The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Time- vs. frequency-domain identification of parametric radiation force models for marine structures at zero speed

The dynamics describing the motion response of a marine structure in waves can be represented within a linear framework by the Cummins Equation. This equation contains a convolution term that represents the component of the radiation forces associated with fluid memory effects. Several methods have been proposed in the literature for the identification of parametric models to approximate and replace this convolution term. This replacement can facilitate the model implementation in simulators and the analysis of motion control designs. Some of the reported identification methods consider the problem in the time domain while other methods consider the problem in the frequency domain. This paper compares the application of these identification methods. The comparison is based not only on the quality of the estimated models, but also on the ease of implementation, ease of use, and the flexibility of the identification method to incorporate prior information related to the model being identified. To illustrate the main points arising from the comparison, a particular example based on the coupled vertical motion of a modern containership vessel is presented.

Hybrid frequency–time domain models for dynamic response analysis of marine structures

Time-domain models of marine structures based on frequency domain data are usually built upon the Cummins equation. This type of model is a vector integro-differential equation which involves convolution terms. These convolution terms are not convenient for analysis and design of motion control systems. In addition, these models are not efficient with respect to simulation time, and ease of implementation in standard simulation packages. For these reasons, different methods have been proposed in the literature as approximate alternative representations of the convolutions. Because the convolution is a linear operation, different approaches can be followed to obtain an approximately equivalent linear system in the form of either transfer function or state-space models. This process involves the use of system identification, and several options are available depending on how the identification problem is posed. This raises the question whether one method is better than the others. This paper therefore has three objectives. The first objective is to revisit some of the methods for replacing the convolutions, which have been reported in different areas of analysis of marine systems: hydrodynamics, wave energy conversion, and motion control systems. The second objective is to compare the different methods in terms of complexity and performance. For this purpose, a model for the response in the vertical plane of a modern containership is considered. The third objective is to describe the implementation of the resulting model in the standard simulation environment Matlab/Simulink.

Development of health risk-based metrics for defining a heatwave : a time series study in Brisbane, Australia

Background: This study attempted to develop health risk-based metrics for defining a heatwave in Brisbane, Australia. Methods: Poisson generalised additive model was performed to assess the impact of heatwaves on mortality and emergency hospital admissions (EHAs) in Brisbane. Results: In general, the higher the intensity and the longer the duration of a heatwave, the greater the health impacts. There was no apparent difference in EHAs risk during different periods of a warm season. However, there was a greater risk of mortality in the second half of a warm season than that in the first half. While elderly (>75 years)were particularly vulnerable to both the EHA and mortality effects of a heatwave, the risk for EHAs also significantly increased for two other age groups (0-64 years and 65-74 years) during severe heatwaves. Different patterns between cardiorespiratory mortality and EHAs were observed. Based on these findings, we propose the use of a teiered heat warning system based on the health risk of heatwave. Conclusions: Health risk-based metrics are a useful tool for the development of local heatwave definitions. thsi tool may have significant implications for the assessment of heatwave-related health consequences and development of heatwave response plans and implementation strategies.

Time-temperature histories of spherical food products during bulk forced-air precooling

A general mathematical model for forced air precooling of spherical food products in bulk is developed. The food products are arranged inline to form a rectangular parallelepiped. Chilled air is blown along the height of the package. The governing equations for the transient two-dimensional conduction with internal heat generation in the product, simultaneous heat and mass transfer at the product-air interface and one-dimensional transient energy and species conservation equations for the moist air are solved numerically using finite difference methods. Results are presented in the form of time-temperature histories. Experiments are conducted with model foods in a laboratory scale air precooling tunnel. The agreement between the theoretical and experimental results is found to be good. In general, a single product analysis fails to predict the precooling characteristics of bulk loads of food products. In the range of values investigated, the respiration heat is found to have a negligible effect.

Analysis of co-current hydraircooling of food products in bulk

A mathematical model is developed to describe the hydraircooling process when the water and air are flowing in the same direction. The governing equations for the simultaneous heat and mass transfer are solved using finite-difference numerical methods. The half cooling time of the food products is correlated as a function of the dimensionless process parameters. It is observed that a process time of approximately double the half cooling time will result in the food products attaining almost a steady state. The process times of the bulk hydraircooling process and the bulk air precooling process are compared.

Analysis of heat and mass transfer during bulk hydraircooling of spherical food products

Hydraircooling is a technique used for precooling food products. In this technique chilled water is sprayed over the food products while cold unsaturated air is blown over them. Hydraircooling combines the advantages of both air- and hydrocooling. The present study is concerned with the analysis of bulk hydraircooling as it occurs in a package filled with several layers of spherical food products with chilled water sprayed from the top and cold unsaturated air blown from the bottom. A mathematical model is developed to describe the hydrodynamics and simultaneous heat and mass transfer occurring inside the package. The non-dimensional governing equations are solved using the finite difference numerical methods. The results are presented in the form of time-temperature charts. A correlation is obtained to calculate the process time in terms of the process parameters.

State Transition Based Embedding in Cepstrum Domain for Audio Copyright Protection

In this paper, we propose a new state transition based embedding (STBE) technique for audio watermarking with high fidelity. Furthermore, we propose a new correlation based encoding (CBE) scheme for binary logo image in order to enhance the payload capacity. The result of CBE is also compared with standard run-length encoding (RLE) compression and Huffman schemes. Most of the watermarking algorithms are based on modulating selected transform domain feature of an audio segment in order to embed given watermark bit. In the proposed STBE method instead of modulating feature of each and every segment to embed data, our aim is to retain the default value of this feature for most of the segments. Thus, a high quality of watermarked audio is maintained. Here, the difference between the mean values (Mdiff) of insignificant complex cepstrum transform (CCT) coefficients of down-sampled subsets is selected as a robust feature for embedding. Mdiff values of the frames are changed only when certain conditions are met. Hence, almost 50% of the times, segments are not changed and still STBE can convey watermark information at receiver side. STBE also exhibits a partial restoration feature by which the watermarked audio can be restored partially after extraction of the watermark at detector side. The psychoacoustic model analysis showed that the noise-masking ratio (NMR) of our system is less than -10dB. As amplitude scaling in time domain does not affect selected insignificant CCT coefficients, strong invariance towards amplitude scaling attacks is also proved theoretically. Experimental results reveal that the proposed watermarking scheme maintains high audio quality and are simultaneously robust to general attacks like MP3 compression, amplitude scaling, additive noise, re-quantization, etc.

A survey on compressed domain video analysis techniques

Image and video analysis requires rich features that can characterize various aspects of visual information. These rich features are typically extracted from the pixel values of the images and videos, which require huge amount of computation and seldom useful for real-time analysis. On the contrary, the compressed domain analysis offers relevant information pertaining to the visual content in the form of transform coefficients, motion vectors, quantization steps, coded block patterns with minimal computational burden. The quantum of work done in compressed domain is relatively much less compared to pixel domain. This paper aims to survey various video analysis efforts published during the last decade across the spectrum of video compression standards. In this survey, we have included only the analysis part, excluding the processing aspect of compressed domain. This analysis spans through various computer vision applications such as moving object segmentation, human action recognition, indexing, retrieval, face detection, video classification and object tracking in compressed videos.

Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a staggered-mesh grid system. The convection terms are discretized with a fifth-order-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth-order difference approximation on a cell-centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented.

Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Domain decomposition hybrid method for numerical simulation of bluff body flows:theoretical model and application

The discrete vortex method is not capable of precisely predicting the bluff body flow separation and the fine structure of flow field in the vicinity of the body surface. In order to make a theoretical improvement over the method and to reduce the difficulty in finite-difference solution of N-S equations at high Reynolds number, in the present paper, we suggest a new numerical simulation model and a theoretical method for domain decomposition hybrid combination of finite-difference method and vortex method. Specifically, the full flow. field is decomposed into two domains. In the region of O(R) near the body surface (R is the characteristic dimension of body), we use the finite-difference method to solve the N-S equations and in the exterior domain, we take the Lagrange-Euler vortex method. The connection and coupling conditions for flow in the two domains are established. The specific numerical scheme of this theoretical model is given. As a preliminary application, some numerical simulations for flows at Re=100 and Re-1000 about a circular cylinder are made, and compared with the finite-difference solution of N-S equations for full flow field and experimental results, and the stability of the solution against the change of the interface between the two domains is examined. The results show that the method of the present paper has the advantage of finite-difference solution for N-S equations in precisely predicting the fine structure of flow field, as well as the advantage of vortex method in efficiently computing the global characteristics of the separated flow. It saves computer time and reduces the amount of computation, as compared with pure N-S equation solution. The present method can be used for numerical simulation of bluff body flow at high Reynolds number and would exhibit even greater merit in that case.

An asymptotic analysis for one dimensional stress wave propagation in damaged viscoelastic media

A regular perturbation technique is suggested to deal with the problem of one dimensional stress wave propagation in viscoelastic media with damage. Based upon the first order asymptotic solution obtained, the characteristics of wave attenuation are studied. In fact, there exist three different time-dependent phenomena featuring the dynamic response of the materials, the first expressing the characteristics of wave propagation, the second indicating the innate effect of visco-elastic matrix and the third coming from the time dependent damage. The comparision of first order asymptotic solution with the numerical results calculated by a finite difference procedure shows that the perturbation expansion technique may offer a useful approach to the problem concerned.

Numerical and experimental analysis on green laser crystallization of amorphous silicon thin films

The effect of laser fluence on the crystallization of amorphous silicon irradiated by a frequency-doubled Nd:YAG laser is studied both theoretically and experimentally. An effective numerical model is set up to predict the melting threshold and the optimized laser fluence for the crystallization of 200-nm-thick amorphous silicon. The variation of the temperature distribution with time and the melt depth is analyzed. Besides the model, the Raman spectra of thin films treated with different fluences are measured to confirm the phase transition and to determine the optimized fluence. The calculating results accord well with those obtained from the experimental data in this research. (C) 2008 Elsevier Ltd. All rights reserved.