G. G. Batrouni

A Two-Dimensional Network Simulator for Two-Phase Flow in Porous Media

We investigate a two-dimensional network simulator that model the dynamics of drainage dominated flow where film flow can be neglected. We present a new method for simulating the temporal evolution of the pressure due to capillary and viscous forces in the displacement process. To model the dynamics, we let the local capillary pressure change as if the menisci move in and out of hour-glass shaped tubes. Furthermore, a method has been developed to allow simultaneous flow of two liquids into one tube. The model is suitable to simulate different time dependencies in two-phase drainage displacements. In this paper, we simulate the temporal evolution of the fluid pressures and analyze the time dependence of the front between the two liquids. The front width was found to be consistent with a scaling relation w ∝ tβ h(t/ts). The dynamical exponent, β, describing the front width evolution as function of time, was estimated to β = 1.0. The results are compared to experimental data of Frette and co-workers.

Mott Domains of Bosons Confined on Optical Lattices

In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.

Local quantum criticality in confined fermions on optical lattices.

Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a nontrivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, which allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical lattices.

Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices

We study static properties of ultra-cold bosonic atoms in two-dimensional optical lattices by quantum Monte Carlo simulations of the bosonic Hubbard model in parabolic confinement potentials. Our focus is on local probes identifying Mott-insulating and superfluid regions, which can coexist in the inhomogenous environment of the trap. By proposing an effective ladder model for the boundary region between the two phases we can show clear evidence for the absence of true quantum critical behavior and explain the absence of critical slowing down at the quantum phase transition in a harmonic trap.

Quantum phase transitions in the two-dimensional hardcore boson model

We use two quantum Monte Carlo algorithms to map out the phase diagram of the two-dimensional hardcore boson Hubbard model with near (V 1 ) and next near (V 2 ) neighbor repulsion. At half filling we find three phases: superfluid (SF), checkerboard solid, and striped solid depending on the relative values of V 1 ,V 2 , and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases coexist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: coexistence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the V 2 interaction.

Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponent is related to the correlation length exponent nu of a stress-weighted percolation problem through zeta=nu/(1+nu). A numerical study of the stress-weighted percolation problem yields nu=1.54 giving zeta=0.61 in close agreement with our numerical results and with experimental observations.

FRACTURE IN THREE-DIMENSIONAL FUSE NETWORKS

We report on large scale numerical simulations of fracture surfaces using random fuse networks for two very different disorders. There are some properties and exponents that are different for the two distributions, but others, notably the roughness exponents, seem universal. For the universal roughness exponent we found a value of zeta = 0.62 +/- 0.05. In contrast to what is observed in two dimensions, this value is lower than that reported in experimental studies of brittle fractures, and rules out the minimal energy surface exponent, 0.41 +/- 0.01.

Supersolid phases in the one-dimensional extended soft-core bosonic Hubbard model.

We present results of quantum Monte Carlo simulations for the soft-core extended bosonic Hubbard model in one dimension exhibiting the presence of supersolid phases similar to those recently found in two dimensions. We find that in one and two dimensions, the insulator-supersolid transition has dynamic critical exponent z = 2 whereas the first order insulator-superfluid transition in two dimensions is replaced by a continuous transition with z = 1 in one dimension. We present evidence that this transition is in the Kosterlitz-Thouless universality class and discuss the mechanism behind this difference. The simultaneous presence of two types of quasi-long-range order results in two solitonlike dips in the excitation spectrum.

Current distribution in the three-dimensional random resistor network at the percolation threshold

We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from

Brownian walker in a confined geometry leading to a space-dependent diffusion coefficient

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