Quantization-based new integration methods for stiff ordinary differential equations

In this paper we introduce new classes of numerical ordinary differential equation (ODE) solvers that base their internal discretization method on state quantization instead of time slicing. These solvers have been coined quantized state system (QSS) simulators. The primary result of the research described in this article is a first-order accurate QSS-based stiff system solver, called the backward QSS (BQSS). The numerical properties of this new algorithm are discussed, and it is shown that this algorithm exhibits properties that make it a potentially attractive alternative to the classical numerical ODE solvers. Some simulation examples illustrate the advantages of this method. As a collateral result, a first-order accurate QSS-based solver designed for solving marginally stable systems is briefly outlined as well. This new method, called the centered QSS (CQSS), is successfully applied to a challenging benchmark problem describing a high-order system that is simultaneously stiff and marginally stable. However, the primary emphasis of this article is on the BQSS method, that is, on a stiff system solver based on state quantization.Fil: Migoni, Gustavo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Kofman, Ernesto Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Cellier, François. Eidgenössische Technische Hochschule Zürich; Suiz

A Stand–Alone Quantized State System Solver for Continuous System Simulation

This article introduces a stand-alone implementation of the quantized state system (QSS) integration methods for continuous and hybrid system simulation. QSS methods replace the time discretization of classic numerical integration by the quantization of the state variables. These algorithms lead to discrete event approximations of the original continuous systems and show some advantages over classic numerical integration schemes. For simplicity, most implementations of QSS methods were confined to discrete event simulation engines. The problem is that they were not fully efficient, as they wasted much of the computational load in the discrete event simulation mechanism. The stand-alone QSS solver presented here overcomes this problem, improving in more than one order of magnitude the computation times of the previous discrete event implementations. Besides describing the solver structure and functionality, the article analyzes four different models and compares the performance of the new solver with that of the discrete event implementation, and with that of different classic solvers.Fil: Kofman, Ernesto Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; ArgentinaFil: Fernandez, Joaquin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentin

Particle decay in the early universe

Particle decay processes have deep and profound implications in cosmology and especially on various early universe particle processes. Common decay rates, which may be experimentally verifed e.g., in particle accelerators, are calculated using a theory which relies on Einstein’s theory of special relativity thereby neglecting gravity which is contained in the general theory of relativity. The early universe is, however, a place where the curvature of the spacetime cannot be neglected anymore. Hence, the fat space quantum feld theory becomes only an approximation and of limited applicability. A more precise picture which includes the role of gravity forces one to view things more generally from the perspective of quantum feld theory in curved spacetime. As a result, particle decay rates, cross sections and lifetimes may be modifed from the common decay rates obtained from fat spacetime theory. The aim of this thesis is to investigate how the known fat space decay rates are modifed in the presence of a gravitational feld and what implica¬tions these have on early universe particle processes. Using quantum feld theory in curved spactime and a conceptually clear method for calculating decay rates in curved spacetime, the decay of a massive scalar is studied in a realistic and cosmologically relevant scenarios in an expanding universe. The results have signifcance when studying early universe cosmological situations but also as the cosmological data and measurements become in¬creasingly more accurate, there might arise a necessity in the future to include the e˙ects of curved spacetime also in particle decay rates.Hiukkasten hajoamisprosesseilla on syvällisiä ja perustavanlaatuisia seurauksia kosmologiassa ja erityisesti varhaisen maailmankaikkeuden hiukkasprosesseissa. Tavanomaiset hajoamisnopeudet, joita voidaan esimerkiksi hiukkaskiihdyttimissä kokeellisesti todentaa, ovat laskettu käyttäen teoriaa joka nojautuu Einsteinin erityiseen suhteellisuusteoriaan jättäen näin huomioimatta painovoiman, joka sisältyy yleiseen suhteellisuusteoriaan. Varhainen maailmankaikkeus on kuitenkin paikka, jossa avaruusajan kaarevuutta ei voida enää jättää huomioimatta. Tällöin tavanomainen litteän (laakean) avaruuden kvanttikenttäteoria on vain approksimaatio ja sen käyttö rajallista. Tarkempi kuvaus ja painovoiman roolin huomioiminen pakottaakin tarkastelemaan asioita laajemmin kaarevan avaruuden kvanttikenttäteorian näkökulmasta. Tämän seurauksena hiukkasten hajoamisnopeudet, vaikutusalat ja eliniät saattavat kuitenkin muuttua tavanomaisista litteän avaruuden teoriasta saaduista tuloksista. Tämän väitöskirjan tarkoitus on tutkia miten tunnetut litteän avaruu¬den hajoamisnopeudet muuttuvat painovoiman vaikutuksen alaisena ja mitä seurauksia tällä on varhaisen maailmankaikkeuden hiukkasprosesseihin. Käyttämällä kaarevan avaruuden kvanttikenttäteoriaa ja käsitteellisesti selkeää tapaa laskea hajoamisnopeuksia kaarevassa avaruudessa, massiivisen skalaarihiukkasen hajoamista on tarkasteltu realistisissa ja kosmologisesti merkityksellisissä skenaarioissa avaruuden laajetessa. Tuloksilla on merkitystä tutkittaessa varhaisen maailmankaikkeuden kosmologisia tapahtumia mutta myös kosmologisen datan ja mittausten tullessa yhä tarkemmiksi, voi tulevaisuudessa syntyä tarve ottaa huomioon myös kaarevan avaruuden seuraukset hiukkasten hajoamisnopeuksiin

Analysis, simulation and design of nonlinear RF circuits

The PhD project consists of two parts. The first part concerns the development of Computer Aided Design (CAD) algorithms for high-frequency circuits. Novel Padébased algorithms for numerical integration of ODEs as arise in high-frequency circuits are proposed. Both single- and multi-step methods are introduced. A large part of this section of the research is concerned with the application of Filon-type integration techniques to circuits subject to modulated signals. Such methods are tested with analog and digital modulated signals and are seen to be very effective. The results confirm that these methods are more accurate than the traditional trapezoidal rule and Runge-Kutta methods. The second part of the research is concerned with the analysis, simulation and design of RF circuits with emphasis on injection-locked frequency dividers (ILFD) and digital delta-sigma modulators (DDSM). Both of these circuits are employed in fractional-N frequency synthesizers. Several simulation methods are proposed to capture the locking range of an ILFD, such as the Warped Multi-time Partial Differential Equation (WaMPDE) and the Multiple-Phase-Condition Envelope Following (MPCENV) methods. The MPCENV method is the more efficient and accurate simulation technique and it is recommended to obviate the need for expensive experiments. The Multi-stAge noise Shaping (MASH) digital delta-sigma modulator (DDSM) is simulated in MATLAB and analysed mathematically. A novel structure employing multimoduli, termed the MM-MASH, is proposed. The goal in this design work is to reduce the noise level in the useful frequency band of the modulator. The success of the novel structure in achieving this aim is confirmed with simulations

Quantum cosmological perfect fluid models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for $\alpha \alpha > - 1$.Comment: Latex file, 12 pages. New paragraphs in the Introduction and Conclusion, and other minor corrections in the text and in some formulas. Accepted for publication in General Relativity and Gravitatio

Quantized State Simulation of Spiking Neural Networks

In this work, we explore the usage of quantized state system (QSS) methods in the simulation of networks of spiking neurons. We compare the simulation results obtained by these discrete-event algorithms with the results of the discrete time methods in use by the neuroscience community. We found that the computational costs of the QSS methods grow almost linearly with the size of the network, while they grows at least quadratically in the discrete time algorithms. We show that this advantage is mainly due to the fact that QSS methods only perform calculations in the components of the system that experience activity. © 2012, Simulation Councils Inc. All rights reserved.Fil: Grinblat, Guillermo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Ahumada, Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Kofman, Ernesto Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentin

A novel parallelization technique for DEVS simulation of continuous and hybrid systems.

In this paper, we introduce a novel parallelization technique for Discrete Event System Specification (DEVS) simulation of continuous and hybrid systems. Here, like in most parallel discrete event simulation methodologies, the models are first split into several sub-models which are than concurrently simulated on different processors. In order to avoid the cost of the global synchronization of all processes, the simulation time of each sub-model is locally synchronized in a real-time fashion with a scaled version of physical time, which implicitly synchronizes all sub-models. The new methodology, coined Scaled Real-Time Synchronization (SRTS), does not ensure a perfect synchronization in its implementation. However, under certain conditions, the synchronization error introduced only provokes bounded numerical errors in the simulation results. SRTS uses the same physical time-scaling parameter throughout the entire simulation. We also developed an adaptive version of the methodology (Adaptive-SRTS) where this parameter automatically evolves during the simulation according to the workload. We implemented the SRTS and Adaptive-SRTS techniques in PowerDEVS , a DEVS simulation tool, under a real-time operating system called the Real-Time Application Interface (RTAI) . We tested their performance by simulating three large-scale models, obtaining in all cases a considerable speedup.Fil: Bergero, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Kofman, Ernesto Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Cellier, François. Swiss Federal Institute Of Technology Zurich. Departament Informatik. Modeling And Simulation Research Group; Suiz

Cosmological dynamics of R^n gravity

A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyze their stability for a generic value of the parameter $n$. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the $R^n$ cosmology. When matter is present a transient almost-Friedman phase can also be present before the transition to an accelerated expansion.Comment: revised and extended version, 35 pages, 12 tables, 14 figures which are not included and can be found at http://www.mth.uct.ac.za/~peter/R