Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Processability, structural evolution and properties of melt processed biaxially stretched HDPE/MWCNT nanocomposites

Biaxial stretching of melt mixed high density polyethylene (HDPE)/multiwalled carbon nanotube (MWCNT) nanocomposites was conducted in the melt state at different stretching ratios (SRs). The addition of MWCNTs leads to significant strain hardening in the HDPE, greatly improving the stability and thus processability of the stretching process. Scanning electron microscopy shows that the MWCNTs in the polymer matrix are gradually disentangled and randomly oriented in the stretching plane with increasing SRs. All the stretched samples exhibit an increase in crystallinity (about 10%) due to strain induced crystallization and a broadened distribution of crystallite size according to the XRD and DSC results. The mechanical properties of the composites improve with increasing SRs, while they drop off after a SR of 2.5 for the neat HDPE which is likely to be due to the relaxation of polymer chains prior to solidification. The presence of the MWCNTs appears to inhibit this relaxation thus helping to maintain the orientation and mechanical properties at high SRs. The modulus, yield strength and breaking strength of stretched composites with 8 wt% MWCNTs increase by approximately 54%, 85% and 193% respectively compared with the neat HDPE at a SR of 3. The electrical percolation threshold for the unstretched material occurs at 1.9 wt% MWCNTs. As SR increases, the values of critical concentration increase from 1.9 wt% to 4.9 wt% implying the destruction of conductive networks due to an increased inter-particle distance. A loading of 6 wt% MWCNTs is sufficient to ensure that the sheet conductivity is robust to changes in the SR. Decreased values of critical exponent from 1.9 to 1.1 and morphological investigation reveal a transformation of the system structure from three dimensional to two dimensional as SR increases.

Three-dimensional graphene-Co3O4 cathodes for rechargeable Li-O2 batteries

A three-dimensional (3D) graphene-Co₃O₄ electrode was prepared by a two-step method in which graphene was initially deposited on a Ni foam with Co₃O₄ then grown on the resulting graphene structure. Cross-linked Co₃O₄ nanosheets with an open pore structure were fully and vertically distributed throughout the graphene skeleton. The free-standing and binder-free monolithic electrode was used directly as a cathode in a Li-O₂ battery. This composite structure exhibited enhanced performance with a specific capacity of 2453 mA h g^-1 at 0.1 mA cm^-2 and 62 stable cycles with 583 mA h g^-1 (1000 mA h g_carbon^-1). The excellent electrochemical performance is associated with the unique architecture and superior catalytic activity of the 3D electrode. 

Evolution and functional relevance of Ataxin-3 paralogues

O gene ataxin-3 (ATXN3; 14q32.1) codifica uma proteína expressa ubiquamente, envolvida na via ubiquitina-proteassoma e na repressão da transcrição. Grande relevância tem sido dada ao gene ATXN3 após a identificação de uma expansão (CAG)n na sua região codificante, responsável pela ataxia mais comum em todo o mundo, SCA3 ou doença de Machado-Joseph (DMJ). A DMJ é uma doença neurodegenerativa, autossómica dominante, de início tardio. O tamanho do alelo expandido explica apenas uma parte do pleomorfismo da doença, evidenciando a importância do estudo de outros modificadores. Em doenças de poliglutaminas (poliQ), a toxicidade é causada por um ganho de função da proteína expandida; no entanto, a proteína normal parece ser, também, um dos agentes modificadores da patogénese. O gene ATXN3 possui dois parálogos humanos gerados por retrotransposição: ataxin-3 like (ATXN3L) no cromossoma X, e LOC100132280, ainda não caracterizado, no cromossoma 8. Estudos in vitro evidenciaram a capacidade da ATXN3L para clivar cadeias de ubiquitina, sendo o seu domínio proteolítico mais eficiente do que o domínio da ATXN3 parental. O objetivo deste estudo foi explorar a origem e a evolução das retrocópias ATXN3L e LOC100132280 (aqui denominadas ATXN3L1 e ATXN3L2), assim como testar a relevância funcional de ambas através de abordagens evolutivas e funcionais. Deste modo, para estudar a divergência evolutiva dos páralogos do gene ATXN3: 1) analisaram-se as suas filogenias e estimou-se a data de origem dos eventos de retrotransposição; 2) avaliaram-se as pressões seletivas a que têm sido sujeitos os três parálogos, ao longo da evolução dos primatas; e 3) explorou-se a evolução das repetições CAG, localizadas em três contextos genómicos diferentes, provavelmente sujeitos a diferentes pressões seletivas. Finalmente, para o retrogene que conserva uma open reading frame (ORF) intacta, ATXN3L1, analisou-se, in silico, a conservação dos locais e domínios proteicos da putativa proteína. Ademais, para este retrogene, foi estudado o padrão de expressão de mRNA, através da realização de PCR de Transcriptase Reversa, em 16 tecidos humanos. Os resultados obtidos sugerem que dois eventos independentes de retrotransposição estiveram na origem dos retrogenes ATXN3L1 e ATXN3L2, tendo o primeiro ocorrido há cerca de 63 milhões de anos (Ma) e o segundo após a divisão Platirrínios-Catarrínios, há cerca de 35 Ma. Adicionalmente, outras retrocópias foram encontradas em primatas e outros mamíferos, correspondendo, no entanto, a eventos mais recentes e independentes de retrotransposição. A abordagem evolutiva mostrou a existência de algumas constrições selectivas associadas à evolução do gene ATXN3L1, à semelhança do que acontece com ATXN3. Por outro lado, ATXN3L2 adquiriu codões stop prematuros que, muito provavelmente, o tornaram num pseudogene processado. Os resultados da análise de expressão mostraram que o gene ATXN3L1 é transcrito, pelo menos, em testículo humano; no entanto, a optimização final da amplificação específica dos transcriptos ATXN3L1 permitirá confirmar se a expressão se estende a outros tecidos. Relativamente ao mecanismo de mutação inerente à repetição CAG, os dois parálogos mostraram diferentes padrões de evolução: a retrocópia ATXN3L1 é altamente interrompida e pouco polimórfica, enquanto a ATXN3L2 apresenta tratos puros de (CAG)n em algumas espécies e tratos hexanucleotídicos de CGGCAG no homem e no chimpanzé. A recente aquisição da repetição CGGCAG pode ter resultado de uma mutação inicial de CAG para CGG, seguida de instabilidade que proporcionou a expansão dos hexanucleótidos.Estudos futuros poderão ser realizados no sentido de confirmar o padrão de expressão do gene ATXN3L1 e de detetar proteína endógena in vivo. Adicionalmente, a caracterização da proteina ataxina-3 like 1 e dos seus interatores moleculares poderá povidenciar informação acerca da sua relevância no estado normal e patológico.

Bi-Dimensional Characterization of a Wimax Radio Channel at 3.5GHz

This paper presents the characterization of an indoor Wimax radio channel using the Finite-Difference Time-Domain (FDTD) [1] method complemented with the Convolutional Perfect Matched Layer (CPML) technique [2]. An indoor 2D scenario is simulated in the 3.5GHz band (IEEE 802.16d-2004 and IEEE 802.16e-2005 [3]). In this study, we used two complementary techniques in both analysis, technique A and B for fading based on delay spread and technique C and D for fading based on Doppler spread. Both techniques converge to the same result. Simulated results define the channel as flat, slow and without inter-symbolic interference (ISI), making the application of the spatial diversity the most appropriate scheme.

Origin and evolution of 3'UTR of flaviviruses: long direct repeats as a basis for the formation of secondary structures and their significance for virus transmission

The 3' untranslated regions (3'UTRs) of flaviviruses are reviewed and analyzed in relation to short sequences conserved as direct repeats (DRs). Previously, alignments of the 3'UTRs have been constructed for three of the four recognized flavivirus groups, namely mosquito-borne, tick-borne, and nonclassified flaviviruses (MBFV, TBFV, and NCFV, respectively). This revealed (1) six long repeat sequences (LRSs) in the 3'UTR and open-reading frame (ORF) of the TBFV, (2) duplication of the 3'UTR of the NCFV by intramolecular recombination, and (3) the possibility of a common origin for all DRs within the MBFV. We have now extended this analysis and review it in the context of all previous published analyses. This has been achieved by constructing a robust alignment between all flaviviruses using the published DRs and secondary RNA structures as "anchors" to reveal additional homologies along the 3'UTR. This approach identified nucleotide regions within the MBFV, NKV (no-known vector viruses), and NCFV 3'UTRs that are homologous to different LRSs in the TBFV 3'UTR and ORF. The analysis revealed that some of the DRs and secondary RNA structures described individually within each flavivirus group share common evolutionary origins. The 3'UTR of flaviviruses, and possibly the ORF, therefore probably evolved through multiple duplication of an RNA domain, homologous to the LRS previously identified only in the TBFV. The short DRs in all virus groups appear to represent the evolutionary remnants of these domains rather than resulting from new duplications. The relevance of these flavivirus DRs to evolution, diversity, 3'UTR enhancer function, and virus transmission is reviewed.

[Co(en)(3)][Sb12S19]: a new antimony sulfide with a zeolite-like structure containing one-dimensional channels

Solvothermal synthesis affords access to the first truly three-dimensional anti mony-sufide framework which contains one-dimensional circular channels.

The three-dimensional morphology of simulated and observed convective storms over southern England

A set of high-resolution radar observations of convective storms has been collected to evaluate such storms in the UK Met Office Unified Model during the DYMECS project (Dynamical and Microphysical Evolution of Convective Storms). The 3-GHz Chilbolton Advanced Meteorological Radar was set up with a scan-scheduling algorithm to automatically track convective storms identified in real-time from the operational rainfall radar network. More than 1,000 storm observations gathered over fifteen days in 2011 and 2012 are used to evaluate the model under various synoptic conditions supporting convection. In terms of the detailed three-dimensional morphology, storms in the 1500-m grid-length simulations are shown to produce horizontal structures a factor 1.5–2 wider compared to radar observations. A set of nested model runs at grid lengths down to 100m show that the models converge in terms of storm width, but the storm structures in the simulations with the smallest grid lengths are too narrow and too intense compared to the radar observations. The modelled storms were surrounded by a region of drizzle without ice reflectivities above 0 dBZ aloft, which was related to the dominance of ice crystals and was improved by allowing only aggregates as an ice particle habit. Simulations with graupel outperformed the standard configuration for heavy-rain profiles, but the storm structures were a factor 2 too wide and the convective cores 2 km too deep.

MAGNETOHYDRODYNAMIC SIMULATIONS OF RECONNECTION AND PARTICLE ACCELERATION: THREE-DIMENSIONAL EFFECTS

Magnetic fields can change their topology through a process known as magnetic reconnection. This process in not only important for understanding the origin and evolution of the large-scale magnetic field, but is seen as a possibly efficient particle accelerator producing cosmic rays mainly through the first-order Fermi process. In this work we study the properties of particle acceleration inserted in reconnection zones and show that the velocity component parallel to the magnetic field of test particles inserted in magnetohydrodynamic (MHD) domains of reconnection without including kinetic effects, such as pressure anisotropy, the Hall term, or anomalous effects, increases exponentially. Also, the acceleration of the perpendicular component is always possible in such models. We find that within contracting magnetic islands or current sheets the particles accelerate predominantly through the first-order Fermi process, as previously described, while outside the current sheets and islands the particles experience mostly drift acceleration due to magnetic field gradients. Considering two-dimensional MHD models without a guide field, we find that the parallel acceleration stops at some level. This saturation effect is, however, removed in the presence of an out-of-plane guide field or in three-dimensional models. Therefore, we stress the importance of the guide field and fully three-dimensional studies for a complete understanding of the process of particle acceleration in astrophysical reconnection environments.

THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF MAGNETIZED WINDS OF SOLAR-LIKE STARS

By means of self-consistent three-dimensional magnetohydrodynamics (MHD) numerical simulations, we analyze magnetized solar-like stellar winds and their dependence on the plasma-beta parameter (the ratio between thermal and magnetic energy densities). This is the first study to perform such analysis solving the fully ideal three-dimensional MHD equations. We adopt in our simulations a heating parameter described by gamma, which is responsible for the thermal acceleration of the wind. We analyze winds with polar magnetic field intensities ranging from 1 to 20 G. We show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. Higher magnetic field intensities lead to faster and hotter winds. For the maximum magnetic intensity simulated of 20 G and solar coronal base density, the wind velocity reaches values of similar to 1000 km s(-1) at r similar to 20r(0) and a maximum temperature of similar to 6 x 10(6) K at r similar to 6r(0). The increase of the field intensity generates a larger ""dead zone"" in the wind, i.e., the closed loops that inhibit matter to escape from latitudes lower than similar to 45 degrees extend farther away from the star. The Lorentz force leads naturally to a latitude-dependent wind. We show that by increasing the density and maintaining B(0) = 20 G the system recover back to slower and cooler winds. For a fixed gamma, we show that the key parameter in determining the wind velocity profile is the beta-parameter at the coronal base. Therefore, there is a group of magnetized flows that would present the same terminal velocity despite its thermal and magnetic energy densities, as long as the plasma-beta parameter is the same. This degeneracy, however, can be removed if we compare other physical parameters of the wind, such as the mass-loss rate. We analyze the influence of gamma in our results and we show that it is also important in determining the wind structure.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

Synthesis optimization, structural evolution and optical properties of Y(0.9)Er(0.1)Al(3)(BO(3))(4) nanopowders obtained by soft chemistry methods

This paper describes the structural evolution of Y(0.9)Er(0.1)Al(3)(BO(3))(4) nanopowders using two soft chemistry routes, the sol-gel and the polymeric precursor methods. Differential scanning calorimetry, differential thermal analyses, thermogravimetric analyses, X-ray diffraction, Fourier-transform infrared, and Raman spectroscopy techniques have been used to study the chemical reactions between 700 and 1200 degrees C temperature range. From both methods the Y(0.9)Er(0.1)Al(3)(BO(3))(4) (Er:YAB) solid solution was obtained almost pure when the powdered samples were heat treated at 1150 degrees C. Based on the results, a schematic phase formation diagram of Er:YAB crystalline solid solution was proposed for powders from each method. The Er:YAB solid solution could be optimized by adding a small amount of boron oxide in excess to the Er:YAB nominal composition. The nanoparticles are obtained around 210 nm. Photoluminescence emission spectrum of the Er:YAB nanocrystalline powders was measured on the infrared region and the Stark components of the (4)I(13/2) and (4)I(15/2) levels were determined. Finally, for the first time the Raman spectrum of Y(0.9)Er(0.1)Al(3)(BO(3))(4) crystalline phase is also presented. (C) 2008 Elsevier Masson SAS. 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.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

A three-dimensional network constructed from the assembly of 1,3-diaminopropane-copper(II) and tetracyanopalladate(II) moieties

The coordination polymer [Cu(Pd(CN)(4))(pn)](n) (pn = 1,3-diaminopropane) has been synthesized and characterized by elemental analysis, infrared spectroscopy and single-crystal X-ray diffraction. The crystal structure showed that three cyano groups of each [Pd(CN)(4)] unit bridge Cu(II) centers leading to the formation of a three-dimensional network. A series of bifurcated hydrogen bonds between the amino groups of the diamine and the nonbridging cyano groups of the cyanometallate result in the organization of suprarnolecular chains and rings along the polymer. (c) 2008 Elsevier B.V. All rights reserved.