Magnetostatic relations including fluctuation fields - the local expansion

Using the approach of local expansion, we analyze the magnetostatic relations in the case of conventional turbulence. The turbulent relations are obtained consisten tly for themomentum equation and induction equation of both the average and fluctuation relations.In comparison with the magnetostatic relations as discussed usually, turbulent fluctuationfields produce forces, one of which 1/(4π)(α1×B0)×B0 may have parallel and perpendicular components in the direction of magnetic field, the other of which 1/(4π)K×B0 is introduced by the boundary value of turbulence and is perpendicular to the magnetic field. In the case of 2-dimensional configuration of magnetic field, the basic equation will be reduced into a second-order elliptic equation, which includes some linear and nonlinear terms introduced by turbulent fluctuation fields. Turbulent fields may change the configuration of magnetic field and even shear it non-uniformly. The study on the influence of turbulent fields is significant since they are observed in many astrophysical environments.

The Linear Ordering Problem Revisited

The Linear Ordering Problem is a popular combinatorial optimisation problem which has been extensively addressed in the literature. However, in spite of its popularity, little is known about the characteristics of this problem. This paper studies a procedure to extract static information from an instance of the problem, and proposes a method to incorporate the obtained knowledge in order to improve the performance of local search-based algorithms. The procedure introduced identifies the positions where the indexes cannot generate local optima for the insert neighbourhood, and thus global optima solutions. This information is then used to propose a restricted insert neighbourhood that discards the insert operations which move indexes to positions where optimal solutions are not generated. In order to measure the efficiency of the proposed restricted insert neighbourhood system, two state-of-the-art algorithms for the LOP that include local search procedures have been modified. Conducted experiments confirm that the restricted versions of the algorithms outperform the classical designs systematically. The statistical test included in the experimentation reports significant differences in all the cases, which validates the efficiency of our proposal.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Enfoque da estatística espacial em modelos dinâmicos de mudança do uso do solo.

O atual nível das mudanças uso do solo causa impactos nas mudanças ambientais globais. Os processos de mudanças do uso e cobertura do solo são processos complexos e não acontecem ao acaso sobre uma região. Geralmente estas mudanças são determinadas localmente, regionalmente ou globalmente por fatores geográficos, ambientais, sociais, econômicos e políticos interagindo em diversas escalas temporais e espaciais. Parte desta complexidade é capturada por modelos de simulação de mudanças do uso e cobertura do solo. Uma etapa do processo de simulação do modelo CLUE-S é a quantificação da influência local dos impulsores de mudança sobre a probabilidade de ocorrência de uma classe de uso do solo. Esta influência local é obtida ajustando um modelo de regressão logística. Um modelo de regressão espacial é proposto como alternativa para selecionar os impulsores de mudanças. Este modelo incorpora a informação da vizinhança espacial existente nos dados que não é considerada na regressão logística. Baseado em um cenário de tendência linear para a demanda agregada do uso do solo, simulações da mudança do uso do solo para a microbacia do Coxim, Mato Grosso do Sul, foram geradas, comparadas e analisadas usando o modelo CLUE-S sob os enfoques da regressão logística e espacial para o período de 2001 a 2011. Ambos os enfoques apresentaram simulações com muito boa concordância, medidas de acurácia global e Kappa altos, com o uso do solo para o ano de referência de 2004. A diferença entre os enfoques foi observada na distribuição espacial da simulação do uso do solo para o ano 2011, sendo o enfoque da regressão espacial que teve a simulação com menor discrepância com a demanda do uso do solo para esse ano.

Semiempirical down-scaling of GCM output to the local scale for temperature, precipitation, and runoff

EXTRACT (SEE PDF FOR FULL ABSTRACT): An empirically derived multiple linear regression model is used to relate a local-scale dependent variable (either temperature, precipitation, or surface runoff) measured at individual gauging stations to six large-scale independent variables (temperature, precipitation, surface runoff, height to the 500-mbar pressure surface, and the zonal and meridional gradient across this surface). ...The area investigated is the western United States. ... The calibration data set is from 1948 through 1988 and includes data from 268 joint temperature and precipitation stations, 152 streamflow stations (which are converted to runoff data), and 24 gridded 500-mbar pressure height nodes.

Heat transfer and aerodynamics of turbine blade tips in a linear cascade

Local measurements of the heat transfer coefficient and pressure coefficient were conducted on the tip and near tip region of a generic turbine blade in a five-blade linear cascade. Two tip clearance gaps were used: 1.6% and 2.8% chord. Data was obtained at a Reynolds number of 2.3 × 10 5 based on exit velocity and chord. Three different tip geometries were investigated: a flat (plain) tip, a suction-side squealer, and a cavity squealer. The experiments reveal that the flow through the plain gap is dominated by flow separation at the pressure-side edge and that the highest levels of heat transfer are located where the flow reattaches on the tip surface. High heat transfer is also measured at locations where the tip-leakage vortex has impinged onto the suction surface of the aerofoil. The experiments are supported by flow visualisation computed using the CFX CFD code which has provided insight into the fluid dynamics within the gap. The suction-side and cavity squealers are shown to reduce the heat transfer in the gap but high levels of heat transfer are associated with locations of impingement, identified using the flow visualisation and aerodynamic data. Film cooling is introduced on the plain tip at locations near the pressure-side edge within the separated region and a net heat flux reduction analysis is used to quantify the performance of the successful cooling design. copyright © 2005 by ASME.

Linear regression under fixed-rank constraints: A Riemannian approach

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms. Copyright 2011 by the author(s)/owner(s).

Global linear stability of the boundary-layer flow over a rotating sphere

We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°-65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk. © 2014 Elsevier Masson SAS. All rights reserved.

Uso da função discriminante linear na classificação dos fatores que determinam o êxodo rural.

A presente aplicacao da funcao discriminante linear na classificacao de fatores que determinam o exodo rural foi realizada a partir dos dados coletados em pequenas propriedades na regiao de Ouricuri, no alto sertao de Pernambuco. Dentro do complexo de problemas que condicionam o exodo rural foi escolhido um conjunto de variaveis que explicariam o fenomeno. Estas variaveis foram estudadas em duas populacoes (com exodo rural e sem exodo), para verificar em que grau se explica esse fenomeno. O objetivo do trabalho consistiu em testar instrumentos tecnicos e metodos estatisticos sobre problemas socio-economicos que possam ser usados posteriormente pelos orgaos de desenvolvimento.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

On the regularization of linear inverse problems in Fourier optics

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Linear inverse problems with discrete data: II. Stability and regularization

For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.

SVD for linear inverse problems

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Superresolution in linear inverse problems

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