Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

New modal feed network for a compact monopole array with isolated ports

An element spacing of less than half a wavelength introduces strong mutual coupling between the ports of compact antenna arrays. The strong coupling causes significant system performance degradation. A decoupling network may compensate for the mutual coupling. Alternatively, port decoupling can be achieved using a modal feed network. In response to an input signal at one of the input ports, this feed network excites the antenna elements in accordance with one of the eigenvectors of the array scattering parameter matrix. In this paper, a novel 4-element monopole array is described. The feed network of the array is implemented as a planar ring-type circuit in stripline with four coupled line sections. The new configuration offers a significant reduction in size, resulting in a very compact array.

Microphone array shape calibration in diffuse noise fields

This correspondence presents a microphone array shape calibration procedure for diffuse noise environments. The procedure estimates intermicrophone distances by fitting the measured noise coherence with its theoretical model and then estimates the array geometry using classical multidimensional scaling. The technique is validated on noise recordings from two office environments.

Infrared spectroscopic investigation of the effects of titania photocatalyst on the degradation of linear low density polyethylene film for commercial applications

There is a need in industry for a commodity polyethylene film with controllable degradation properties that will degrade in an environmentally neutral way, for applications such as shopping bags and packaging film. Additives such as starch have been shown to accelerate the degradation of plastic films, however control of degradation is required so that the film will retain its mechanical properties during storage and use, and then degrade when no longer required. By the addition of a photocatalyst it is hoped that polymer film will breakdown with exposure to sunlight. Furthermore, it is desired that the polymer film will degrade in the dark, after a short initial exposure to sunlight. Research has been undertaken into the photo- and thermo-oxidative degradation processes of 25 ìm thick LLDPE (linear low density polyethylene) film containing titania from different manufacturers. Films were aged in a suntest or in an oven at 50 °C, and the oxidation product formation was followed using IR spectroscopy. Degussa P25, Kronos 1002, and various organic-modified and doped titanias of the types Satchleben Hombitan and Hunstsman Tioxide incorporated into LLDPE films were assessed for photoactivity. Degussa P25 was found to be the most photoactive with UVA and UVC exposure. Surface modification of titania was found to reduce photoactivity. Crystal phase is thought to be among the most important factors when assessing the photoactivity of titania as a photocatalyst for degradation. Pre-irradiation with UVA or UVC for 24 hours of the film containing 3% Degussa P25 titania prior to aging in an oven resulted in embrittlement in ca. 200 days. The multivariate data analysis technique PCA (principal component analysis) was used as an exploratory tool to investigate the IR spectral data. Oxidation products formed in similar relative concentrations across all samples, confirming that titania was catalysing the oxidation of the LLDPE film without changing the oxidation pathway. PCA was also employed to compare rates of degradation in different films. PCA enabled the discovery of water vapour trapped inside cavities formed by oxidation by titania particles. Imaging ATR/FTIR spectroscopy with high lateral resolution was used in a novel experiment to examine the heterogeneous nature of oxidation of a model polymer compound caused by the presence of titania particles. A model polymer containing Degussa P25 titania was solvent cast onto the internal reflection element of the imaging ATR/FTIR and the oxidation under UVC was examined over time. Sensitisation of 5 ìm domains by titania resulted in areas of relatively high oxidation product concentration. The suitability of transmission IR with a synchrotron light source to the study of polymer film oxidation was assessed as the Australian Synchrotron in Melbourne, Australia. Challenges such as interference fringes and poor signal-to-noise ratio need to be addressed before this can become a routine technique.

Air vehicle simulator : An application for a cable array robot

The development of autonomous air vehicles can be an expensive research pursuit. To alleviate some of the financial burden of this process, we have constructed a system consisting of four winches each attached to a central pod (the simulated air vehicle) via cables - a cable-array robot. The system is capable of precisely controlling the three dimensional position of the pod allowing effective testing of sensing and control strategies before experimentation on a free-flying vehicle. In this paper, we present a brief overview of the system and provide a practical control strategy for such a system. ©2005 IEEE.

A cable-array robot for air vehicle simulation

The development of autonomous air vehicles can be an expensive research pursuit. To alleviate some of the financial burden of this process, we have constructed a system consisting of four winches each attached to a central pod (the simulated air vehicle) via cables - a cable-array robot. The system is capable of precisely controlling the three dimensional position of the pod allowing effective testing of sensing and control strategies before experimentation on a free-flying vehicle. In this paper, we present a brief overview of the system and provide a practical control strategy for such a system.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.