A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Formulation and Implementation of Air Quality Control Pogrammes : Patterns of Interest Consideration

This article investigates some central aspects of the relationships between programme structure and implementation of sulphur dioxide air quality control policies. Previous implementation research, primarily adopting American approaches, has neglected the connections between the processes of programme formulation and implementation. 'Programme', as the key variable in implementation studies, has been defined too narrowly. On the basis of theoretical and conceptual reflections and provisional empirical results from studies in France, Italy, England, and the Federal Republic of Germany, the authors demonstrate that an integral process analysis using a more extended programme concept is necessary if patterns of interest recognition in policies are to be discovered. Otherwise, the still important question of critical social science cannot be answered, namely, what is the impact of special interests upon implementation processes.

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.

Implementation of a DC-DC converter with variable structure control of switched systems

This paper presents a control method for a class of continuous-time switched systems, using state feedback variable structure controllers. The method is applied to the control of a two-cell dc-dc buck converter and a control circuit design using the software PSpice is proposed. The design is based on Lyapunov-Metzler-SPR systems and the performance of the resulting control system is superior to that afforded by a recently-proposed alternative sliding-mode control technique. The dc-dc power converters are very used in industrial applications, for instance, in power systems of hybrid electric vehicles and aircrafts. Good results were obtained and the proposed design is also inexpensive because it uses electric components that can be easily found for the hardware implementation. Future researches on the subject include the hardware validation of the dc-dc converter controller and the robust control design of switched systems, with structural failures. © 2011 IEEE.

Design and implementation of a dc-dc converter based on variable structure control of switched systems

This paper presents a control method for a class of continuous-time switched systems, using state feedback variable structure controllers. The method is applied to the control of a non-trivial dc-dc power converter and a simple and inexpensive control circuit design, that was simulated using the software PSpice, is proposed. The design is based on Lyapunov-Metzler-SPR systems and the performance of the resulting control system is superior to that afforded by a recently proposed alternative sliding-mode control technique. © 2011 IFAC.

Implementation of a Variable Compression Ratio Mechanism in a Four Cylinder Engine

Ever since the invention of the internal combustion engine, generating more power and achieving better efficiency has been a major goal for the designers. Variable compression ratio technology is way to achieve those goals. This paper will discuss the method of varying the compression ratio of an inline 4-cylinder engine through the use of a 4-bar linkage and gear mechanism. This mechanism was proven to easily vary the compression ratio of the engine and shows promise of becoming a technology used for future engine designer.

Inductive inference in the variable valued predicate logic system VL 21 : methodology and computer implementation /

Vita.

Design and implementation of generalized topologies of time-interleaved variable bandpass Σ−Δ modulators

In this thesis, novel analog-to-digital and digital-to-analog generalized time-interleaved variable bandpass sigma-delta modulators are designed, analysed, evaluated and implemented that are suitable for high performance data conversion for a broad-spectrum of applications. These generalized time-interleaved variable bandpass sigma-delta modulators can perform noise-shaping for any centre frequency from DC to Nyquist. The proposed topologies are well-suited for Butterworth, Chebyshev, inverse-Chebyshev and elliptical filters, where designers have the flexibility of specifying the centre frequency, bandwidth as well as the passband and stopband attenuation parameters. The application of the time-interleaving approach, in combination with these bandpass loop-filters, not only overcomes the limitations that are associated with conventional and mid-band resonator-based bandpass sigma-delta modulators, but also offers an elegant means to increase the conversion bandwidth, thereby relaxing the need to use faster or higher-order sigma-delta modulators. A step-by-step design technique has been developed for the design of time-interleaved variable bandpass sigma-delta modulators. Using this technique, an assortment of lower- and higher-order single- and multi-path generalized A/D variable bandpass sigma-delta modulators were designed, evaluated and compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity for ideal and non-ideal topologies. Extensive behavioural-level simulations verified that one of the proposed topologies not only used fewer coefficients but also exhibited greater robustness to non-idealties. Furthermore, second-, fourth- and sixth-order single- and multi-path digital variable bandpass digital sigma-delta modulators are designed using this technique. The mathematical modelling and evaluation of tones caused by the finite wordlengths of these digital multi-path sigmadelta modulators, when excited by sinusoidal input signals, are also derived from first principles and verified using simulation and experimental results. The fourth-order digital variable-band sigma-delta modulator topologies are implemented in VHDL and synthesized on Xilinx® SpartanTM-3 Development Kit using fixed-point arithmetic. Circuit outputs were taken via RS232 connection provided on the FPGA board and evaluated using MATLAB routines developed by the author. These routines included the decimation process as well. The experiments undertaken by the author further validated the design methodology presented in the work. In addition, a novel tunable and reconfigurable second-order variable bandpass sigma-delta modulator has been designed and evaluated at the behavioural-level. This topology offers a flexible set of choices for designers and can operate either in single- or dual-mode enabling multi-band implementations on a single digital variable bandpass sigma-delta modulator. This work is also supported by a novel user-friendly design and evaluation tool that has been developed in MATLAB/Simulink that can speed-up the design, evaluation and comparison of analog and digital single-stage and time-interleaved variable bandpass sigma-delta modulators. This tool enables the user to specify the conversion type, topology, loop-filter type, path number and oversampling ratio.

Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks

Secret communication over public channels is one of the central pillars of a modern information society. Using quantum key distribution this is achieved without relying on the hardness of mathematical problems, which might be compromised by improved algorithms or by future quantum computers. State-of-the-art quantum key distribution requires composable security against coherent attacks for a finite number of distributed quantum states as well as robustness against implementation side channels. Here we present an implementation of continuous-variable quantum key distribution satisfying these requirements. Our implementation is based on the distribution of continuous-variable Einstein–Podolsky–Rosen entangled light. It is one-sided device independent, which means the security of the generated key is independent of any memoryfree attacks on the remote detector. Since continuous-variable encoding is compatible with conventional optical communication technology, our work is a step towards practical implementations of quantum key distribution with state-of-the-art security based solely on telecom components.

Scalable continuous-variable entanglement of light beams produced by optical parametric oscillators

We show that scalable multipartite entanglement among light fields may be generated by optical parametric oscillators (OPOs). The tripartite entanglement existent among the three bright beams produced by a single OPO-pump, signal, and idler-is scalable to a system of many OPOs by pumping them in cascade with the same optical field. This latter serves as an entanglement distributor. The special case of two OPOs is studied, as it is shown that the resulting five bright beams share genuine multipartite entanglement. In addition, the structure of entanglement distribution among the fields can be manipulated to some degree by tuning the incident pump power. The scalability to many fields is straightforward, allowing an alternative implementation of a multipartite quantum information network with continuous variables.

Hardware/firmware implementation of a soft sensor using an improved version of a fuzzy identification algorithm

This paper presents the design and implementation of an embedded soft sensor, i. e., a generic and autonomous hardware module, which can be applied to many complex plants, wherein a certain variable cannot be directly measured. It is implemented based on a fuzzy identification algorithm called ""Limited Rules"", employed to model continuous nonlinear processes. The fuzzy model has a Takagi-Sugeno-Kang structure and the premise parameters are defined based on the Fuzzy C-Means (FCM) clustering algorithm. The firmware contains the soft sensor and it runs online, estimating the target variable from other available variables. Tests have been performed using a simulated pH neutralization plant. The results of the embedded soft sensor have been considered satisfactory. A complete embedded inferential control system is also presented, including a soft sensor and a PID controller. (c) 2007, ISA. Published by Elsevier Ltd. All rights reserved.

Polarization squeezing and continuous-variable polarization entanglement

A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.