Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary correlations are always present in practice. We show that introducing hidden variables and introducing rotation in the RNG output, accompanied with the proper initialization, dramatically suppress these correlations. We analyze the mechanisms of the single-cat-map correlations analytically and show how to diminish them. We generalize the Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We present efficient practical realizations for the RNGs and check our predictions numerically. We also test our RNGs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators.Comment: 18 pages, 3 figures, 9 table

Energy estimators for random series path-integral methods

We perform a thorough analysis on the choice of estimators for random series path integral methods. In particular, we show that both the thermodynamic (T-method) and the direct (H-method) energy estimators have finite variances and are straightforward to implement. It is demonstrated that the agreement between the T-method and the H-method estimators provides an important consistency check on the quality of the path integral simulations. We illustrate the behavior of the various estimators by computing the total, kinetic, and potential energies of a molecular hydrogen cluster using three different path integral techniques. Statistical tests are employed to validate the sampling strategy adopted as well as to measure the performance of the parallel random number generator utilized in the Monte Carlo simulation. Some issues raised by previous simulations of the hydrogen cluster are clarified.Comment: 15 pages, 1 figure, 3 table

GATE : a simulation toolkit for PET and SPECT

Monte Carlo simulation is an essential tool in emission tomography that can assist in the design of new medical imaging devices, the optimization of acquisition protocols, and the development or assessment of image reconstruction algorithms and correction techniques. GATE, the Geant4 Application for Tomographic Emission, encapsulates the Geant4 libraries to achieve a modular, versatile, scripted simulation toolkit adapted to the field of nuclear medicine. In particular, GATE allows the description of time-dependent phenomena such as source or detector movement, and source decay kinetics. This feature makes it possible to simulate time curves under realistic acquisition conditions and to test dynamic reconstruction algorithms. A public release of GATE licensed under the GNU Lesser General Public License can be downloaded at the address http://www-lphe.epfl.ch/GATE/

Chaos-based true random number generators

Random number (bit) generators are crucial to secure communications, data transfer and storage, and electronic transactions, to carry out stochastic simulations and to many other applications. As software generated random sequences are not truly random, fast entropy sources such as quantum systems or classically chaotic systems can be viable alternatives provided they generate high-quality random sequences sufficiently fast. The discovery of spontaneous chaos in semiconductor superlattices at room temperature has produced a valuable nanotechnology option. Here we explain a mathematical model to describe spontaneous chaos in semiconductor superlattices at room temperature, solve it numerically to reveal the origin and characteristics of chaotic oscillations, and discuss the limitations of the model in view of known experiments. We also explain how to extract verified random bits from the analog chaotic signal produced by the superlattice.This work has been supported by the Spanish Ministerio de Economía y Competitividad grants FIS2011-28838-C02-01 and MTM2014-56948-C2-2-P

Development of a Quasi-Monte Carlo Method for Thermal Radiation

Radiative heat transfer in participating media is among the most challenging computational engineering problems due to the complex nonlinear, nonlocal nature of radiation transport. Many approximate methods have been developed in order to resolve radiative heat transfer in participating media; but approximate methods, by the nature of their approximations, suffer from various shortcomings both in terms of accuracy and robustness. The only methods that can resolve radiative transfer accurately in all configurations are the statistical Monte Carlo-based methods. While the Monte Carlo (MC) method is the most accurate method for resolving radiative heat transfer, it is also notoriously computationally prohibitive in large-scale simulations. To overcome this computational burden, this study details the development of a quasi-Monte Carlo (QMC) method for thermal radiation in participating media with a focus on combustion-related problems. The QMC method employs a low-discrepancy sequence (LDS) in place of the traditional random number sampling mechanism used in Monte Carlo methods to increase computational efficiency. In order to analyze the performance of the QMC method, a systematic comparison of accuracy and computational expense was performed. The QMC method was validated against formal solutions of radiative heat transfer in several one-dimensional configurations and extended to three practical combustion configurations: a turbulent jet flame, a high-pressure industrial gas turbine, and a high-pressure spray combustion chamber. The results from QMC and traditional Monte Carlo are compared against benchmark solutions for each case. It is shown that accuracy of the predicted radiation field from QMC is comparable to MC at lower computational costs. Three different low-discrepancy sequences – Sobol, Halton, and Niederreiter – were examined as part of this work. Finally, recommendations are made in terms of choice of the sequence and the number of the dimensions of the LDS for combustion-relevant configurations. In conclusion, significant improvements in computational costs and accuracy seen in the QMC method makes it a viable alternative to traditional Monte Carlo methods in high-fidelity simulations

STOCHASTIC AND DETERMINISTIC SIMULATION TECHNIQUES FOR TRAFFIC AND ECONOMICS

In this work I present the result of different investigations conducted in the last years in the context of stochastic modeling for decision making in the areas of traffic simulation and economics. Traffic simulation has seen us from the Center for Modeling, Computing and Statistics involved in a project for the evaluation and planning of two highway stretches in the area around Ferrara. In particular we conducted the modeling and numerical simulation of the highway network, in collaboration with Michael Herty. Later the study of kinetic analysis and simulation techniques proved useful in another related setting, that is agent based models in economics, a discipline of growing importance in understanding the workings of markets, be they financial or centered on tangible goods. Due to my job in the asset management industry some of the research activity has been tilted towards practical methods for financial simulations, and in particular that of parallel random number generation is a topic that has been gaining importance during these last years. While at Eurizon Capital I developed a novel fast algorithm for moving over certain widely used random number streams, and at NEC Labs Europe this was further reimplemented as a core block of a professional C++ library for parallel Monte Carlo simulation in finance. Finally I present a small note on a common numerical artifact arising in Monte Carlo simulations when only a limited number of kinetic particles are used. Already with simple kernels the resulting probability distributions differ significantly from those predicted by theory and obtained with large particle sets

Cyclotron production of 11^C: experimental assessment of saturation yield and validation with Monte Carlo simulation

Nell'ambito della Fisica Medica, le simulazioni Monte Carlo sono uno strumento sempre più diffuso grazie alla potenza di calcolo dei moderni calcolatori, sia nell'ambito diagnostico sia in terapia. Attualmente sono disponibili numerosi pacchetti di simulazione Monte Carlo di carattere "general purpose", tra cui Geant4. Questo lavoro di tesi, svolto presso il Servizio di Fisica Sanitaria del Policlinico "S.Orsola-Malpighi", è basato sulla realizzazione, utilizzando Geant4, di un modello Monte Carlo del target del ciclotrone GE-PETtrace per la produzione di C-11. Nel modello sono stati simulati i principali elementi caratterizzanti il target ed il fascio di protoni accelerato dal ciclotrone. Per la validazione del modello sono stati valutati diversi parametri fisici, tra i quali il range medio dei protoni nell'azoto ad alta pressione e la posizione del picco di Bragg, confrontando i risultati con quelli forniti da SRIM. La resa a saturazione relativa alla produzione di C-11 è stata confrontata sia con i valori forniti dal database della IAEA sia con i dati sperimentali a nostra disposizione. Il modello è stato anche utilizzato per la stima di alcuni parametri di interesse, legati, in particolare, al deterioramento dell'efficienza del target nel corso del tempo. L'inclinazione del target, rispetto alla direzione del fascio di protoni accelerati, è influenzata dal peso del corpo del target stesso e dalla posizione in cui questo é fissato al ciclotrone. Per questo sono stati misurati sia il calo della resa della produzione di C-11, sia la percentuale di energia depositata dal fascio sulla superficie interna del target durante l'irraggiamento, al variare dell'angolo di inclinazione del target. Il modello che abbiamo sviluppato rappresenta, dunque, un importante strumento per la valutazione dei processi che avvengono durante l'irraggiamento, per la stima delle performance del target nel corso del tempo e per lo sviluppo di nuovi modelli di target