Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Operation and control of a hybrid microgrid containing unbalanced and nonlinear loads

This paper shows how the power quality can be improved in a microgrid that is supplying a nonlinear and unbalanced load. The microgrid contains a hybrid combination of inertial and converter interfaced distributed generation units where a decentralized power sharing algorithm is used to control its power management. One of the distributed generators in the microgrid is used as a power quality compensator for the unbalanced and harmonic load. The current reference generation for power quality improvement takes into account the active and reactive power to be supplied by the micro source which is connected to the compensator. Depending on the power requirement of the nonlinear load, the proposed control scheme can change modes of operation without any external communication interfaces. The compensator can operate in two modes depending on the entire power demand of the unbalanced nonlinear load. The proposed control scheme can even compensate system unbalance caused by the single-phase micro sources and load changes. The efficacy of the proposed power quality improvement control and method in such a microgrid is validated through extensive simulation studies using PSCAD/EMTDC software with detailed dynamic models of the micro sources and power electronic converters

Optical absorption, infrared, Raman and EPR spectral studies on natural Iowaite mineral

Natural iowaite, magnesium–ferric oxychloride mineral having light green color originating from Australia has been characterized by EPR, optical, IR, and Raman spectroscopy. The optical spectrum exhibits a number of electronic bands due to both Fe(III) and Mn(II) ions in iowaite. From EPR studies, the g values are calculated for Fe(III) and g and A values for Mn(II). EPR and optical absorption studies confirm that Fe(III) and Mn(II) are in distorted octahedral geometry. The bands that appear both in NIR and Raman spectra are due to the overtones and combinations of water and carbonate molecules. Thus EPR, optical, and Raman spectroscopy have proven most useful for the study of the chemistry of natural iowaite and chemical changes in the mineral.

Impact and energy absorption of empty and foam-filled conical tubes

Foam-filled conical tubes have recently emerged as efficient energy absorbing devices to mitigate the adverse effects of impacts. The primary aim of this thesis was to generate research and design information on the impact and energy absorption response of empty and foam-filled conical tubes, and to facilitate their application in energy absorbing systems under axial and oblique loading conditions representative of those typically encountered in crashworthiness and impact applications. Finite element techniques supported by experiments and existing results were used in the investigation. Major findings show that the energy absorption response can be effectively controlled by varying geometry and material parameters. A useful empirical formula was developed for providing engineering designers with an initial estimate of the load ratio and hence energy absorption performances of these devices. It was evident that foam-filled conical tubes enhance the energy absorption capacity and stabilise the crush response for both axial and oblique impact loading without a significant increase in the initial peak load. This is practically beneficial when higher kinetic energy needs to be absorbed, thus reducing the impact force transmitted to the protected structure and occupants. Such tubes also increase and maintain the energy absorption capacity under global bending as well as minimise the reduction of energy absorption capacity with increasing load angle. Furthermore, the results also highlight the feasibility of adding a foam-filled conical tube as a supplementary device in energy absorbing systems, since the overall energy absorption performance of such systems can be favourably enhanced by only including a relatively small energy absorbing device. Above all, the results demonstrate the superior performance of foam-filled conical tube for mitigating impact energy in impact and crashworthiness applications.

Optical absorption near infrared and EPR studies of mottramite

Mottramite mineral originated from Tsumeb Corporation Mine, Tsumeb, Otavi, Namibia, is used in the present work. The mineral contains of vanadium and copper to the extent of 22.73% and 16.84% by weight respectively as V2O5 and CuO. An EPR study of sample confirms the presence of Cu(II) with g = 2.2. Optical absorption spectrum of mottramite indicates that Cu(II) is present in rhombic environment. NIR results are due to water fundamentals.

EPR and optical absorption spectral studies on voglite mineral

A voglite mineral sample of Volrite Canyon #1 mine, Frey Point, White Canyon Mine District, San Juan County, Utah, USA is used in the present study. An EPR study on powdered sample confirms the presence of Mn(II) and Cu(II). Optical absorption spectral results are due to Cu(II) which is in distorted octahedron. NIR results are indicating the presence of water fundamentals.

Nonlinear control of the Reaction Wheel Pendulum

In this paper we introduce the Reaction Wheel Pendulum, a novel mechanical system consisting of a physical pendulum with a rotating bob. This system has several attractive features both from a pedagogical standpoint and from a research standpoint. From a pedagogical standpoint, the dynamics are the simplest among the various pendulum experiments available so that the system can be introduced to students earlier in their education. At the same time, the system is nonlinear and underactuated so that it can be used as a benchmark experiment to study recent advanced methodologies in nonlinear control, such as feedback linearization, passivity methods, backstepping and hybrid control. In this paper we discuss two control approaches for the problems of swingup and balance, namely, feedback linearization and passivity based control. We first show that the system is locally feedback linearizable by a local diffeomorphism in state space and nonlinear feedback. We compare the feedback linearization control with a linear pole-placement control for the problem of balancing the pendulum about the inverted position. For the swingup problem we discuss an energy approach based on collocated partial feedback linearization, and passivity of the resulting zero dynamics. A hybrid/switching control strategy is used to switch between the swingup and the balance control. Experimental results are presented.

Dynamic energy absorption characteristics of foam-filled conical tubes under oblique impact loading

This paper treats the crush behaviour and energy absorption response of foam-filled conical tubes subjected to oblique impact loading. Dynamic computer simulation techniques validated by experimental testing are used to carry out a parametric study of such devices. The study aims at quantifying the energy absorption of empty and foam-filled conical tubes under oblique impact loading, for variations in the load angle and geometry parameters of the tube. It is evident that foam-filled conical tubes are preferable as impact energy absorbers due to their ability to withstand oblique impact loads as effectively as axial impact loads. Furthermore, it is found that the energy absorption capacity of filled tubes is better maintained compared to that of empty tubes as the load orientation increases. The primary outcome of this study is design information for the use of foam-filled conical tubes as energy absorbers where oblique impact loading is expected.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis.