Efficient computer search of large-order multiple recursive pseudo-random number generators

AbstractUtilizing some results in number theory, we propose an efficient method to speed up the computer search of large-order maximum-period Multiple Recursive Generators (MRGs). We conduct the computer search and identify many efficient and portable MRGs of order up to 25,013, which have the equi-distribution property in up to 25,013 dimensions and the period lengths up to 10233,361 approximately. In addition, a theoretical test is adopted to further evaluate and compare these generators. An extensive empirical study shows that these generators behave well when tested with the stringent Crush battery of the test package TestU01

Correlated Prompt Fission Data in Transport Simulations

Detailed information on the fission process can be inferred from the observation, modeling and theoretical understanding of prompt fission neutron and $\gamma$-ray~observables. Beyond simple average quantities, the study of distributions and correlations in prompt data, e.g., multiplicity-dependent neutron and \gray~spectra, angular distributions of the emitted particles, $n$-$n$, $n$-$\gamma$, and $\gamma$-$\gamma$~correlations, can place stringent constraints on fission models and parameters that would otherwise be free to be tuned separately to represent individual fission observables. The FREYA~and CGMF~codes have been developed to follow the sequential emissions of prompt neutrons and $\gamma$-rays~from the initial excited fission fragments produced right after scission. Both codes implement Monte Carlo techniques to sample initial fission fragment configurations in mass, charge and kinetic energy and sample probabilities of neutron and $\gamma$~emission at each stage of the decay. This approach naturally leads to using simple but powerful statistical techniques to infer distributions and correlations among many observables and model parameters. The comparison of model calculations with experimental data provides a rich arena for testing various nuclear physics models such as those related to the nuclear structure and level densities of neutron-rich nuclei, the $\gamma$-ray~strength functions of dipole and quadrupole transitions, the mechanism for dividing the excitation energy between the two nascent fragments near scission, and the mechanisms behind the production of angular momentum in the fragments, etc. Beyond the obvious interest from a fundamental physics point of view, such studies are also important for addressing data needs in various nuclear applications. (See text for full abstract.)Comment: 39 pages, 57 figure files, published in Eur. Phys. J. A, reference added this versio

Importance sampling for high speed statistical Monte-Carlo simulations

As transistor dimensions of Static Random AccessMemory (SRAM) become smaller with each new technology generation, they become increasingly susceptible to statistical variations in their parameters. These statistical variations can result in failing memory. SRAM is used as a building block for the construction of large Integrated Circuits (IC). To ensure SRAM does not degrade the yield (fraction of functional devices) of ICs, very low failure probabilities of Pfail = 10-10 are strived for. For instance in SRAMmemory design one aims to get a 0.1% yield loss for 10Mbit memory, which means that 1 in 10 billion cells fails (Pfail = 10-10; this corresponds with an occurrence of -6.4s when dealing with a normal distribution). To simulate such probabilities, traditional Monte-Carlo simulations are not sufficient and more advanced techniques are required. Importance Sampling is a technique that is relatively easy to implement and provides sufficiently accurate results. Importance sampling is a well known technique in statistics to estimate the occurrences of rare events. Rare or extreme events can be associated with dramatic costs, like in finance or because of reasons of safety in environment (dikes, power plants). Recently this technique also received new attention in circuit design. Importance sampling tunes Monte Carlo to the area in parameter space from where the rare events are generated. By this a speed up of several orders can be achieved when compared to standard Monte Carlo methods. We describe the underlying mathematics. Experiments reveal the intrinsic power of the method. The efficiency of the method increases when the dimension of the parameter space increases. The method could be a valuable extension to the statistical capacities of any circuit simulator A Matlab implementation is included in the Appendix

Confinement, chiral symmetry, and the lattice

Two crucial properties of QCD, confinement and chiral symmetry breaking, cannot be understood within the context of conventional Feynman perturbation theory. Non-perturbative phenomena enter the theory in a fundamental way at both the classical and quantum level. Over the years a coherent qualitative picture of the interplay between chiral symmetry, quantum mechanical anomalies, and the lattice has emerged and is reviewed here.Comment: 126 pages, 36 figures. Revision corrects additional typos and renumbers equations to be more consistent with the published versio

Paper-based ZnO self-powered sensors and nanogenerators by plasma technology

Nanogenerators and self-powered nanosensors have shown the potential to power low-consumption electronics and human-machine interfaces, but their practical implementation requires reliable, environmentally friendly and scalable, processes for manufacturing and processing. This article presents a plasma synthesis approach for the fabrication of piezoelectric nanogenerators (PENGs) and self-powered sensors on paper substrates. Polycrystalline ZnO nanocolumnar thin films are deposited by plasma-enhanced chemical vapour deposition on common paper supports using a microwave electron cyclotron resonance reactor working at room temperature yielding high growth rates and low structural and interfacial stresses. Applying Kinetic Monte Carlo simulation, we elucidate the basic shadowing mechanism behind the characteristic microstructure and porosity of the ZnO thin films, relating them to an enhanced piezoelectric response to periodic and random inputs. The piezoelectric devices are assembled by embedding the ZnO films in PMMA and using Au electrodes in two different configurations: laterally and vertically contacted devices. We present the response of the laterally connected devices as a force sensor for low-frequency events with different answers to the applied force depending on the impedance circuit, i.e. load values range, a behaviour that is theoretically analyzed. The vertical devices reach power densities as high as 80 nW/cm2 with a mean power output of 20 nW/cm2. We analyze their actual-scenario performance by activation with a fan and handwriting. Overall, this work demonstrates the advantages of implementing plasma deposition for piezoelectric films to develop robust, flexible, stretchable, and enhanced-performance nanogenerators and self-powered piezoelectric sensors compatible with inexpensive and recyclable supportsComment: 30 pages, 8 figures in main tex

Holography, large N, and supersymmetry on the lattice

Lattice studies of strongly coupled gauge theories started with the pioneering work of Wilson. The success of lattice QCD since then has improved our understanding of strong dynamics, crucial for a proper understanding of many interesting phenomena in Physics. However, it is now known that the Standard model is only an approximation to some richer underlying theory. It is believed that supersymmetry has a special role to play in the framework of that theory. Even if nature is non-supersymmetric at all energy scales and we see no experimental evidence for it in the coming decades, the beautiful structure of these theories could still be very important in our quest to understand the universe. In four dimensions, a special supersymmetric theory has drastically altered our understanding of the holographic principle. In view of these observations, the study of supersymmetric gauge theories on the lattice at strong couplings is crucial. Even though lattice supersymmetry has a long history going back four decades, it has been very difficult to simulate the four-dimensional theory at strong couplings until now. This is because supersymmetry on the lattice is far from trivial and is broken at the clas- sical level because of the supersymmetric algebra. However, substantial progress has been made in studying these theories on the lattice. Several wonderful ideas like topological twisting, differential forms, point group symmetries of the lattice, and integer form fermions all come together and has enabled us to study these supersymmetric theories by preserving a subset of supersymmetries exactly on the lattice. This thesis deals with the numerical studies of super Yang-Mills (SYM) theories in various dimensions, their large N limit, and their role in a better understanding of gauge/gravity duality