948 resultados para power-law distributions


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We report a measurement of the flux of cosmic rays with unprecedented precision and Statistics using the Pierre Auger Observatory Based on fluorescence observations in coincidence with at least one Surface detector we derive a spectrum for energies above 10(18) eV We also update the previously published energy spectrum obtained with the surface detector array The two spectra are combined addressing the systematic uncertainties and, in particular. the influence of the energy resolution on the spectral shape The spectrum can be described by a broken power law E(-gamma) with index gamma = 3 3 below the ankle which is measured at log(10)(E(ankle)/eV) = 18 6 Above the ankle the spectrum is described by a power law with index 2 6 followed by a flux suppression, above about log(10)(E/eV) = 19 5, detected with high statistical significance (C) 2010 Elsevier B V All rights reserved

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The relationship between the structure and function of biological networks constitutes a fundamental issue in systems biology. Particularly, the structure of protein-protein interaction networks is related to important biological functions. In this work, we investigated how such a resilience is determined by the large scale features of the respective networks. Four species are taken into account, namely yeast Saccharomyces cerevisiae, worm Caenorhabditis elegans, fly Drosophila melanogaster and Homo sapiens. We adopted two entropy-related measurements (degree entropy and dynamic entropy) in order to quantify the overall degree of robustness of these networks. We verified that while they exhibit similar structural variations under random node removal, they differ significantly when subjected to intentional attacks (hub removal). As a matter of fact, more complex species tended to exhibit more robust networks. More specifically, we quantified how six important measurements of the networks topology (namely clustering coefficient, average degree of neighbors, average shortest path length, diameter, assortativity coefficient, and slope of the power law degree distribution) correlated with the two entropy measurements. Our results revealed that the fraction of hubs and the average neighbor degree contribute significantly for the resilience of networks. In addition, the topological analysis of the removed hubs indicated that the presence of alternative paths between the proteins connected to hubs tend to reinforce resilience. The performed analysis helps to understand how resilience is underlain in networks and can be applied to the development of protein network models.

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The addition of lithium salts to ionic liquids causes an increase in viscosity and a decrease in ionic mobility that hinders their possible application as an alternative solvent in lithium ion batteries. Optically heterodyne-detected optical Kerr effect spectroscopy was used to study the change in dynamics, principally orientational relaxation, caused by the addition of lithium bis(trifluoromethylsulfonyl)imide to the ionic liquid 1-buty1-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. Over the time scales studied (1 ps-16 ns) for the pure ionic liquid, two temperature-independent power laws were observed: the intermediate power law (1 ps to similar to 1 ns), followed by the von Schweidler power law. The von Schweidler power law is followed by the final complete exponential relaxation, which is highly sensitive to temperature. The lithium salt concentration, however, was found to affect both power laws, and a discontinuity could be found in the trend observed for the intermediate power law when the concentration (mole fraction) of lithium salt is close to chi(LiTf(2)N) = 0.2. A mode coupling theory (MCT) schematic model was also used to fit the data for both the pure ionic liquid and the different salt concentration mixtures. It was found that dynamics in both types of liquids are described very well by MCT.

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Molecular dynamics (MD) simulations of LiCl center dot 6H(2)O Showed that the diffusion coefficient D, and also I lie structural relaxation time , follow a power law at high temperatures, D(-1) proportional to (T - T(0))(-mu), with the same experimental parameters for viscosity (T(0) = 207 K, mu = 2.08). Decoupling between D and occurs at T(x) similar to 1.1 T(0). High frequency acoustic excitations for the LiCl center dot 6H(2)O model were obtained by the calculation of time correlation functions of mass current fluctuations. The temperature dependence of the instantaneous shear modulus, G,(T), was considered in the shoving model for supercooled liquids [J.C. Dyre, T. Christensen, N.B. Olsen, J. Non-Cryst. Solids 352 (2006) 4635] resulting in a linear relationship log (D(-1)) vs. G root T. (C) 2009 Elsevier B.V. All rights reserved.

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O objetivo deste trabalho é a simulação numérica de escoamentos incompressíveis bidimensionais em dutos com expansão brusca, considerando o raio de expansão de 3 : 1. As equações governantes implementadas são as de Navier, que junto com relações constitutivas para a tensão visam representar comportamentos não newtonianos. A integração temporal é feita usando o esquema explícito de Runge-Kutta com três estágios e de segunda ordem; as derivadas espaciais são aproximadas pelo método de diferenças finitas centrais. Escoamentos em expansões bruscas para fluidos newtonianos apresentam um número de Reynolds crítico, dependente do raio de expansão, na qual três soluções passam a ser encontradas: uma solução sim étrica instável e duas soluções assimétricas rebatidas estáveis. Aumentando o número de Reynolds, a solução passa a ser tridimensional e dependente do tempo. Dessa forma, o objetivo é encontrar as diferenças que ocorrem no comportamento do fluxo quando o fluido utilizado possui características não newtonianas. As relações constitutivas empregadas pertencem à classe de fluidos newtonianos generalizados: power-law, Bingham e Herschel-Bulkley. Esses modelos prevêem comportamentos pseudoplásticos e dilatantes, plásticos e viscoplásticos, respectivamente. Os resultados numéricos mostram diferenças entre as soluções newtonianas e não newtonianas para Reynolds variando de 30 a 300. Os valores de Reynolds críticos para o modelo power-law não apresentaram grandes diferenças em comparação com os da solução newtoniana. Algumas variações foram percebidas nos perfis de velocidade. Entretanto, os resultados obtidos com os modelos de Bingham e Herschel-Bulkley apresentaram diferenças significativas quando comparados com os newtonianos com o aumento do parâmetro adimensional Bingham; à medida que Bingham é aumentado, o tamanho dos vórtices diminui. Além disso, os perfis de velocidade apresentam diferenças relevantes, uma vez que o fluxo possui regiões onde o fluido se comporta como sólido.

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The community of lawyers and their clients form a scale-free bipartite network that develops naturally as the outcome of the recommendation process through which lawyers form their client base. This process is an example of preferential attachment where lawyers with more clients are more likely to be recommended to new clients. Consumer litigation is an important market for lawyers. In large consumer societies, there always a signi cant amount of consumption disputes that escalate to court. In this paper we analyze a dataset of thousands of lawsuits, reconstructing the lawyer-client network embedded in the data. Analyzing the degree distribution of this network we noticed that it follows that of a scale-free network built by preferential attachment, but for a few lawyers with much larger client base than could be expected by preferential attachment. Incidentally, most of these also gured on a list put together by the judiciary of Lawyers which openly advertised the bene ts of consumer litigation. According to the code of ethics of their profession, lawyers should not stimulate clients into litigation, but it is not strictly illegal. From a network formation point of view, this stimulation can be seen as a separate growth mechanism than preferential attachment alone. In this paper we nd that this composite growth can be detected by a simple statistical test, as simulations show that lawyers which use both mechanisms quickly become the \Dragon-Kings" of the distribution of the number of clients per lawyer.

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This thesis explores the possibility of directly detecting blackbody emission from Primordial Black Holes (PBHs). A PBH might form when a cosmological density uctuation with wavenumber k, that was once stretched to scales much larger than the Hubble radius during ination, reenters inside the Hubble radius at some later epoch. By modeling these uctuations with a running{tilt power{law spectrum (n(k) = n0 + a1(k)n1 + a2(k)n2 + a3(k)n3; n0 = 0:951; n1 = ????0:055; n2 and n3 unknown) each pair (n2,n3) gives a di erent n(k) curve with a maximum value (n+) located at some instant (t+). The (n+,t+) parameter space [(1:20,10????23 s) to (2:00,109 s)] has t+ = 10????23 s{109 s and n+ = 1:20{2:00 in order to encompass the formation of PBHs in the mass range 1015 g{1010M (from the ones exploding at present to the most massive known). It was evenly sampled: n+ every 0.02; t+ every order of magnitude. We thus have 41 33 = 1353 di erent cases. However, 820 of these ( 61%) are excluded (because they would provide a PBH population large enough to close the Universe) and we are left with 533 cases for further study. Although only sub{stellar PBHs ( 1M ) are hot enough to be detected at large distances we studied PBHs with 1015 g{1010M and determined how many might have formed and still exist in the Universe. Thus, for each of the 533 (n+,t+) pairs we determined the fraction of the Universe going into PBHs at each epoch ( ), the PBH density parameter (PBH), the PBH number density (nPBH), the total number of PBHs in the Universe (N), and the distance to the nearest one (d). As a rst result, 14% of these (72 cases) give, at least, one PBH within the observable Universe, one{third being sub{stellar and the remaining evenly spliting into stellar, intermediate mass and supermassive. Secondly, we found that the nearest stellar mass PBH might be at 32 pc, while the nearest intermediate mass and supermassive PBHs might be 100 and 1000 times farther, respectively. Finally, for 6% of the cases (four in 72) we might have substellar mass PBHs within 1 pc. One of these cases implies a population of 105 PBHs, with a mass of 1018 g(similar to Halley's comet), within the Oort cloud, which means that the nearest PBH might be as close as 103 AU. Such a PBH could be directly detected with a probability of 10????21 (cf. 10????32 for low{energy neutrinos). We speculate in this possibility.

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The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

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(The Mark and Recapture Network: a Heliconius case study). The current pace of habitat destruction, especially in tropical landscapes, has increased the need for understanding minimum patch requirements and patch distance as tools for conserving species in forest remnants. Mark recapture and tagging studies have been instrumental in providing parameters for functional models. Because of their popularity, ease of manipulation and well known biology, butterflies have become model in studies of spatial structure. Yet, most studies on butterflies movement have focused on temperate species that live in open habitats, in which forest patches are barrier to movement. This study aimed to view and review data from mark-recapture as a network in two species of butterfly (Heliconius erato and Heliconius melpomene). A work of marking and recapture of the species was carried out in an Atlantic forest reserve located about 20km from the city of Natal (RN). Mark recapture studies were conducted in 3 weekly visits during January-February and July-August in 2007 and 2008. Captures were more common in two sections of the dirt road, with minimal collection in the forest trail. The spatial spread of captures was similar in the two species. Yet, distances between recaptures seem to be greater for Heliconius erato than for Heliconius melpomene. In addition, the erato network is more disconnected, suggesting that this specie has shorter traveling patches. Moving on to the network, both species have similar number of links (N) and unweighed vertices (L). However, melpomene has a weighed network 50% more connections than erato. These network metrics suggest that erato has more compartmentalized network and restricted movement than melpomene. Thus, erato has a larger number of disconnected components, nC, in the network, and a smaller network diameter. The frequency distribution of network connectivity for both species was better explained by a Power-law than by a random, Poissom distribution, showing that the Power-law provides a better fit than the Poisson for both species. Moreover, the Powerlaw erato is much better adjusted than in melpomene, which should be linked to the small movements that erato makes in the network

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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The static and cyclic assays are common to test materials in structures.. For cycling assays to assess the fatigue behavior of the material and thereby obtain the S-N curves and these are used to construct the diagrams of living constant. However, these diagrams, when constructed with small amounts of S-N curves underestimate or overestimate the actual behavior of the composite, there is increasing need for more testing to obtain more accurate results. Therewith, , a way of reducing costs is the statistical analysis of the fatigue behavior. The aim of this research was evaluate the probabilistic fatigue behavior of composite materials. The research was conducted in three parts. The first part consists of associating the equation of probability Weilbull equations commonly used in modeling of composite materials S-N curve, namely the exponential equation and power law and their generalizations. The second part was used the results obtained by the equation which best represents the S-N curves of probability and trained a network to the modular 5% failure. In the third part, we carried out a comparative study of the results obtained using the nonlinear model by parts (PNL) with the results of a modular network architecture (MN) in the analysis of fatigue behavior. For this we used a database of ten materials obtained from the literature to assess the ability of generalization of the modular network as well as its robustness. From the results it was found that the power law of probability generalized probabilistic behavior better represents the fatigue and composites that although the generalization ability of the MN that was not robust training with 5% failure rate, but for values mean the MN showed more accurate results than the PNL model

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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The great majority of analytical models for extragalactic radio sources suppose self-similarity and can be classified into three types: I, II and III. We have developed a model that represents a generalization of most models found in the literature and showed that these three types are particular cases. The model assumes that the area of the head of the jet varies with the jet size according to a power law and the jet luminosity is a function of time. As it is usually done, the basic hypothesis is that there is an equilibrium between the pressure exerted both by the head of the jet and the cocoon walls and the ram pressure of the ambient medium. The equilibrium equations and energy conservation equation allow us to express the size and width of the source and the pressure in the cocoon as a power law and find the respective exponents. All these assumptions can be used to calculate the evolution of the source size, width and radio luminosity. This can then be compared with the observed width-size relation for radio lobes and the power-size (P-D) diagram of both compact (GPS and CSS) and extended sources from the 3CR catalogue. In this work we introduce two important improvement as compared with a previous work: (1)We have put together a larger sample of both compact and extended radio sources

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This work is a detailed study of self-similar models for the expansion of extragalactic radio sources. A review is made of the definitions of AGN, the unified model is discussed and the main characteristics of double radio sources are examined. Three classification schemes are outlined and the self-similar models found in the literature are studied in detail. A self-similar model is proposed that represents a generalization of the models found in the literature. In this model, the area of the head of the jet varies with the size of the jet with a power law with an exponent γ. The atmosphere has a variable density that may or may not be spherically symmetric and it is taken into account the time variation of the cinematic luminosity of the jet according to a power law with an exponent h. It is possible to show that models Type I, II and III are particular cases of the general model and one also discusses the evolution of the sources radio luminosity. One compares the evolutionary curves of the general model with the particular cases and with the observational data in a P-D diagram. The results show that the model allows a better agreement with the observations depending on the appropriate choice of the model parameters.