Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

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.

Effects of switching time on output voltages of a multilevel inverter used in high frequency applications

Employing multilevel inverters is a proper solution to reduce harmonic content of output voltage and electromagnetic interference in high power electronic applications. In this paper, a new pulse width modulation method for multilevel inverters is proposed in which power devices’ on-off switching times have been considered. This method can be surveyed in order to analyse the effect of switching time on harmonic contents of output voltage in high frequency applications when a switching time is not negligible compared to a switching cycle. Fast Fourier transform calculation and analysis of output voltage waveforms and harmonic contents with regard to switching time variation are presented in this paper for a single phase (3, 5)-level inverters used in high voltage and high frequency converters. Mathematical analysis and MATLAB simulation results have been carried out to validate the proposed method.

Cross voltage control with inner hysteresis current control for multi-output boost converter

Multi-output boost (MOB) converter is a novel DC-DC converter unlike the regular boost converter, has the ability to share its total output voltage and to have different series output voltage from a given duty cycle for low and high power applications. In this paper, discrete voltage control with inner hysteresis current control loop has been proposed to keep the simplicity of the control law for the double-output MOB converter, which can be implemented by a combination of analogue and logical ICs or simple microcontroller to constrain the output voltages of MOB converter at their reference voltages against variation in load or input voltage. The salient features of the proposed control strategy are simplicity of implementation and ease to extend to multiple outputs in the MOB converter. Simulation and experimental results are presented to show the validity of control strategy.

Multi-output DC-DC converters based on diode-clamped converters configuration : topology and control strategy

This paper presents a new DC-DC Multi-Output Boost (MOB) converter which can share its total output between different series of output voltages for low and high power applications. This configuration can be utilised instead of several single output power supplies. This is a compatible topology for a diode-clamed inverter in the grid connection systems, where boosting low rectified output-voltage and series DC link capacitors is required. To verify the proposed topology, steady state and dynamic analysis of a MOB converter are examined. A simple control strategy has been proposed to demonstrate the performance of the proposed topology for a double-output boost converter. The topology and its control strategy can easily be extended to offer multiple outputs. Simulation and experimental results are presented to show the validity of the control strategy for the proposed converter.

A new family of multi-output DC-DC converter topologies to supply an asymmetrical four-level diode-clamped inverter

Purpose Multi-level diode-clamped inverters have the challenge of capacitor voltage balancing when the number of DC-link capacitors is three or more. On the other hand, asymmetrical DC-link voltage sources have been applied to increase the number of voltage levels without increasing the number of switches. The purpose of this paper is to show that an appropriate multi-output DC-DC converter can resolve the problem of capacitor voltage balancing and utilize the asymmetrical DC-link voltages advantages. Design/methodology/approach A family of multi-output DC-DC converters is presented in this paper. The application of these converters is to convert the output voltage of a photovoltaic (PV) panel to regulate DC-link voltages of an asymmetrical four-level diode-clamped inverter utilized for domestic applications. To verify the versatility of the presented topology, simulations have been directed for different situations and results are presented. Some related experiments have been developed to examine the capabilities of the proposed converters. Findings The three-output voltage-sharing converters presented in this paper have been mathematically analysed and proven to be appropriate to improve the quality of the residential application of PV by means of four-level asymmetrical diode-clamped inverter supplying highly resistive loads. Originality/value This paper shows that an appropriate multi-output DC-DC converter can resolve the problem of capacitor voltage balancing and utilize the asymmetrical DC-link voltages advantages and that there is a possibility of operation at high-modulation index despite reference voltage magnitude and power factor variations.

Multi-output buck-boost converter with enhanced dynamic response to load and input voltage changes

This paper presents a new multi-output DC/DC converter topology that has step-up and step-down conversion capabilities. In this topology, several output voltages can be generated which can be used in different applications such as multilevel converters with diode-clamped topology or power supplies with several voltage levels. Steady state and dynamic equations of the proposed multi-output converter have been developed, that can be used for steady state and transient analysis. Two control techniques have been proposed for this topology based on constant and dynamic hysteresis band height control to address different applications. Simulations have been performed for different operating modes and load conditions to verify the proposed topology and its control technique. Additionally, a laboratory prototype is designed and implemented to verify the simulation results.

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.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Sustained convergence, axial length, and corneal topography

Purpose: To investigate the influence of convergence on axial length and corneal topography in young adult subjects.---------- Methods: Fifteen emmetropic young adult subjects with normal binocular vision had axial length and corneal topography measured immediately before and after a 15-min period of base out (BO) prismatic spectacle lens wear. Two different magnitude prismatic spectacles were worn in turn (8 [DELTA] BO and 16 [DELTA] BO), and for both tasks, distance fixation was maintained for the duration of lens wear. Eight subjects returned on a separate day for further testing and had axial length measured before, during, and immediately after a 15-min convergence task.---------- Results: No significant change was found to occur in axial length either during or after the sustained convergence tasks (p > 0.6). Some small but significant changes in corneal topography were found to occur after sustained convergence. The most significant corneal change was observed after the 16 [DELTA] BO prism wear. The corneal refractive power spherocylinder power vector J0 was found to change by a small (mean change of 0.03 D after the 16 [DELTA] BO task) but statistically significant (p = 0.03) amount as a result of the convergence task (indicative of a reduction in with-the-rule corneal astigmatism after convergence). Corneal axial power was found to exhibit a significant flattening in superior regions. Conclusions: Axial length appears largely unchanged by a period of sustained convergence. However, small but significant changes occur in the topography of the cornea after convergence.

A ∑GIi/D/1/∞ queue with heterogeneous input/output slot times

In this paper, we present a ∑GIi/D/1/∞ queue with heterogeneous input/output slot times. This queueing model can be regarded as an extension of the ordinary GI/D/1/∞ model. For this ∑GIi/D/1/∞ queue, we assume that several input streams arrive at the system according to different slot times. In other words, there are different slot times for different input/output processes in the queueing model. The queueing model can therefore be used for an ATM multiplexer with heterogeneous input/output link capacities. Several cases of the queueing model are discussed to reflect different relationships among the input/output link capacities of an ATM multiplexer. In the queueing analysis, two approaches: the Markov model and the probability generating function technique, are adopted to develop the queue length distributions observed at different epochs. This model is particularly useful in the performance analysis of ATM multiplexers with heterogeneous input/output link capacities.