Model for the overall phase-space acceptance in a Zeeman decelerator

We present a new formalism to calculate phase-space acceptance in a Zeeman decelerator. Using parameters closely mimicking previous Zeeman deceleration experiments, this approach reveals a hitherto unconsidered velocity dependence of the phase stability which we ascribe to the finite rise and fall times of the current pulses that generate the magnetic fields inside the deceleration coils. It is shown that changing the current switch-off times as the sequence progresses, so as to maintain a constant mean acceleration per pulse, can lead to a constant phase stability and hence a beam with well-defined characteristics. We also find that the time overlap between fields of adjacent coils has an influence on the phase-space acceptance. Previous theoretical and experimental results suggested unfilled regions in phase space that influence particle transmission through the decelerator. Our model provides, for the first time, a means to directly identify the origin of these effects due to coupling between longitudinal and transverse dynamics. Since optimum phase stability is restricted to a rather small parameter range in terms of the reduced position of the synchronous particle, only a limited range of final velocities can be attained using a given number of coils. We evaluate phase stability for different Zeeman deceleration sequences, and, by comparison with numerical three-dimensional particle trajectory simulations, we demonstrate that our model provides a valuable tool to find optimum parameter sets for improved Zeeman deceleration schemes. An acceleration-deceleration scheme is shown to be a useful approach to generating beams with well-defined properties for variable-energy collision experiments. More generally, the model provides significant physical insights applicable to other types of particle decelerators with finite rise and fall time fields

Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences

The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach based on wavelet analysis for study of the cluster hierarchy. The analytic power of the approach is demonstrated by derivation of a formula for counting of {\it two-fold de Bruijn sequences}, the extension of the notion of de Bruijn sequences. Possible advantages of the developed description is also discussed in context of applied

Artin-Schreier, Erdős, and Kurepa\u27s conjecture

We discuss possible generalizations of Erdŏs\u27s problem about factorials in Fp to the Artin-Schreier extension Fpp of Fp. The generalizations are related to Bell numbers in Fp and to Kurepa\u27s conjecture

Quantum Electrodynamics vacuum polarization solver

The self-consistent modeling of vacuum polarization due to virtual electron-positron fluctuations is of relevance for many near term experiments associated with high intensity radiation sources and represents a milestone in describing scenarios of extreme energy density. We present a generalized finite-difference time-domain solver that can incorporate the modifications to Maxwell's equations due to vacuum polarization. Our multidimensional solver reproduced in one dimensional configurations the results for which an analytic treatment is possible, yielding vacuum harmonic generation and birefringence. The solver has also been tested for two-dimensional scenarios where finite laser beam spot sizes must be taken into account. We employ this solver to explore different types of counter-propagating configurations that can be relevant for future planned experiments aiming to detect quantum vacuum dynamics at ultra-high electromagnetic field intensities

Enhanced Generic Architecture for Safety Increase of True Random Number Generators

Conventionally used generic architecture of true random number generators does not allow testing of random numbers during their generation. This paper introduces an extension of the conventionally used generic architecture and describes mechanisms that can be implemented in new blocks and ensures safety increase of true random number generators. Objective of new architecture extension is detection of deliberate malicious attacks that are directed against noise source and revelation of a significant decrease of the approximate entropy in the subsequences of generated random number sequences. The enhanced generic architecture has been implemented into known software model. Obtained results show that described mechanisms allow increasing quality of the generated random numbers sequences

Topics in combinatorics: A statistical application

The discrete math area known as combinatorics has specific applications in statistics. In this paper, the relationship between combinatorics and statistics will be explored. Major areas of concentration will include: generating functions, special combinatorial numbers and their use in statistics, and the specific relationship of these functions and numbers to some of the more common discrete distributions found in statistics

Artificial Intelligence in the Context of Human Consciousness

Artificial intelligence (AI) can be defined as the ability of a machine to learn and make decisions based on acquired information. AI’s development has incited rampant public speculation regarding the singularity theory: a futuristic phase in which intelligent machines are capable of creating increasingly intelligent systems. Its implications, combined with the close relationship between humanity and their machines, make achieving understanding both natural and artificial intelligence imperative. Researchers are continuing to discover natural processes responsible for essential human skills like decision-making, understanding language, and performing multiple processes simultaneously. Artificial intelligence attempts to simulate these functions through techniques like artificial neural networks, Markov Decision Processes, Human Language Technology, and Multi-Agent Systems, which rely upon a combination of mathematical models and hardware

Large Eddy Simulations of gaseous flames in gas turbine combustion chambers

Recent developments in numerical schemes, turbulent combustion models and the regular increase of computing power allow Large Eddy Simulation (LES) to be applied to real industrial burners. In this paper, two types of LES in complex geometry combustors and of specific interest for aeronautical gas turbine burners are reviewed: (1) laboratory-scale combustors, without compressor or turbine, in which advanced measurements are possible and (2) combustion chambers of existing engines operated in realistic operating conditions. Laboratory-scale burners are designed to assess modeling and funda- mental flow aspects in controlled configurations. They are necessary to gauge LES strategies and identify potential limitations. In specific circumstances, they even offer near model-free or DNS-like LES computations. LES in real engines illustrate the potential of the approach in the context of industrial burners but are more difficult to validate due to the limited set of available measurements. Usual approaches for turbulence and combustion sub-grid models including chemistry modeling are first recalled. Limiting cases and range of validity of the models are specifically recalled before a discussion on the numerical breakthrough which have allowed LES to be applied to these complex cases. Specific issues linked to real gas turbine chambers are discussed: multi-perforation, complex acoustic impedances at inlet and outlet, annular chambers.. Examples are provided for mean flow predictions (velocity, temperature and species) as well as unsteady mechanisms (quenching, ignition, combustion instabil- ities). Finally, potential perspectives are proposed to further improve the use of LES for real gas turbine combustor designs