Biomedical subjects

D P Landau

Publications and source records attributed to D P Landau.

10 recordsLinked to original sources

PubMed2004

Hybrid Monte Carlo-molecular dynamics algorithm for the study of islands and step edges on semiconductor surfaces: application to Si/Si (001).

A classical, hybrid Monte Carlo-molecular dynamic (MC-MD) algorithm is introduced for the study of phenomena like two-dimensional (2D) island stability or step-edge evolution on semiconductor surfaces. This method presents the advantages of working off lattice and utilizing bulk-fitted potentials. It is based on the introduction of collective moves, such as dimer jumps, in the MC algorithm. MD-driven local relaxations are considered as trial moves for the MC. The algorithm is applied to the analysis of 2D Si islands on Si(001). Results on early stages of island formation, island stability versus temperature and system size, and step-edge evolution are presented. In all cases good qualitative agreement with experimental results is found.

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PubMed2004

Driven diffusive systems: how steady states depend on dynamics.

In contrast to equilibrium systems, nonequilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber, and heat bath rates, we illustrate this expectation for an Ising lattice gas, driven far from equilibrium by an "electric" field. While heat bath and Glauber rates generate essentially identical data for structure factors and two-point correlations, Metropolis rates give noticeably weaker correlations, as if the "effective" temperature were higher in the latter case. We also measure energy histograms and define a simple ratio which is exactly known and closely related to the Boltzmann factor for the equilibrium case. For the driven system, the ratio probes a thermodynamic derivative which is found to be dependent on dynamics.

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PubMed2003

Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields.

Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic LxLxL(y) Ising lattices with nearest neighbor ferromagnetic exchange and four free LxL(y) surfaces, at which antisymmetric surface fields +/-H(s) act, are studied for a wide range of linear dimensions (4</=L</=320, 30</=L(y)</=1000), in an attempt to clarify finite size effects on the wedge filling transition in this "double-wedge" geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature T(c) this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,L(y)--> infinity and T larger than the filling transition temperature T(f)(H(s)), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For T T(f)(H(s)) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l(0) for T>T(f)(H(s)) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length xi(y) in the y direction along the wedges is also studied, and we find no transition for finite L and L(y)--> infinity. For L--> infinity the prediction l(0) proportional, variant (H(sc)-H(s))(-1/4) is verified, where H(sc)(T) is the inverse function of T(f)(H(s)) and xi(y) proportional, variant (H(sc)-H(s))(-3/4), respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.

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PubMed2003

Dynamical scaling of surface growth in simple lattice models.

We present extensive simulations of the atomistic Edwards-Wilkinson (EW) and Restricted Edwards-Wilkinson (REW) models in 2+1 dimensions. Dynamic finite-size scaling analyses of the interfacial width and structure factor provide the estimates for the dynamic exponent z=1.65+/-0.05 for the EW model and z=2.0+/-0.1 for the REW model. The stochastic contribution to the interface velocity U due to the deposition and diffusion of particles is characterized for both the models using a blocking procedure. For the EW model the time-displaced temporal correlations in U show nonexponential decay, while the temporal correlations decay exponentially for the REW model. Dynamical scaling of the temporal correlation function for the EW model yields a value of z, which is consistent with the estimate obtained from finite-size scaling of the interfacial width and structure factor.

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PubMed2003

Interface localization-delocalization in a double wedge: a new universality class with strong fluctuations and anisotropic scaling.

Using Monte Carlo simulations and finite-size scaling methods we study "wetting" in Ising systems in a LxLxL(y) pore with quadratic cross section. Antisymmetric surface fields H(s) act on the free LxL(y) surfaces of the opposing wedges, and periodic boundary conditions are applied along the y direction. In the limit L--> infinity, L(y)/L(3)=const, the system exhibits a new type of phase transition, which is the analog of the "filling transition" that occurs in a single wedge. It is characterized by critical exponents alpha=3/4, beta=0, and gamma=5/4 for the specific heat, order parameter, and susceptibility, respectively.

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PubMed2003

Universality and double critical end points.

A double critical end point in the two-dimensional spin-3/2 Blume-Capel model is studied via extensive Monte Carlo simulations. The resultant scaling character of the probability distribution of the mixing scaling operators allows us to locate the double critical end point precisely and also to convincingly show that it indeed belongs to the same universality class as the critical points.

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PubMed2002

Cluster hybrid Monte Carlo simulation algorithms.

We show that addition of Metropolis single spin flips to the Wolff cluster-flipping Monte Carlo procedure leads to a dramatic increase in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the Metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious (such as the spin-3/2 Ising model) can substantially reduce the statistical errors of the simulations. A further advantage of these methods is that systematic errors introduced by the use of imperfect random-number generation may be largely healed by hybridizing single spin flips with cluster flipping.

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PubMed2001

Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram.

We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy level is visited to produce a flat histogram. By carefully controlling the modification factor, we allow the density of states to converge to the true value very quickly, even for large systems. From the density of states at the end of the random walk, we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature. Using this method, we not only can avoid repeating simulations at multiple temperatures, but we can also estimate the free energy and entropy, quantities that are not directly accessible by conventional Monte Carlo simulations. This algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability. As with the multicanonical Monte Carlo technique, our method overcomes the tunneling barrier between coexisting phases at first-order phase transitions. In this paper, we apply our algorithm to both first- and second-order phase transitions to demonstrate its efficiency and accuracy. We obtained direct simulational estimates for the density of states for two-dimensional ten-state Potts models on lattices up to 200 x 200 and Ising models on lattices up to 256 x 256. Our simulational results are compared to both exact solutions and existing numerical data obtained using other methods. Applying this approach to a three-dimensional +/-J spin-glass model, we estimate the internal energy and entropy at zero temperature; and, using a two-dimensional random walk in energy and order-parameter space, we obtain the (rough) canonical distribution and energy landscape in order-parameter space. Preliminary data suggest that the glass transition temperature is about 1.2 and that better estimates can be obtained with more extensive application of the method. This simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space.

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PubMed2001

Dynamic finite-size scaling of the normalized height distribution in kinetic surface roughening.

Using well-known simple growth models, we have studied the dynamic finite-size scaling theory for the normalized height distribution of a growing surface. We find a simple functional form that explains size-dependent behavior of the skewness and kurtosis in the transient regime, and obtain the transient- and long-time values of the skewness and kurtosis for the models. Scaled distributions of the models are obtained, and the shape of each distribution is discussed in terms of the interfacial width, skewness, and kurtosis, and compared with those for other models. Exponents eta(+) and eta(-), which characterize the form of the distribution, are determined from an exponential fitting of scaling functions. Our detailed results reveal that eta(+)+eta(-) approximately 4 for a model obeying usual scaling in contrast to eta(+)+eta(-)<4 with eta(-)=1 for a model exhibiting anomalous scaling as well as multiscaling. Since we obtain eta(+)+eta(-) approximately 4 for a model exhibiting anomalous scaling but no multiscaling, we conclude that the deviation from eta(+)+eta(-) approximately 4 is due to the presence of multiscaling behavior in a model.

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PubMed2001

Efficient, multiple-range random walk algorithm to calculate the density of states.

We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant density of states is modified continuously to produce locally flat histograms. This method permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions. It should also be useful for the study of complex systems with a rough energy landscape.

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