159 research outputs found
Shear-Induced Isotropic-to-Lamellar Transition in a Lattice-Gas Model of Ternary Amphiphilic Fluids
Although shear-induced isotropic-to-lamellar transitions in ternary systems
of oil, water and surfactant have been observed experimentally and predicted
theoretically by simple models for some time now, their numerical simulation
has not been achieved so far. In this work we demonstrate that a recently
introduced hydrodynamic lattice-gas model of amphiphilic fluids is well suited
for this purpose: the two-dimensional version of this model does indeed exhibit
a shear-induced isotropic-to-lamellar phase transition.Comment: 17 pages, LaTeX with epsf and REVTeX, PostScript and EPS
illustrations included. To appear in J. Phys. Cond. Ma
A Robust Numerical Method for Integration of Point-Vortex Trajectories in Two Dimensions
The venerable 2D point-vortex model plays an important role as a simplified
version of many disparate physical systems, including superfluids,
Bose-Einstein condensates, certain plasma configurations, and inviscid
turbulence. This system is also a veritable mathematical playground, touching
upon many different disciplines from topology to dynamic systems theory.
Point-vortex dynamics are described by a relatively simple system of nonlinear
ODEs which can easily be integrated numerically using an appropriate adaptive
time stepping method. As the separation between a pair of vortices relative to
all other inter-vortex length scales decreases, however, the computational time
required diverges. Accuracy is usually the most discouraging casualty when
trying to account for such vortex motion, though the varying energy of this
ostensibly Hamiltonian system is a potentially more serious problem. We solve
these problems by a series of coordinate transformations: We first transform to
action-angle coordinates, which, to lowest order, treat the close pair as a
single vortex amongst all others with an internal degree of freedom. We next,
and most importantly, apply Lie transform perturbation theory to remove the
higher-order correction terms in succession. The overall transformation
drastically increases the numerical efficiency and ensures that the total
energy remains constant to high accuracy.Comment: 21 pages, 4 figure
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
Lattice-Gas Simulations of Ternary Amphiphilic Fluid Flow in Porous Media
We develop our existing two-dimensional lattice-gas model to simulate the
flow of single-phase, binary-immiscible and ternary-amphiphilic fluids. This
involves the inclusion of fixed obstacles on the lattice, together with the
inclusion of ``no-slip'' boundary conditions. Here we report on preliminary
applications of this model to the flow of such fluids within model porous
media. We also construct fluid invasion boundary conditions, and the effects of
invading aqueous solutions of surfactant on oil-saturated rock during
imbibition and drainage are described.Comment: 9 pages, 6 figures (1 and 6 are in color), RevTeX with epsf and
graphic
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
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
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
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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