Paula A. Whitlock

The structure of hyperspherical fluids in various dimensions

The structure of hard, hyperspherical fluids in dimension one, two, three, four, and five has been examined by calculating the pair correlation function using a Monte Carlo simulation. The pair correlation functions match known results in one, two, and three dimensions. The contact value of the pair correlation functions in all the different dimensions agrees well with the theory of Song, Mason, and Stratt [J. Phys. Chem. 93, 6916 (1989)]. The decrease in ordering as the dimension is increased is readily apparent in the structure of the pair correlation function.

The equation of state of hard hyperspheres in four and five dimensions

The equation of state of hard hyperspheres in four and five dimensions is calculated from the value of the pair correlation function at contact, as determined by Monte Carlo simulations. These results are compared to equations of state obtained by molecular dynamics and theoretical approaches. In all cases the agreement is excellent.

Femtosecond relaxation of hot electrons by phonon emission in presence of electric field

Abstract The femtosecond relaxation of an initial distribution of electrons which interact with phonons in presence of applied electric field is studied numerically. The evolution at such a time scale cannot be described in terms of Boltzmann transport. Here, the Barker–Ferry equation is utilized as a quantum-kinetic model of the process. The numerical treatment of the original formulation of the Barker–Ferry equation becomes difficult since coordinates and time variables are coupled by the field. A transformation which decouples coordinates and time variables in the equation is proposed. A randomized iterative Monte Carlo algorithm is developed to solve the transformed equation. The quantum character of the equation is investigated. An instantaneously created initial condition is favored above the physically more adequate generation term in order to point out the quantum effects. Simulation results are obtained for GaAs material at different evolution times. Effects of collisional broadening and retardation are observed already in the fieldless case. The intracollisional field effect is clearly demonstrated as an effective change of the phonon energy, which depends on the field direction and the evolution time. Moreover, the collisional broadening and retardation are affected by the applied field. The observed phenomena are understood from the structure and the properties of the model equation.

The equation of state of hard hyperspheres in nine dimensions for low to moderate densities

The equation of state of hard hyperspheres in nine dimensions is calculated both from the values of the first ten virial coefficients and from a Monte Carlo simulation of the pair correlation function at contact. The results are in excellent agreement. In addition, we find that the virial series appears to be dominated by an unphysical singularity or singularities on or near the negative density axis, in qualitative agreement with the recently solved Percus-Yevick equation of state in nine dimensions.

Theory and application of Marsaglia's monkey test for pseudorandom number generators

A theoretical analysis is given for a new test, the “Monkey” test, for pseudorandom number sequences, which was proposed by Marsaglia. Selected results, using the test on several pseudorandom number generators in the literature, are also presented.

The fluid to solid phase transition of hard hyperspheres in four and five dimensions

Molecular dynamics and Monte Carlo simulations are performed for four- and five-dimensional hard hyperspheres at a variety of densities, ranging from the fluid state to the solid regime of A(4), D(4), D(4)*, and D(5) lattices. The equation of state, the radial distribution functions, and the average number of hyperspheres in a coordination layer are determined. The equations of state are in excellent agreement with values obtained from both theoretical approaches and other simulations. The results for the average number of hyperspheres in a coordination layer are in agreement with the theoretical predictions for the different lattices. The radial distribution function gives better insight about the fluid to solid transition than the equation of state.

Statistical Algorithms for Simulation of Electron Quantum Kinetics in Semiconductors - Part II

In this work we solve the Barker-Ferry equation which accounts for the quantum character of the electron-phonon interaction in semiconductors in the framework of the Monte Carlo (MC) method. The first part of the work considers the zero electric field formulation of the equation in spherical coordinates. Different MC algorithms for solving the equation are suggested and investigated.In the second part of the work we consider the case of an applied electric field. It is shown that the second algorithm from the first part can be successfully modified to account for the cylindrical symmetry of the task.

Structure factor for hard hyperspheres in higher dimensions

The structure factor for hard hyperspheres in two to eight dimensions is computed by Fourier transforming the pair correlation function obtained by computer simulation at a variety of densities. The resulting structure factors are compared to the known Percus-Yevick equations for odd dimensions and to the model proposed by Leutheusser [J. Chem. Phys. 84, 1050 (1986)] and Rosenfeld [J. Chem. Phys. 87, 4865 (1987)] in even dimensions. It is found that there is fine agreement among all these approaches at low to moderate densities but that the accuracy of the analytical models breaks down as the freezing transition is approached. The structure factor gives another insight into the decrease in the ordering of the hyperspheres as the dimension is increased.

Efficient deterministic and non-deterministic pseudorandom number generation

A high performance and high quality pseudorandom number generator is presented in this paper. It takes less than one clock cycle to generate a pseudorandom byte on an Intel core i3 processor and passes all the 6 TestU01 batteries of tests. The generator can work in either deterministic mode or non-deterministic mode. When working in deterministic mode, it can be used for high speed data encryption and in other applications that require deterministic and reproducible pseudorandom sequences. When working in non-deterministic mode, the generator behaves much like a true random number generator, but with the advantages of low cost, high performance, and general availability. It is good for many applications that currently rely on true random number generators

A new empirical test for parallel pseudo-random number generators

Recently, Percus derived probabilities and distributions for parallel, i.i.d. random sequences of integers. This was accomplished by considering s given bit locations in each random variable (represented as a predetermined number of bits) in each sequence. These s bits were used to create a new binary sequence whose expected behavior can be analyzed. Based upon Percus work, an empirical test for parallel pseudo-random number generators has been devised. For each generator, parallel sequences of various lengths are considered and analyzed as proposed by Percus and the results are statistically compared to the expected behavior for truly random sequences. A variety of parallel pseudo-random number generators from the literature are studied and the usefulness of the new empirical test is discussed.