Research Articles, Center for Stochastic Processes in Science and Engineering (CSPISE)
http://hdl.handle.net/10919/24709
2019-07-23T02:50:11ZTransmutation of the vicinal surface exponent due to gravity
http://hdl.handle.net/10919/47902
Avron, J. E.; Zia, R. K. P.
1988-04-01T00:00:00ZNear the edge of a facet, vicinal surfaces curve away from the plane with exponent (3/2. With gravity normal to the facet the exponent may change to 3. Generally, there will be a crossover from 3 to (3/2 as the facet edge is approached. Comparison with experiments is made.Spin-charge separation in the two-dimensional Hubbard and t-J models at low electronic density
http://hdl.handle.net/10919/47891
Chen, Y. C.; Moreo, A.; Ortolani, F.; Dagotto, E.; Lee, T. K.
1994-07-01T00:00:00ZThe spin- and density-correlation functions of the two-dimensional Hubbard model at low electronic density [n] are calculated in the ground state by using the power method, and at finite temperatures by using the quantum Monte Carlo technique. Both approaches produce similar results, which are in close agreement with numerical and high-temperature-expansion results for the two-dimensional t-J model. Using perturbative approximations, we show that the examination of the density-correlation function alone is not enough to support recent claims in the literature that suggested spin and charge separation in the low electronic density regime of the t-J model.t-J model studied by the power Lanczos method
http://hdl.handle.net/10919/47893
Chen, Y. C.; Lee, T. K.
1995-03-01T00:00:00ZThe initial trial wave function used in a simple ground-state projection method, the power method, is systematically improved by using Lanczos algorithm. Much faster convergence to the ground state achieved by using these wave functions significantly reduces the effect of the fermion sign problem. The results for the ground state of the two-dimensional t-J model are presented. The density correlation function for the t-J model at small J shows a surprisingly good agreement with that of a system of noninteracting hard-core bosons.Roughness, spatial, and temporal correlations of an interface in a driven nonequilibrium lattice gas
http://hdl.handle.net/10919/47884
Leung, K. T.; Mon, K. K.; Valles, J. L.; Zia, R. K. P.
1989-05-01T00:00:00ZThe interface of a stochastic Ising lattice gas driven into a nonequilibrium steady state by a constant, uniform electric field E parallel to the interface is studied by extensive Monte Carlo simulation in two dimensions. Dependence on the system size and the field strength of the interface profile, roughness, time, and spatial correlation functions and structure factors are found numerically, by means of a coarse-graining method. The interface at zero field is shown to be rough by the divergence of both the interface width and correlation time. As soon as E is turned on, the interface becomes smooth. We argue that the general results may be extended to other similar nonequilibrium systems, and in higher dimensions.New phase in the one-dimensional t-J model
http://hdl.handle.net/10919/47867
Chen, Y. C.; Lee, T. K.
1993-05-01T00:00:00ZA new phase of a gas of pairs of electrons bounded in a singlet state is found in the one-dimensional t -J model for J > 2t and the density of electrons less than 0.2. This phase was conjectured in the study of the diagonalization of small lattices [Phys. Rev. Lett. 66, 2388 (1991)]. The existence of this new phase for much larger lattice sizes is demonstrated by a combination of two numerical methods, the variational Monte Carlo and the power method. A trial wave function for this phase is proposed and shown to be in good agreement with the ground state obtained by the power method.Effects of gravity on equilibrium crystal shapes: Droplets hung on a wall
http://hdl.handle.net/10919/47835
Zia, R. K. P.; Gittis, A.
1987-04-01T00:00:00ZGeneral properties of equilibrium crystal shapes pinned on a vertical wall and subject to gravity are sought. For two-dimensional crystals, or three-dimensional ones with axial symmetry held in suitable geometries, we are able to express the results in terms of the well-known gravity-free Wulff-Winterbottom shapes. All results are valid for an arbitrary, given, orientation-dependent surface-tension function.Bistability in an Ising model with non-Hamiltonian dynamics
http://hdl.handle.net/10919/47812
Heringa, J. R.; Shinkai, H.; Blote, H. W. J.; Hoogland, A.; Zia, R. K. P.
1992-03-01T00:00:00ZWe investigate the phenomenon of magnetization bistability in a two-dimensional Ising model with a non-Hamiltonian Glauber dynamics by means of Monte Carlo simulations. This effect has previously been observed in the Toom model, which supports two stable phases with different magnetizations, even in the presence of a nonzero field. We find that such bistability is also present in an Ising model in which the transition probabilities are expressed in terms of Boltzmann factors depending only on the nearest-neighbor spins and the associated bond strengths. The strength on each bond assumes different values with respect to the spins at either of its ends, introducing an asymmetry like that of the Toom model.equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles
http://hdl.handle.net/10919/47691
Miao, L.; Fourcade, B.; Rao, M. D.; Wortis, M.; Zia, R. K. P.
1991-06-01T00:00:00ZAccording to a model introduced by Helfrich [Z. Naturforsch. 28c, 693 (1973)], the shape of a closed lipid vesicle is determined by minimization of the total bending energy at fixed surface area and enclosed volume. We show that, in the appropriate regime, this model predicts both budding (the eruption of a satellite connected to the parent volume via a neck) and vesiculation (the special case when the neck radius goes to zero). Vesiculation occurs when the minimum is located at a boundary in the space of configurations. Successive vesiculations produce multiplets, in which the minimum-energy configuration consists of several bodies coexisting through infinitesimal necks. We study the sequence of shapes and shape transitions followed by a spherical vesicle of radius R(v), large on the scale R0 set by the spontaneous curvature, as its area A increases at constant volume V = 4-pi-R(v)3/3. Such a vesicle periodically sheds excess area into a set of smaller spheres with radii comparable to R0. We map out this (shape) phase diagram at large volume. In this region the phase diagram is dominated by multiples and reflects the details of the shedding process. The overall effect of successive vesiculations is to reduce the energy from a quantity of order R(v)2 down to zero or near zero when the area reaches 3V/R0; however, the decrease is not uniform and the energy E(A,V) is not convex.finger formation in a driven diffusive system
http://hdl.handle.net/10919/47690
Boal, D. H.; Schmittmann, B.; Zia, R. K. P.
1991-05-01T00:00:00ZA driven diffusive lattice gas is studied in a rectangular geometry: particles are fed in at one side and extracted at the other, after being swept through the system by a uniform driving field. Being periodic in the transverse direction, the lattice lies on the surface of a cylinder. The resulting nonequilibrium steady state depends strongly on this choice of boundary conditions. Both Monte Carlo and analytic techniques are employed to investigate the structure of typical configurations, the density profile, the steady-state current, and the nearest-neighbor correlations. As the temperature is lowered in a finite system, the simulations indicate a crossover from a disordered to an ordered state that is characterized by a backgammonlike pattern of alternating high- and low-density regions ("fingers"). For fixed strengths of the field and interparticle attraction, the average number of fingers is controlled by the ratio of the transverse to the longitudinal system size. Whether the crossover corresponds to an actual phase transition, where typical thermodynamic observables become singular, remains to be determined.Estimate Of The Incoherent-Scattering Contribution To Lidar Backscatter From Clouds
http://hdl.handle.net/10919/46895
de Wolf, D. A.; Russchenberg, H. W. J.; Lighthart, L. P.
1999-09-01T00:00:00ZLidar backscatter from clouds in the Delft University of Technology experiment is complicated by the fact that the transmitter has a narrow beam width, whereas the receiver has a much wider one. The issue here is whether reception of light scattered incoherently by cloud particles can contribute appreciably to the received power. The incoherent contribution can come from within as well as from outside the transmitter beam but in any case is due to at least two scattering processes in the cloud that are not included in the coherent forward scatter that leads to the usual exponentially attenuated contribution from single-particle backscatter. It is conceivable that a sizable fraction of the total received power within the receiver beam width is due to such incoherent-scattering processes. The ratio of this contribution to the direct (but attenuated) reflection from a single particle is estimated here by means of a distorted-Born approximation to the wave equation (with an incident cw monochromatic wave) and by comparison of the magnitude of the doubly scattered to that of the singly scattered flux. The same expressions are also obtained from a radiative-transfer formalism. The ratio underestimates incoherent multiple scattering when it is not small. Corrections that are due to changes in polarization are noted. (C) 1999 Optical Society of America.