P-values found were 13.5% using the 2pt-L method, 1.0% using the 2pt+ method and 1.1% using the 3pt method for the highest 100 energy events. In view of the multiple (correlated) scans performed on the data set, these catalog-independent methods do not yield strong evidence of anisotropy in the highest energy cosmic rays.

Carbothermal Reduction of Iron Ore Applying Microwave Energy

This paper presents the results of a study on carbothermal reduction of iron ore made under the microwave field in equipment specially developed for this purpose. The equipment allows the control of radiated and reflected microwave power, and therefore measures the microwave energy actually applied to the load in the reduction process. It also allows performing energy balances and determining the reaction rate with high levels of confidence by simultaneously measuring temperature and mass of the material upon reduction with high reproducibility. We used a microwave generator of 2.45?GHz with variable power up to 3000?W. Self-reducing pellets under argon atmosphere, containing iron ore and petroleum coke, with 3.5?g of mass and 15?mm of diameter were declined. We obtained the kinetic curves of reduction of iron ore and of energy consumption to the process in the maximum electric field, in the maximum magnetic field and at different values of power/mass. The data allow analyzing how the microwave energy was actually consumed in the reduction of ore.

Paper-based diffusive gradients in thin films technique coupled to energy dispersive X-ray fluorescence spectrometry for the determination of labile Mn, Co, Ni, Cu, Zn and Pb in river water

The diffusive gradients in thin films (DGT) technique has shown enormous potential for labile metal monitoring in fresh water due to the preconcentration, time-integrated, matrix interference removal and speciation analytical features. In this work, the coupling of energy dispersive X-ray fluorescence (EDXRF) with paper-based DGT devices was evaluated for the direct determination of Mn, Co. Ni, Cu, Zn and Pb in fresh water. The DGT samplers were assembled with cellulose (Whatman 3 MM chromatography paper) as the diffusion layer and a cellulose phosphate ion exchange membrane (Whatman P 81 paper) as the binding agent. The diffusion coefficients of the analytes on 3 MM chromatography paper were calculated by deploying the DGT samplers in synthetic solutions containing 500 mu g L-1 of Mn. Co, Ni, Cu, Zn and Pb (4 L at pH 5.5 and ionic strength at 0.05 mol L-1). After retrieval, the DGT units were disassembled and the P81 papers were dried and analysed by EDXRF directly. The 3 MM chromatographic paper diffusion coefficients of the analytes ranged from 1.67 to 1.87 x 10(-6) cm(2) s(-1). The metal retention and phosphate group homogeneities on the P81 membrane was studied by a spot analysis with a diameter of 1 mm. The proposed approach (DGT-EDXRF coupling) was applied to determine the analytes at five sampling sites (48 h in situ deployment) on the Piracicaba river basin, and the results (labile fraction) were compared with 0.45 mu m dissolved fractions determined by synchrotron radiation-excited total reflection X-ray fluorescence (SR-TXRF). The limits of detection of DGT-EDXRF coupling for the analytes (from 7.5 to 26 mu g L-1) were similar to those obtained by the sensitive SR-TXRF technique (3.8 to 9.1 mu g L-1). (C) 2012 Elsevier B.V. All rights reserved.

Influence of pattern gradation on the design of piezocomposite energy harvesting devices using topology optimization

Piezoelectric materials can be used to convert oscillatory mechanical energy into electrical energy. Energy harvesting devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. The design of energy harvesting devices is not obvious, requiring optimization procedures. This paper investigates the influence of pattern gradation using topology optimization on the design of piezocomposite energy harvesting devices based on bending behavior. The objective function consists of maximizing the electric power generated in a load resistor. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. Examples of two-dimensional piezocomposite energy harvesting devices are presented and discussed using the proposed method. The numerical results illustrate that pattern gradation constraints help to increase the electric power generated in a load resistor and guides the problem toward a more stable solution. (C) 2012 Elsevier Ltd. All rights reserved.

Cost and energy density of diet in Brazil, 2008-2009

This study aimed to evaluate the relationship between the cost and energy density of diet consumed in Brazilian households. Data from the Brazilian Household Budget Survey (POF 200812009) were used to identify the main foods and their prices. Similar items were grouped, resulting in a basket of 67 products. Linear programming was applied for the composition of isoenergetic baskets, minimizing the deviation from the average household diet. Restrictions were imposed on the inclusion of items and the energy contribution of the various food groups. A reduction in average cost of diet was applied at intervals of R$0.15 to the lowest possible cost. We identified an inverse association between energy density and cost of diet (p < 0.05), and at the lowest possible cost we obtained the maximum value of energy density Restrictions on the diet's cost resulted in the selection of diets with higher energy density, indicating that cost of diet may lead to the adoption of inadequate diets in Brazil.

SEARCH FOR POINT-LIKE SOURCES OF ULTRA-HIGH ENERGY NEUTRINOS AT THE PIERRE AUGER OBSERVATORY AND IMPROVED LIMIT ON THE DIFFUSE FLUX OF TAU NEUTRINOS

The surface detector array of the Pierre Auger Observatory can detect neutrinos with energy E-nu between 10(17) eV and 10(20) eV from point-like sources across the sky south of +55 degrees and north of -65 degrees declinations. A search has been performed for highly inclined extensive air showers produced by the interaction of neutrinos of all flavors in the atmosphere (downward-going neutrinos), and by the decay of tau leptons originating from tau neutrino interactions in Earth's crust (Earth-skimming neutrinos). No candidate neutrinos have been found in data up to 2010 May 31. This corresponds to an equivalent exposure of similar to 3.5 years of a full surface detector array for the Earth-skimming channel and similar to 2 years for the downward-going channel. An improved upper limit on the diffuse flux of tau neutrinos has been derived. Upper limits on the neutrino flux from point-like sources have been derived as a function of the source declination. Assuming a differential neutrino flux k(PS) . E-nu(-2). from a point-like source, 90% confidence level upper limits for k(PS) at the level of approximate to 5x10(-7) and 2.5x10(-6) GeV cm(-2) s(-1) have been obtained over a broad range of declinations from the searches for Earth-skimming and downward-going neutrinos, respectively.

Energy-level statistics of interacting trapped bosons

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P(s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P(s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.