181 research outputs found
Lattice Boltzmann scheme for relativistic fluids
A Lattice Boltzmann formulation for relativistic fluids is presented and
numerically verified through quantitative comparison with recent hydrodynamic
simulations of relativistic shock-wave propagation in viscous quark-gluon
plasmas. This formulation opens up the possibility of exporting the main
advantages of Lattice Boltzmann methods to the relativistic context, which
seems particularly useful for the simulation of relativistic fluids in
complicated geometries.Comment: Submitted to PR
Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic
fluids recently proposed in Ref. [1], is presented. The method is numerically
validated and applied to the case of two quite different relativistic fluid
dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the
impact of a supernova blast-wave on massive interstellar clouds. Close to
second order convergence with the grid resolution, as well as linear dependence
of computational time on the number of grid points and time-steps, are
reported
Interface Roughening in a Hydrodynamic Lattice-Gas Model with Surfactant
Using a hydrodynamic lattice-gas model, we study interface growth in a binary
fluid with various concentrations of surfactant. We find that the interface is
smoothed by small concentrations of surfactant, while microemulsion droplets
form for large surfactant concentrations. To assist in determining the
stability limits of the interface, we calculate the change in the roughness and
growth exponents and as a function of surfactant concentration
along the interface.Comment: 4 pages with 4 embedded ps figures. Requires psfig.tex. Will appear
in PRL 14 Oct 199
Higher Order Methods for Simulations on Quantum Computers
To efficiently implement many-qubit gates for use in quantum simulations on
quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2
+ ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2
\Delta t], ... which is accurate to 3rd or 4th order in \Delta t. The methods
we derive are an extended form of symplectic method and can also be used for
the integration of classical Hamiltonians on classical computers. We derive
both integral and irrational methods, and find the most efficient methods in
both cases.Comment: 21 pages, Latex, one figur
Superstatistics
We consider nonequilibrium systems with complex dynamics in stationary states
with large fluctuations of intensive quantities (e.g. the temperature, chemical
potential, or energy dissipation) on long time scales. Depending on the
statistical properties of the fluctuations, we obtain different effective
statistical mechanics descriptions. Tsallis statistics is one, but other
classes of generalized statistics are obtained as well. We show that for small
variance of the fluctuations all these different statistics behave in a
universal way.Comment: 12 pages /a few more references and comments added in revised versio
Two-dimensional hydrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic fluid flow through porous media
The behaviour of two dimensional binary and ternary amphiphilic fluids under
flow conditions is investigated using a hydrodynamic lattice gas model. After
the validation of the model in simple cases (Poiseuille flow, Darcy's law for
single component fluids), attention is focussed on the properties of binary
immiscible fluids in porous media. An extension of Darcy's law which explicitly
admits a viscous coupling between the fluids is verified, and evidence of
capillary effects are described. The influence of a third component, namely
surfactant, is studied in the same context. Invasion simulations have also been
performed. The effect of the applied force on the invasion process is reported.
As the forcing level increases, the invasion process becomes faster and the
residual oil saturation decreases. The introduction of surfactant in the
invading phase during imbibition produces new phenomena, including
emulsification and micellisation. At very low fluid forcing levels, this leads
to the production of a low-resistance gel, which then slows down the progress
of the invading fluid. At long times (beyond the water percolation threshold),
the concentration of remaining oil within the porous medium is lowered by the
action of surfactant, thus enhancing oil recovery. On the other hand, the
introduction of surfactant in the invading phase during drainage simulations
slows down the invasion process -- the invading fluid takes a more tortuous
path to invade the porous medium -- and reduces the oil recovery (the residual
oil saturation increases).Comment: 48 pages, 26 figures. Phys. Rev. E (in press
Toward Generalized Entropy Composition with Different q Indices and H-Theorem
An attempt is made to construct composable composite entropy with different
indices of subsystems and address the H-theorem problem of the composite
system. Though the H-theorem does not hold in general situations, it is shown
that some composite entropies do not decrease in time in near-equilibrium
states and factorized states with negligibly weak interaction between the
subsystems.Comment: 25 pages, corrected some typos, to be published in J. Phys. Soc. Ja
Correlations and Renormalization in Lattice Gases
A complete formulation is given of an exact kinetic theory for lattice gases.
This kinetic theory makes possible the calculation of corrections to the usual
Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of
correlations. It is shown that renormalized transport coefficients can be
calculated perturbatively by summing terms in an infinite series. A
diagrammatic notation for the terms in this series is given, in analogy with
the diagrammatic expansions of continuum kinetic theory and quantum field
theory. A closed-form expression for the coefficients associated with the
vertices of these diagrams is given. This method is applied to several standard
lattice gases, and the results are shown to correctly predict experimentally
observed deviations from the Boltzmann analysis.Comment: 94 pages, pure LaTeX including all figure
A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
We describe a new polynomial time quantum algorithm that uses the quantum
fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian
operator, and that can be applied in cases (commonly found in ab initio physics
and chemistry problems) for which all known classical algorithms require
exponential time. Applications of the algorithm to specific problems are
considered, and we find that classically intractable and interesting problems
from atomic physics may be solved with between 50 and 100 quantum bits.Comment: 10 page
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