Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Acoustic source characteristics, across-formant integration, and speech intelligibility under competitive conditions

An important aspect of speech perception is the ability to group or select formants using cues in the acoustic source characteristics-for example, fundamental frequency (F0) differences between formants promote their segregation. This study explored the role of more radical differences in source characteristics. Three-formant (F1+F2+F3) synthetic speech analogues were derived from natural sentences. In Experiment 1, F1+F3 were generated by passing a harmonic glottal source (F0 = 140 Hz) through second-order resonators (H1+H3); in Experiment 2, F1+F3 were tonal (sine-wave) analogues (T1+T3). F2 could take either form (H2 or T2). In some conditions, the target formants were presented alone, either monaurally or dichotically (left ear = F1+F3; right ear = F2). In others, they were accompanied by a competitor for F2 (F1+F2C+F3; F2), which listeners must reject to optimize recognition. Competitors (H2C or T2C) were created using the time-reversed frequency and amplitude contours of F2. Dichotic presentation of F2 and F2C ensured that the impact of the competitor arose primarily through informational masking. In the absence of F2C, the effect of a source mismatch between F1+F3 and F2 was relatively modest. When F2C was present, intelligibility was lowest when F2 was tonal and F2C was harmonic, irrespective of which type matched F1+F3. This finding suggests that source type and context, rather than similarity, govern the phonetic contribution of a formant. It is proposed that wideband harmonic analogues are more effective informational maskers than narrowband tonal analogues, and so become dominant in across-frequency integration of phonetic information when placed in competition.

Hand somatosensory sub-cortical sources arehypoactive in migraine interictally: a functionalsource separation analysis

Background: Recent morpho-functional evidences pointed out that abnormalities in the thalamus could play a major role in the expression of migraine neurophysiological and clinical correlates. Whether this phenomenon is primary or secondary to its functional disconnection from the brain stem remains to be determined.Aim: We used a Functional Source Separation algorithmof EEG signal to extract the activity of the different neuronal pools recruited at different latencies along the somatosensory pathway in interictal migraine without aura(MO) patients. Method: Twenty MO patients and 20 healthy volunteers(HV) underwent EEG recording. Four ad-hoc functional constraints, two sub-cortical (FS14 at brain stem andFS16 at thalamic level) and two cortical (FS20 radial andFS22 tangential parietal sources), were used to extract the activity of successive stages of somatosensory information processing in response to the separate left and right median nerve electric stimulation. A band-pass digital filter (450–750 Hz) was applied offline in order to extract high-frequency oscillatory (HFO) activity from the broadband EEG signal. Results: In both stimulated sides, significant reduced subcortical brain stem (FS14) and thalamic (FS16) HFO activations characterized MO patients when compared with HV. No difference emerged in the two cortical HFO activations between two groups. Conclusion: Present results are the first neurophysiological evidence supporting the hypothesis that a functional disconnection of the thalamus from the subcortical monoaminergicsystem may underline the interictal cortical abnormal information processing in migraine. Further studiesare needed to investigate the precise directional connectivity across the entire primary subcortical and cortical somatosensory pathway in interictal MO.

Across-formant integration and speech intelligibility:effects of acoustic source properties in the presence and absence of a contralateral interferer

The role of source properties in across-formant integration was explored using three-formant (F1+F2+F3) analogues of natural sentences (targets). In experiment 1, F1+F3 were harmonic analogues (H1+H3) generated using a monotonous buzz source and second-order resonators; in experiment 2, F1+F3 were tonal analogues (T1+T3). F2 could take either form (H2 or T2). Target formants were always presented monaurally; the receiving ear was assigned randomly on each trial. In some conditions, only the target was present; in others, a competitor for F2 (F2C) was presented contralaterally. Buzz-excited or tonal competitors were created using the time-reversed frequency and amplitude contours of F2. Listeners must reject F2C to optimize keyword recognition. Whether or not a competitor was present, there was no effect of source mismatch between F1+F3 and F2. The impact of adding F2C was modest when it was tonal but large when it was harmonic, irrespective of whether F2C matched F1+F3. This pattern was maintained when harmonic and tonal counterparts were loudness-matched (experiment 3). Source type and competition, rather than acoustic similarity, governed the phonetic contribution of a formant. Contrary to earlier research using dichotic targets, requiring across-ear integration to optimize intelligibility, H2C was an equally effective informational masker for H2 as for T2.

Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution. (C) 2009 American Institute of Physics. [doi:10.1063/1.3253297]

Extra phase noise from thermal fluctuations in nonlinear optical crystals

We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Dual source/dual energy-renal applications

Development of Dual Source Computed Tomography (Definition, Siemens Medical Solutions, Erlanger, Germany) allowed advances in temporal resolution, with the addition of a second X-ray source and an array of detectors to the TCM 64 slices. The ability to run exams on Dual Energy, allows greater differentiation of tissues, showing differences between closer attenuation coefficients. In terms of renal applications, the distinction of kidney stones and masses become one of the main advantages of the use of dual-energy technology. This article pretends to demonstrate operating principles of this equipment, as its main renal applications.

Visual programming of XSLT from examples

Vishnu is a tool for XSLT visual programming in Eclipse - a popular and extensible integrated development environment. Rather than writing the XSLT transformations, the programmer loads or edits two document instances, a source document and its corresponding target document, and pairs texts between then by drawing lines over the documents. This form of XSLT programming is intended for simple transformations between related document types, such as HTML formatting or conversion among similar formats. Complex XSLT programs involving, for instance, recursive templates or second order transformations are out of the scope of Vishnu. We present the architecture of Vishnu composed by a graphical editor and a programming engine. The editor is an Eclipse plug-in where the programmer loads and edits document examples and pairs their content using graphical primitives. The programming engine receives the data collected by the editor and produces an XSLT program. The design of the engine and the process of creation of an XSLT program from examples are also detailed. It starts with the generation of an initial transformation that maps source document to the target document. This transformation is fed to a rewrite process where each step produces a refined version of the transformation. Finally, the transformation is simplified before being presented to the programmer for further editing.

Otimização da extração sólido-líquido de antioxidantes de subprodutos florestais pelo método de superfície de resposta

Portugal continental apresenta uma vasta área florestal, que representa cerca de 35,4% da ocupação total do solo, com predominância de espécies como o eucalipto (Eucalyptus globulus) e o pinheiro-bravo (Pinus pinaster). Estas espécies apresentam uma elevada importância a nível económico, designadamente devido à sua ampla utilização, nomeadamente na indústria de celulose e papel, gerando elevadas quantidades de resíduos. Este resíduo de biomassa florestal é utilizado, na sua totalidade, para a geração de energia, na forma de eletricidade ou aquecimento. No entanto, existem outras opções viáveis, a nível económico, tais como a valorização destes subprodutos como fonte de compostos polifenólicos tornando-os, assim, um produto de valor acrescentado. A extração de compostos fenólicos de subprodutos florestais, como folhas de eucalipto e agulhas de pinheiros tem vindo a aumentar devido, principalmente, à substituição de antioxidantes sintéticos, contribuindo para a valorização de subprodutos florestais. Contudo, apesar de todas as potenciais aplicações e vantagens, apenas algumas centenas de espécies aromáticas identificadas são utilizadas à escala comercial. Neste trabalho foi avaliada a capacidade antioxidante de subprodutos da floresta, otimizando as condições de extração através do estudo dos fatores: tempo de extração, temperatura e composição de solvente através do método de superfície de resposta. O planeamento experimental utilizado teve como base um planeamento de compósito central e a avaliação do perfil de antioxidantes das matrizes analisadas foi realizada através de métodos de quantificação total, como o teor fenólico total, a atividade anti-radicalar – método do DPPH (radical 2,2-difenil-1-picrilhidrazilo) e o método de FRAP. Estes métodos analíticos convencionais foram modificados e, devidamente validados, para a análise em leitor de microplacas. Verificou-se que os extratos de pinheiro e de eucalipto, tanto as amostras verdes com as amostras, apresentam uma promissora capacidade antioxidante. O planeamento fatorial aplicado permitiu otimizar as condições de extração em relação às matrizes verdes. Contudo, o mesmo não se verificou em relação às matrizes secas. A composição (% de água) é sem dúvida o fator com mais efeito em todas as amostras (coeficientes de primeira e segunda ordem no modelo). Também a temperatura foi identificada como um fator com efeito significativo sobre os sistemas em análise.

GNSS signal detection based on first-order absolute statistics

Aquest projecte es centra principalment en el detector no coherent d’un GPS. Per tal de caracteritzar el procés de detecció d’un receptor, es necessita conèixer l’estadística implicada. Pel cas dels detectors no coherents convencionals, l’estadística de segon ordre intervé plenament. Les prestacions que ens dóna l’estadística de segon ordre, plasmada en la ROC, són prou bons tot i que en diferents situacions poden no ser els millors. Aquest projecte intenta reproduir el procés de detecció mitjançant l’estadística de primer ordre com a alternativa a la ja coneguda i implementada estadística de segon ordre. Per tal d’aconseguir-ho, s’usen expressions basades en el Teorema Central del Límit i de les sèries Edgeworth com a bones aproximacions. Finalment, tant l’estadística convencional com l’estadística proposada són comparades, en termes de la ROC, per tal de determinar quin detector no coherent ofereix millor prestacions en cada situació.

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.