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We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described,(More)
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.(More)
The very small scales of isotropic, Navier-Stokes turbulence at Reynolds number R λ ≈ 15 are studied by high-resolution direct numerical simulation (DNS) and by integration of the direct-interaction (DIA) equations. The DNS follows the tail of the energy spectrum over more than thirty decades of magnitude. The energy spectrum in the far-dissipation range 5k(More)
High resolution, direct numerical simulations of the three-dimensional incompressible Navier-Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k=k d) exp[k=k d ] is conrmed. The possible values of the parameters and , a s w ell as their dependence on Reynolds numbers and length scales,(More)
(Abstract • j 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(More)
A learning algorithm based on a default hierarchy of high-order neural networks has been developed that is able to generalize as well as handle exceptions. It learns the 'building blocks' or clusters of symbols in a stream that appear repeatedly and that convey certain messages. The default hierarchy prevents a combinatoric generation of rules. A simulator(More)
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(More)
The perturbation theory is developed based on small parameters which naturally appear in solid state quantum computation. We report the simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain is considered in which selective excitations of spins are provided by having a uniform gradient of the(More)