Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

Introductory remarks

The very first numerical models which were developed more than 20 years ago were drastic simplifications of the real atmosphere and they were mostly restricted to describe adiabatic processes. For prediction of a day or two of the mid tropospheric flow these models often gave reasonable results but the result deteriorated quickly when the prediction was extended further in time. The prediction of the surface flow was unsatisfactory even for short predictions. It was evident that both the energy generating processes as well as the dissipative processes have to be included in numerical models in order to predict the weather patterns in the lower part of the atmosphere and to predict the atmosphere in general beyond a day or two. Present-day computers make it possible to attack the weather forecasting problem in a more comprehensive and complete way and substantial efforts have been made during the last decade in particular to incorporate the non-adiabatic processes in numerical prediction models. The physics of radiational transfer, condensation of moisture, turbulent transfer of heat, momentum and moisture and the dissipation of kinetic energy are the most important processes associated with the formation of energy sources and sinks in the atmosphere and these have to be incorporated in numerical prediction models extended over more than a few days. The mechanisms of these processes are mainly related to small scale disturbances in space and time or even molecular processes. It is therefore one of the basic characteristics of numerical models that these small scale disturbances cannot be included in an explicit way. The reason for this is the discretization of the model's atmosphere by a finite difference grid or the use of a Galerkin or spectral function representation. The second reason why we cannot explicitly introduce these processes into a numerical model is due to the fact that some physical processes necessary to describe them (such as the local buoyance) are a priori eliminated by the constraints of hydrostatic adjustment. Even if this physical constraint can be relaxed by making the models non-hydrostatic the scale problem is virtually impossible to solve and for the foreseeable future we have to try to incorporate the ensemble or gross effect of these physical processes on the large scale synoptic flow. The formulation of the ensemble effect in terms of grid-scale variables (the parameters of the large-scale flow) is called 'parameterization'. For short range prediction of the synoptic flow at middle and high latitudes, very simple parameterization has proven to be rather successful.

Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.

A moving point approach to model shallow ice sheets: a study case with radially-symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly and the waiting time behaviours to be modelled efficiently. A finite difference moving point scheme is derived and applied in a simplified context (continental radially-symmetrical shallow ice approximation). The scheme, which is inexpensive, is validated by comparing the results with moving-margin exact solutions and steady states. In both cases the scheme is able to track the position of the ice sheet margin with high precision.

A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving-point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly. Our approach is also well suited to capture waiting-time behaviour efficiently. A finite-difference moving-point scheme is derived and applied in a simplified context (continental radially symmetrical shallow ice approximation). The scheme, which is inexpensive, is verified by comparing the results with steady states obtained from an analytic solution and with exact moving-margin transient solutions. In both cases the scheme is able to track the position of the ice sheet margin with high accuracy.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Disfunção autonômica e doença vascular periférica em pacientes com diabete melito tipo 2

A disfunção autonômica está associada com aumento da mortalidade em pacientes diabéticos, especialmente naqueles com doença cardiovascular. Neuropatia periférica, mau controle glicêmico, dislipidemia e hipertensão são alguns dos fatores de risco para o desenvolvimento de doença vascular periférica (DVP) nestes pacientes. O objetivo deste estudo foi avaliar os fatores de risco associados com a presença de DVP em pacientes com DM tipo 2. Um estudo transversal foi realizado em 84 pacientes com DM tipo 2 ( 39 homens, idade média de 64,9 ± 7,5 anos). Os pacientes foram submetidos a uma avaliação clínica e laboratorial. A presença de DVP foi definida, utilizando-se um um aparelho manual de ultrasom com doppler (índice perna-braço < 0,9). A atividade autonômica foi avaliada através da análise da variabilidade da freqüência cardíaca (HRV) por métodos no domínio do tempo e da freqüência (análise espectral), e pelo mapa de retorno tridimensional durante o período do dia e da noite. Para a análise da HRV, um eletrocardiograma de 24 horas foi gravado e as fitas analisadas em um analisador de Holter Mars 8000 (Marquete). A potência espectral foi quantificada pela área em duas bandas de freqüência: 0,04-0,15 Hz – baixa freqüência (BF), 0,015-0,5 Hz – alta freqüência (AF). A razão BF/AF foi calculada em cada paciente. O mapa de retorno tridimensional foi construído através de um modelo matemático onde foram analisados os intervalos RR versus a diferença entre os intervalos RR adjacentes versus o número de contagens verificadas, e quantificado por três índices refletindo a modulação simpática (P1) e vagal (P2 e P3). DVP estava presente em 30 (36%) pacientes. Na análise univariada, pacientes com DVP apresentaram índices que refletem a modulação autonômica (análise espectral) diminuídos quando comparados aos pacientes sem DVP, respectivamente: BF = 0,19 ± 0,07 m/s2 vs. 0,29 ± 0,11 m/s2 P = 0,0001; BF/AF = 1,98 ± 0,9 m/s2 vs. 3,35 ± 1,83 m/s2 p = 0,001. Além disso, o índice que reflete a atividade simpática no mapa de retorno tridimensional (P1), foi mais baixo em pacientes com DVP (61,7 ± 9,4 vs. 66,8 ± 9,7 unidades arbitrárias, P = 0,04) durante a noite, refletindo maior ativação simpática neste período. Estes pacientes também apresentavam uma maior duração do diabetes (20 ± 8,1 vs. 15,3 ± 6,7 anos, P = 0,006), níveis de pressão arterial sistólica (154 ± 20 vs. 145 ± 20 mmHg, P = 0,04), razão cintura-quadril ( 0,98 ± 0,09 vs.0,92 ± 0,08, P = 0,01), e níveis de HbA1c mais elevados (7,7 ± 1,6 vs. 6,9 ± 1,7 %, P = 0,04), bem como valores de triglicerídeos ( 259 ± 94 vs. 230 ± 196 mg/dl, P= 0,03) e de excreção urinária de albumina ( 685,5 ± 1359,9 vs. 188,2 ± 591,1 μ/min, P = 0,02) superiores aos dos pacientes sem DVP.. Nos pacientes com DVP observou-se uma presença aumentada de nefropatia diabética (73,3% vs. 29,6% P = 0,0001), de retinopatia (73,3% vs. 44,4% P = 0,02) e neuropatia periférica (705 vs. 35,1% P = 0,006). Os grupos não diferiram quanto à idade, índice de massa corporal, tabagismo e presença de doença arterial coronariana. Na análise logística multivariada, a DVP permaneceu associada com a disfunção autonômica, mesmo após ter sido controlada pela pressão arterial sistólica, duração do DM, HbA1c, triglicerídeos e excreção urinária de albumina. Concluindo, pacientes com DVP e DM tipo 2 apresentam índices que refletem a modulação autonômica diminuídos, o que pode representar um fator de risco adicional para o aumento da mortalidade nestes pacientes.

Terapia de reposição hormonal não altera a variabilidade da frequência cardíaca em mulheres pós-menopáusicas

INTRODUÇÃO. Mulheres pós-menopáusicas apresentam maior risco de desenvolvimento de doença arterial coronariana. Estudos observacionais demonstraram que a terapia de reposição hormonal produz efeitos benéficos no perfil lipídico e na modulação autonômica cardíaca. O aumento da variabilidade da freqüência cardíaca (VFC), até então atribuído à reposição hormonal, não foi testado em estudos randomizados, placebo-controlados, delineados para permitir a comparação entre as duas formas mais utilizadas de reposição hormonal. A VFC de 24 horas calculada pelo método não linear Mapa de Retorno Tridimensional permite avaliar tanto a modulação vagal como a simpática. OBJETIVOS Avaliar a modulação autonômica cardíaca de mulheres pósmenopáusicas através da análise da VFC no domínio do tempo e dos índices do Mapa de Retorno Tridimensional no ECG de 24 horas. Testar a hipótese de que a reposição hormonal contínua, seja com estradiol isolado (TRE), seja com estradiol associado à noretisterona (TRH), por um período de três meses, aumenta a VFC nessas mulheres. MÉTODOS Quarenta mulheres pós-menopáusicas (46 a 63 anos; média = 54,6 ± 4,2) foram randomizadas para um dos três tratamentos, de forma contínua: TRH, estrogenioterapia (TRE) ou placebo, por três meses consecutivos. Previamente, todas as mulheres foram submetidas a exames clínico, ginecológico e laboratorial (glicose, estradiol, HDL, LDL, triglicerídios; mamografia e ultrassonografia transvaginal). O ECG de 24 horas foi gravado em cada paciente, antes e após o tratamento, para calcular os índices da VFC. RESULTADOS Não houve diferença estatisticamente significativa entre os três grupos, após 3 meses de tratamento, nos índices da VFC e do Mapa de Retorno Tridimensional. A TRH diferiu da TRE apenas quanto ao perfil lipídico. A associação com a noretisterona provocou uma redução de 12,4 % no HDL (p = 0,008). CONCLUSÃO Em mulheres pós-menopáusicas, a terapia de reposição hormonal contínua com estradiol, ou com estradiol associado à noretisterona, por um período de 3 meses, não altera a modulação autonômica cardíaca avaliada pela VFC.

Análise teórica e experimental de superfícies seletivas de freqüência e suas aplicações em antenas planares

This work presents a theoretical and numerical analysis of structures using frequency selective surfaces applied on patch antennas. The FDTD method is used to determine the time domain reflected fields. Applications of frequency selective surfaces and patch antennas cover a wide area of telecommunications, especially mobile communications, filters and WB antennas. scattering parameters are obteained from Fourier Transformer of transmited and reflected fields in time domain. The PML are used as absorbing boundary condition, allowing the determination of the fields with a small interference of reflections from discretized limit space. Rectangular patches are considered on dielectric layer and fed by microstrip line. Frequency selective surfaces with periodic and quasi-periodic structures are analyzed on both sides of antenna. A literature review of the use of frequency selective surfaces in patch antennas are also performed. Numerical results are also compared with measured results for return loss of analyzed structures. It is also presented suggestions of continuity to this work