arXiv subjects
Publications and source records attributed to Gary D. Doolen.
Within a class of exact time-dependent non-singular N-logarithmic solutions (Mineev-Weinstein and Dawson, Phys. Rev. E 50, R24 (1994); Dawson and Mineev-Weinstein, Phys. Rev. E 57, 3063 (1998)), we have found solutions which describe the development and pinching off of viscous droplets in the Hele-Shaw cell in the absence of surface tension.
We investigate the influence of superpositional wave function oscillations on the performance of Shor's quantum algorithm for factorization of integers. It is shown that the wave function oscillations can destroy the required quantum interference. This undesirable effect can be routinely eliminated using a resonant pulse implementation of quantum computation, but requires special analysis for non-resonant implementations.
We study numerically the process of nuclear spin measurement in a solid-state quantum computer of the type proposed by Kane by modeling the quantum dynamics of two coupled nuclear spins on $^{31}$P donors implanted in silicon. We estimate the minimum measurement time necessary for the reliable transfer of quantum information from the nuclear spin subsystem to the electronic subsystem. We also calculate the probability of error for typical values of the external noise.
The lattice Boltzmann model is a simplified kinetic method based on the particle distribution function. We use this method to simulate problems in MEMS, in which the velocity slip near the wall plays an important role. It is demonstrated that the lattice Boltzmann method can capture the fundamental behavior in micro-channel flow, including velocity slip and nonlinear pressure drop along the channel. The Knudsen number dependence of the position of the vortex center and the pressure contour in micro-cavity flows is also demonstrated.
When dealing with macroscopic objects one usually observes quasiclassical phenomena, which can be described in terms of quasiclassical (or classical) equations of motion. Recent development of the theory of quantum computation is based on implementation of the entangled states which do not have a classical analogy. Using a simple example of a paramagnetic spin system we show that the entangled states can be detected in standard macroscopic experiments as a sharp deviation from quasiclassical motion.
We investigate numerically a single-pulse implementation of a quantum Control-Not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time-evolution of the density matrix, for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of quantum CN gate in this system at finite temperature, using electromagnetic $π$-pulse.
The physical implementation of the quantum Control-Not gate for a two-spin system is investigated numerically. The concept of a generalized quantum Control-Not gate, with arbitrary phase shift, is introduced. It is shown that a resonant $π$-pulse provides a simple example of a generalized quantum Control-Not gate.
Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $τ$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.
A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives accurate results over a wide range of Reynolds numbers. Studies of errors and convergence rates are carried out. Compressibility effects are quantified for different maximum velocities, and parameter ranges are found for stable simulations. The paper's objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers.