Gyrokinetic modelling of plasma transport and investigation on test particle dynamics

Turbulent plasmas inside tokamaks are modeled and studied using guiding center theory, applied to charged test particles, in a Hamiltonian framework. The equations of motion for the guiding center dynamics, under the conditions of a constant and uniform magnetic field and turbulent electrostatic field are derived by averaging over the fast gyroangle, for the first and second order in the guiding center potential, using invertible changes of coordinates such as Lie transforms. The equations of motion are then made dimensionless, exploiting temporal and spatial periodicities of the model chosen for the electrostatic potential. They are implemented numerically in Python. Fast Fourier Transform and its inverse are used. Improvements to the original Python scripts are made, notably the introduction of a power-law curve fitting to account for anomalous diffusion, the possibility to integrate the equations in two steps to save computational time by removing trapped trajectories, and the implementation of multicolored stroboscopic plots to distinguish between trapped and untrapped guiding centers. The post-processing of the results is made in MATLAB. The values and ranges of the parameters chosen for the simulations are selected based on numerous simulations used as feedback tools. In particular, a recurring value for the threshold to detect trapped trajectories is evidenced. Effects of the Larmor radius, the amplitude of the guiding center potential and the intensity of its second order term are studied by analyzing their diffusive regimes, their stroboscopic plots and the shape of guiding center potentials. The main result is the identification of cases anomalous diffusion depending on the values of the parameters (mostly the Larmor radius). The transitions between diffusive regimes are identified. The presence of highways for the super-diffusive trajectories are unveiled. The influence of the charge on these transitions from diffusive to ballistic behaviors is analyzed.

Generation of self-similar Gaussian time series by means of the DWT and DWPT variance maps

Due to the several kinds of services that use the Internet and data networks infra-structures, the present networks are characterized by the diversity of types of traffic that have statistical properties as complex temporal correlation and non-gaussian distribution. The networks complex temporal correlation may be characterized by the Short Range Dependence (SRD) and the Long Range Dependence - (LRD). Models as the fGN (Fractional Gaussian Noise) may capture the LRD but not the SRD. This work presents two methods for traffic generation that synthesize approximate realizations of the self-similar fGN with SRD random process. The first one employs the IDWT (Inverse Discrete Wavelet Transform) and the second the IDWPT (Inverse Discrete Wavelet Packet Transform). It has been developed the variance map concept that allows to associate the LRD and SRD behaviors directly to the wavelet transform coefficients. The developed methods are extremely flexible and allow the generation of Gaussian time series with complex statistical behaviors.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Complex natural resonances of conducting planar objects buried in a dielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT), The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. We investigate the pole trajectories as we vary the distance between strips and the depth and orientation of single, buried strips, The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.

Parametrització de contorns oberts

Un dels principals problemes quan es realitza un anàlisi de contorns és la gran quantitat de dades implicades en la descripció de la figura. Per resoldre aquesta problemàtica, s’aplica la parametrització que consisteix en obtenir d’un contorn unes dades representatives amb els mínims coeficients possibles, a partir dels quals es podrà reconstruir de nou sense pèrdues molt evidents d’informació. En figures de contorns tancats, la parametrització més estudiada és l’aplicació de la transformada discreta de Fourier (DFT). Aquesta s’aplica a la seqüència de valors que descriu el comportament de les coordenades x i y al llarg de tots els punts que formen el traç. A diferència, en els contorns oberts no es pot aplicar directament la DFT ja que per fer-ho es necessita que el valor de x i de y siguin iguals tan en el primer punt del contorn com en l’últim. Això és degut al fet que la DFT representa sense error senyals periòdics. Si els senyals no acaben en el mateix punt, representa que hi ha una discontinuïtat i apareixen oscil·lacions a la reconstrucció. L’objectiu d’aquest treball és parametritzar contorns oberts amb la mateixa eficiència que s’obté en la parametrització de contorns tancats. Per dur-ho a terme, s’ha dissenyat un programa que permet aplicar la DFT en contorns oberts mitjançant la modificació de les seqüencies de x i y. A més a més, també utilitzant el programari Matlab s’han desenvolupat altres aplicacions que han permès veure diferents aspectes sobre la parametrització i com es comporten els Descriptors El·líptics de Fourier (EFD). Els resultats obtinguts han demostrat que l’aplicació dissenyada permet la parametrització de contorns oberts amb compressions òptimes, fet que facilitarà l’anàlisi quantitatiu de formes en camps com l’ecologia, medicina, geografia, entre d’altres.

Efficient self-synchronised blind audio watermarking system based on time domain and FFT amplitude modification

Many audio watermarking schemes divide the audio signal into several blocks such that part of the watermark is embedded into each of them. One of the key issues in these block-oriented watermarking schemes is to preserve the synchronisation, i.e. to recover the exact position of each block in the mark recovery process. In this paper, a novel time domain synchronisation technique is presented together with a new blind watermarking scheme which works in the Discrete Fourier Transform (DFT or FFT) domain. The combined scheme provides excellent imperceptibility results whilst achieving robustness against typical attacks. Furthermore, the execution of the scheme is fast enough to be used in real-time applications. The excellent transparency of the embedding algorithm makes it particularly useful for professional applications, such as the embedding of monitoring information in broadcast signals. The scheme is also compared with some recent results of the literature.

Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.

Analysis of outliers in electricity spot prices with exampleof New England and New Zealand markets

Electricity spot prices have always been a demanding data set for time series analysis, mostly because of the non-storability of electricity. This feature, making electric power unlike the other commodities, causes outstanding price spikes. Moreover, the last several years in financial world seem to show that ’spiky’ behaviour of time series is no longer an exception, but rather a regular phenomenon. The purpose of this paper is to seek patterns and relations within electricity price outliers and verify how they affect the overall statistics of the data. For the study techniques like classical Box-Jenkins approach, series DFT smoothing and GARCH models are used. The results obtained for two geographically different price series show that patterns in outliers’ occurrence are not straightforward. Additionally, there seems to be no rule that would predict the appearance of a spike from volatility, while the reverse effect is quite prominent. It is concluded that spikes cannot be predicted based only on the price series; probably some geographical and meteorological variables need to be included in modeling.

Parametrització de contorns oberts

Un dels principals problemes quan es realitza un anàlisi de contorns és la gran quantitat de dades implicades en la descripció de la figura. Per resoldre aquesta problemàtica, s’aplica la parametrització que consisteix en obtenir d’un contorn unes dades representatives amb els mínims coeficients possibles, a partir dels quals es podrà reconstruir de nou sense pèrdues molt evidents d’informació. En figures de contorns tancats, la parametrització més estudiada és l’aplicació de la transformada discreta de Fourier (DFT). Aquesta s’aplica a la seqüència de valors que descriu el comportament de les coordenades x i y al llarg de tots els punts que formen el traç. A diferència, en els contorns oberts no es pot aplicar directament la DFT ja que per fer-ho es necessita que el valor de x i de y siguin iguals tan en el primer punt del contorn com en l’últim. Això és degut al fet que la DFT representa sense error senyals periòdics. Si els senyals no acaben en el mateix punt, representa que hi ha una discontinuïtat i apareixen oscil·lacions a la reconstrucció. L’objectiu d’aquest treball és parametritzar contorns oberts amb la mateixa eficiència que s’obté en la parametrització de contorns tancats. Per dur-ho a terme, s’ha dissenyat un programa que permet aplicar la DFT en contorns oberts mitjançant la modificació de les seqüencies de x i y. A més a més, també utilitzant el programari Matlab s’han desenvolupat altres aplicacions que han permès veure diferents aspectes sobre la parametrització i com es comporten els Descriptors El·líptics de Fourier (EFD). Els resultats obtinguts han demostrat que l’aplicació dissenyada permet la parametrització de contorns oberts amb compressions òptimes, fet que facilitarà l’anàlisi quantitatiu de formes en camps com l’ecologia, medicina, geografia, entre d’altres.

Studies on the Characteristics of Vertical Circulation and Equatorial Waves using Indian MST Radar

The aim of the present study is to understand the characteristics and properties of different wave modes and the vertical circulation pattern in the troposphere and lower stratosphere over Indian region using data obtained from the Indian Mesosphere-Stratosphere Troposphere (MST) radar, National Center for Environmental Prediction/National Centres of Atmospheric Research (NCEP/NCAR) reanalysed data and radiosonde observations.Studies on the vertical motion in monsoon Hadley circulation are carried out and the results are discussed . From the analysis of MST radar data, an overall picture of vertical motion of air over Indian region is explained and noted that there exists sinking motion both during winter and summer. Besides, the study shows that there is an anomalous northerly wind in the troposphere over the southern peninsular region during southwest monsoon season.The outcome of the study on intrusion of mid-latitude upper tropospheric trough and associated synoptic-scale vertical velocity over the tropical Indian latitudes are reported and discussed . It shows that there is interaction between north Indian latitudes and tropical easterly region, when there is an eastward movement of Western Disturbance across the country. It explains the strengthening of westerlies and a change of winter westerlies into easterlies in the tropical troposphere and lower stratosphere. The divergence field computed over the MST radar station shows intensification in the downward motion in association with the synoptic systems of the northwest Indian region.

Análise das curvas de luz do CoroT usando diferentes processos comparativos: estimando períodos de rotação estelar

One of the main goals of CoRoT Natal Team is the determination of rotation period for thousand of stars, a fundamental parameter for the study of stellar evolutionary histories. In order to estimate the rotation period of stars and to understand the associated uncertainties resulting, for example, from discontinuities in the curves and (or) low signal-to-noise ratio, we have compared three different methods for light curves treatment. These methods were applied to many light curves with different characteristics. First, a Visual Analysis was undertaken for each light curve, giving a general perspective on the different phenomena reflected in the curves. The results obtained by this method regarding the rotation period of the star, the presence of spots, or the star nature (binary system or other) were then compared with those obtained by two accurate methods: the CLEANest method, based on the DCDFT (Date Compensated Discrete Fourier Transform), and the Wavelet method, based on the Wavelet Transform. Our results show that all three methods have similar levels of accuracy and can complement each other. Nevertheless, the Wavelet method gives more information about the star, from the wavelet map, showing the variations of frequencies over time in the signal. Finally, we discuss the limitations of these methods, the efficiency to give us informations about the star and the development of tools to integrate different methods into a single analysis

Metodologia para identificação do componente fundamental da tensão da rede baseada no algoritmo recursivo da TDF

Considerando a crescente utilização de técnicas de processamento digital de sinais em aplicações de sistemas eletrônicos e ou de potência, este artigo discute o uso da Transformada Discreta de Fourier Recursiva (TDFR) para identificação do ângulo de fase, da freqüência e da amplitude das tensões fundamentais da rede, independente de distorções na forma de onda ou de transitórios na amplitude. Será discutido que, se a freqüência fundamental das tensões medidas coincide com a freqüência a qual a TDF foi projetada, um simples algoritmo TDFR é completamente capaz de fornecer as informações requeridas de fase, freqüência e amplitude. Dois algoritmos adicionais são propostos para garantir seu desempenho correto quando a freqüência difere do seu valor nominal: um deles para a correção do erro de fase do sinal de saída e outro para identificação da amplitude do componente fundamental. Além disto, destaca-se que através dos algoritmos propostos, independentemente do sinal de entrada, a identificação do componente fundamental pode ser realizada em, no máximo, 2 ciclos da rede. Uma análise dos resultados evidenciados pela TDFR foi desenvolvida através de simulações computacionais. Também serão apresentados resultados experimentais referentes ao sincronismo de um gerador síncrono com a rede elétrica, através dos sinais fornecidos pela TDFR.

Comparative analysis of synchronization algorithms based on PLL, RDFT and Kalman Filter

This paper discusses the main characteristics and presents a comparative analysis of three synchronization algorithms based respectively, on a Phase-Locked Loop, a Kalman Filter and a Discrete Fourier Transform. It will be described the single and three-phase models of the first two methods and the single-phase model of the third one. Details on how to modify the filtering properties or dynamic response of each algorithm will be discussed in terms of their design parameters. In order to compare the different algorithms, these parameters will be set for maximum filter capability. Then, the dynamic response, during input amplitude and frequency deviations will be observed, as well as during the initialization procedure. So, advantages and disadvantages of all considered algorithms will be discussed. ©2007 IEEE.

Methodology analysis of a computational tool used in electronic circuit design

This paper considers the importance of using a top-down methodology and suitable CAD tools in the development of electronic circuits. The paper presents an evaluation of the methodology used in a computational tool created to support the synthesis of digital to analog converter models by translating between different tools used in a wide variety of applications. This tool is named MS 2SV and works directly with the following two commercial tools: MATLAB/Simulink and SystemVision. Model translation of an electronic circuit is achieved by translating a mixed-signal block diagram developed in Simulink into a lower level of abstraction in VHDL-AMS and the simulation project support structure in SystemVision. The method validation was performed by analyzing the power spectral of the signal obtained by the discrete Fourier transform of a digital to analog converter simulation model. © 2011 IEEE.