Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Grid-based method for ranking images with multiple objects

One of the content-based image retrieval techniques is the shape-based technique, which allows users to ask for objects similar in shape to a query object. Sajjanhar and Lu proposed a method for shape representation and similarity measure called the grid-based method [1]. They have shown that the method is effective for the retrieval of segmented objects based on shape. In this paper, we describe a system which uses the grid-based method for retrieval of images with multiple objects. We perform experiments on the prototype system to compare the performance of the grid-based method with the Fourier descriptors method [2]. Preliminary results have been presented.

An exact series solution for the vibration analysis of cylindrical shells with arbitrary boundary conditions

In this paper, an exact series solution for the vibration analysis of circular cylindrical shells with arbitrary boundary conditions is obtained, using the elastic equations based on Flügge's theory. Each of the three displacements is represented by a Fourier series and auxiliary functions and sought in a strong form by letting the solution exactly satisfy both the governing differential equations and the boundary conditions on a point-wise basis. Since the series solution has to be truncated for numerical implementation, the term exactly satisfying should be understood as a satisfaction with arbitrary precision. One of the important advantages of this approach is that it can be universally applied to shells with a variety of different boundary conditions, without the need of making any corresponding modifications to the solution algorithms and implementation procedures as typically required in other techniques. Furthermore, the current method can be easily used to deal with more complicated boundary conditions such as point supports, partial supports, and non-uniform elastic restraints. Numerical examples are presented regarding the modal parameters of shells with various boundary conditions. The capacity and reliability of this solution method are demonstrated through these examples. © 2012 Elsevier Ltd. All rights reserved.

Oscilador harmônico unidimensional via transformada unilateral de Fourier e mapeamento do potencial de morse unidimensional nos potenciais pseudo-harmônico e de kratzer tridimensionais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Oscilador harmônico unidimensional via transformada unilateral de Fourier e mapeamento do potencial de morse unidimensional nos potenciais pseudo-harmônico e de kratzer tridimensionais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Autoregressive spectral array for graphical display of EEG data

A graphical display of the frequency content of background,electroencephalogram (EEG) activity is obtained by calculating the spectral estimates using autocorrelation autoregressive method and the classical Fourier transform method, Display of spectral content of consecutive data segments is made using hidden-line suppression technique so as to get a spectral array, The autoregressive spectral array (ASA) is found to be sensitive to baseline drift, Following baseline correction the autoregressive technique is found to be superior to the Fourier method of compressed spectral array (CSA) in detecting the transitions in the frequencies of the signal. The smoothed ASA gives a better picture of transitions and changes in the background activity, The ASA can be made to adapt to specific changes of dominant frequencies while eliminating unnecessary peaks in the spectrum. The utility,of the ASA for background EEG analysis is discussed,

Photoluminescence study of mixed doped Ge-Se-In-Bi glasses

Photoluminescence studies, carried out using the Fourier Transform method rather than the conventional monochromator-dispersion method,are reported on glassy samples of indium-bismuth mixed doped Ge (10) Se(90-x-y) In (x) Bi (y) system (x,y = 5,10). The amorphous Bi2Se3 is found to be n-type like the crystalline counterpart. The possible contributions from microscopic cluster-level phase separation of Bi2Se3 and from the defects to the change in conductivity from p- to n- typein this system is discussed. The similar situation in related systems is also pointed out.

Time and Frequency Domain Finite Element Models for Axial Wave Analysis in Hyperelastic Rods

The propagation of axial waves in hyperelastic rods is studied using both time and frequency domain finite element models. The nonlinearity is introduced using the Murnaghan strain energy function and the equations governing the dynamics of the rod are derived assuming linear kinematics. In the time domain, the standard Galerkin finite element method, spectral element method, and Taylor-Galerkin finite element method are considered. A frequency domain formulation based on the Fourier spectral method is also developed. It is found that the time domain spectral element method provides the most efficient numerical tool for the problem considered.

Generation of large-scale vortex dislocations in a three-dimensional wake-type flow

Numerical study of three-dimensional evolution of wake-type flow and vortex dislocations is performed by using a compact finite diffenence-Fourier spectral method to solve 3-D incompressible Navier-Stokes equations. A local spanwise nonuniformity in momentum defect is imposed on the incoming wake-type flow. The present numerical results have shown that the flow instability leads to three-dimensional vortex streets, whose frequency, phase as well as the strength vary with the span caused by the local nonuniformity. The vortex dislocations are generated in the nonuniform region and the large-scale chain-like vortex linkage structures in the dislocations are shown. The generation and the characteristics of the vortex dislocations are described in detail.

Characters of Surface Deformation and Surface Wave in Thermal Capillary Convection

In the field of fluid mechanics, free surface phenomena is one of the most important physical processes. In the present research work, the surface deformation and surface wave caused by temperature difference of sidewalls in a rectangular cavity have been investigated. The horizontal cross-section of the container is 52 mmx42 mm, and there is a silicon oil layer of height 3.5 mm in the experimental cavity. Temperature difference between the two side walls of the cavity is increased gradually, and the flow on the liquid layer will develop from stable convection to un-stable convection. An optical diagnostic system consisting of a modified Michelson interferometer and image processor has been developed for study of the surface deformation and surface wave of thermal capillary convection. The Fourier transformation method is used to interferometer fringe analysis. The quantitative results of surface deformation and surface wave have been calculated from a serial of the interference fringe patterns.The characters of surface deformation and surface wave have been obtained. They are related with temperature gradient and surface tension. Surface deformation is fluctuant with time, which shows the character of surface wave. The cycle period of the wave is 4.8 s, and the amplitudes are from 0 to 0.55 mu m. The phase of the wave near the cool side of the cavity is opposite and correlative to that near the hot side. The present experiment proves that the surface wave of thermal capillary convection exists on liquid free surface, and it is wrapped in surface deformation.

Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

Accurate determination of the absolute phase and temporal-pulse phase of few-cycle laser pulses

A Fourier analysis method is used to accurately determine not only the absolute phase but also the temporal-pulse phase of an isolated few-cycle (chirped) laser pulse. This method is independent of the pulse shape and can fully characterize the light wave even though only a few samples per optical cycle are available. It paves the way for investigating the absolute phase-dependent extreme nonlinear optics, and the evolutions of the absolute phase and the temporal-pulse phase of few-cycle laser pulses.

超连续谱干涉方法测量古依相移

利用两束超连续光干涉得到的信号,测量了透镜焦点附近飞秒激光脉冲的古依(Gouy)相移。根据得到的光谱干涉信号,利用傅里叶变换得到相对相位值。激光光束在聚焦透镜后的束腰半径可以由成像方法测得。根据测量得到的激光光束束腰半径,用非线性拟合的方法得到了古依相移曲线,拟合曲线与实验结果符合得非常好。给出了古依相位在焦点前后1 mm区域内的移动量。

Generation of millimeter-wave in optical pulse carrier by using an apodized Moire fiber grating

A novel scheme is proposed to transform a Gaussian pulse to a millimeter-wave frequency modulation pulse by using an apodized Moire fiber Bragg grating in radio-over-fiber system. The relation between the input and output pulses is analyzed theoretically by Fourier transformation method and the requirements for the proposed fiber grating are presented. An apodized Moire fiber Bragg grating is designed and its characteristics are studied. It is shown that the proposed device is feasible, and the new scheme is believed to be an effective solution for the generation of millimeter-wave sub-carrier in future radio-over-fiber systems. (c) 2006 Elsevier B.V. All rights reserved.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.