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.

This paper demonstrates that thermodynamically consistent lattice Boltzmann models for single-component multiphase flows can be derived from a kinetic equation using both Enskog's theory for dense fluids and mean-field theory for long-range molecular interaction. The lattice Boltzmann models derived this way satisfy the correct mass, momentum, and energy conservation equations. All the thermodynamic variables in these LBM models are consistent. The strengths and weaknesses of previous lattice Boltzmann multiphase models are analyzed.

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The character of hydrodynamic modes of the system is discussed. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.

Turbulent combustion is ubiquitously used in practical combustion devices. However, even chemically non-reacting turbulent flows are complex phenomena, and chemical reactions make the problem even more complicated. Due to the limitation of the computational costs, conventional numerical methods are impractical in carrying out direct 3D numerical simulations at high Reynolds numbers with detailed chemistry. Recently, the lattice Boltzmann method has emerged as an efficient alternative for numerical simulation of complex flows. Compared with conventional methods, the lattice Boltzmann scheme is simple and easy for parallel computing. In this study, we present a lattice Boltzmann model for simulation of combustion, which includes reaction, diffusion, and convection. We assume the chemical reaction does not affect the flow field. Flow, temperature, and concentration fields are decoupled and solved separately. As a preliminary simulation, we study the so-called “counter-flow” laminar flame. The particular flow geometry has two opposed uniform combustible jets which form a stagnation flow. The results are compared with those obtained from solving Navier–Stokes equations.

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 behaviors in micro-channel flow, including velocity slip, nonlinear pressure drop along the channel and mass flow rate variation with Knudsen number. The Knudsen number dependence of the position of the vortex center and the pressure contour in micro-cavity flows is also demonstrated.

The two-dimensional Kelvin–Helmholtz instability is studied using a lattice Boltzmann multi-phase model in the nearly incompressible limit. This study focuses on the effects of surface tension on the evolution of vortex pairing in a two-dimensional mixing layer. Several types of interface pinch-off are observed and the corresponding mechanisms are discussed. The contribution of surface tension to the flow kinetic energy is mainly negative. Part of this kinetic energy can be transformed to potential energy stored in the surface tension. The contribution of surface tension to the flow enstrophy is positive and small vortices are generated near interfaces. Broken interfaces and small vortices near interfaces dominate the late stage of flow fields with strong surface tension.

We study numerically the process of nuclear spin measurement in a solid-state quantum computer of the type proposed by Kane, by calculating the quantum dynamics of two coupled nuclear spins on 31 P donors implanted in 28 Si. We estimate the time of the `quantum swap operation' - the minimum measurement time required for the reliable transfer of quantum information from the nuclear spin subsystem to the electronic subsystem. Our calculations show that for realistic values of the parameters this time is of the order of swap ~5 × 10-5 s. We also calculate the probability of error for typical values of the external noise.

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.

The Turing machine binary system and Boolean algebra the quantum computer the discrete Fourier transform quantum factorization of integers logic gates implementation of logic gates using transistors reversible logic gates quantum logic gates tow and three Qubit quantum logic gates on-Qubit rotation Aj transformation Bjk transformation unitary transformations and quantum dynamics quantum dynamics at finite temperature physical realization of quantum computations Control-Not gate in an ion trap Aj and Bjk gates in an ion trap linear chains of nuclear spins digital gates in a spin chain nonresonant action of pi-pulses experimental logic gates in quantum systems - achievements and opportunities error correction for quantum gates in a two-spin system quantum logic gates in a spin ensemble at room temperature evolution of an ensemble of four-spin molecules how to get the desired density matrix?

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.