Bulletin of the American Physical Society
78th Annual Meeting of the Southeastern Section of the APS
Volume 56, Number 9
Wednesday–Saturday, October 19–22, 2011; Roanoke, Virginia
Session PB: Statistical and Nonlinear Physics II |
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Chair: Uwe Tauber, Virginia Polytechnic Institute and State University Room: Crystal Ballroom B |
Saturday, October 22, 2011 10:45AM - 10:57AM |
PB.00001: Effect of Diffusion on Size Distribution Dynamics of Desorption in KMC Simulations of a Lattice-Gas Model of Pulsed Electrodeposition Tjipto Juwono We have studied the effect of diffusion during the desorption phase in pulsed electrodeposition in a square lattice-gas model using Kinetic Monte Carlo simulations. The effect of diffusion on correlation length and size distribution during the desorption were studied. During the process, the correlation length increased up to a maximum and then decreased. We found that diffusion increase correlation length by small percentage in the regime where correlation length is decreasing, and increase it more significantly when the correlation length is increasing. By studying size distributions we found that diffusion tends to shrink large clusters and grow or create medium clusters. When the clusters growth or creation by diffusion is small, the increase of correlation length by diffusion is small and large otherwise. [Preview Abstract] |
Saturday, October 22, 2011 10:57AM - 11:09AM |
PB.00002: Effect of the size distributions of magnetic nanoparticles on metastability across dynamic phase boundary Yoh Yamamoto, Kyungwha Park Recent experiments showed that magnetic nanoparticles have distributions of sizes and shapes, and that the distributions greatly influence static and dynamic properties of the nanoparticles. Therefore, it is critical to understand their properties as functions of the distributions. Previously, we studied an effect of particle size distributions on metastability in magnetization relaxation, using a spin $S=1$ Blume-Capel model, in the single-droplet regime where a critical droplet comprises a single flipped spin. The particle size distributions were simulated using distributions of magnetic anisotropy parameter $D$ with spins fixed. We found that the lifetime of the metastable state is governed by the smallest particle or the particle with the smallest value of $D$ in a given system. In this work, we present the effect of size distributions on metastability in the region where the values of $D$ are distributed across the phase boundary between different critical droplets for constant $D$. Interesting phenomena may occur in this region because particles with low values of $D$ expect different critical droplets from particles with high values of $D$ in a given distribution of $D$. We examine magnetization relaxation in this region using kinetic Monte Carlo simulations for the spin $S=1$ Blume-Capel model. [Preview Abstract] |
Saturday, October 22, 2011 11:09AM - 11:21AM |
PB.00003: Non-equilibrium phases of the two-dimensional Ising model in contact with two heat baths Linjun Li, Michel Pleimling The equilibrium phase diagram of the two-dimensional Ising model in contact with a single heat bath is well understood. We here study the properties of the two-dimensional Ising model with conserved dynamics where the two halves of the system are in contact with different heat baths. Using Monte Carlo simulations, we identify three different phases for this non-equilibrium system, as a function of the aspect ratio of the lattice and of the temperatures. The first phase is characterized by the complete disorder of the particles, while the second phase is characterized by the complete order of the particles. The third phase is the most interesting one as it displays stripes with widths that depend on the system parameters. The full phase diagram of our non-equilibrium system is determined through the study of the structure factor. [Preview Abstract] |
Saturday, October 22, 2011 11:21AM - 11:33AM |
PB.00004: Langevin Molecular Dynamics of Driven Magnetic Flux Lines Ulrich Dobramysl, Michel Pleimling, Uwe C. T\"{a}uber The characterization of type-II superconducting materials and their technological applications in external magnetic fields require a thorough understanding of the stationary and dynamical properties of vortex matter. The competition of repulsive interactions and attractive material defects renders the physics of externally driven magnetic flux lines very rich. We study the non-equilibrium steady states as well as transient relaxation properties of driven vortex lines in the presence of randomly distributed point pinning centers. We model the vortices as interacting elastic lines and employ a Langevin Molecular Dynamics (LMD) algorithm to extract steady-state and non-stationary time-dependent behavior. We compare the efficiency and accuracy of LMD to previously obtained Metropolis Monte Carlo steady-state force-velocity and gyration radius data. In future work we intend investigate the transient two-time height-height correlation and response functions. [Preview Abstract] |
Saturday, October 22, 2011 11:33AM - 11:45AM |
PB.00005: An Approximation to the Periodic Solution of a Differential Equation of Abel Ronald E. Mickens The Abel equation, in canonical form, is y$^{'}$ = sint- y$^{3 }$(*) and corresponds to the singular ($\varepsilon $ --$>$ 0) limit of the nonlinear, forced oscillator $\varepsilon $y$^{''}$ + y$^{'}$ + y$^{3}$ = sint, $\varepsilon ->$ 0. (**) Equation (*) has the property that it has a unique periodic solution defined on (-$\infty $,$\infty )$. Further, as t increases, all solutions are attracted into the strip $\vert $y$\vert \quad <$ 1 and any two different solutions y$_{1}$(t) and y$_{2}$(t) satisfy the condition \begin{center} Lim [y$_{1}$(t) - y$_{2}$(t)] = 0, (***) \end{center} t --$> \quad \infty $ and for t negatively decreasing, each solution, except for the periodic solution, becomes unbounded.\footnote{U. Elias, American Mathematical Monthly, vol.115, (Feb. 2008), pps. 147-149.} Our purpose is to calculate an approximation to the unique periodic solution of Eq. (*) using the method of harmonic balance. We also determine an estimation for the blow-up time of the non-periodic solutions. [Preview Abstract] |
Saturday, October 22, 2011 11:45AM - 11:57AM |
PB.00006: An Averaged-Separation of Variable Solution to the Burger Equation 'Kale Oyedeji, Ronald E. Mickens The Burger Partial Differential Equation (PDE) provides a nonlinear model that incorporates several of the important properties of fluid behavior. However, no general solution to it is known for given arbitrary initial and/or boundary conditions. We propose a ``new'' method for determining approximations for the solutions. Our method combines the separation of variables technique, combined with an averaging over the space variable. A test of this procedure is made for the following problem, where u = u(x,t): \begin{center} 0 $\le $ x $\le $ 1, t $>$ 0, \end{center} \begin{center} u(0,t) = 0, u(1,t) = 0, \end{center} \begin{center} u(x,0) = x(1-x), \end{center} \begin{center} u$_{t}$ + uu$_{x}$ = Du$_{xx}$, \end{center} where D is a non-negative parameter. The validity of the calculated solution is made by comparing it to an exact analytic solution, as well as an accurate numerical solution for the special case where D = 0. [Preview Abstract] |
Saturday, October 22, 2011 11:57AM - 12:09PM |
PB.00007: A two-Lane model with anomalous slow dynamics Dan Linford, Trevor Richards, Michel Pleimling It is known that in one-dimensional equilibrium systems with short range interactions a phase transition cannot exist at finite, non-zero temperatures. However, far from equilibrium, one-dimensional systems with local interactions can exhibit a phase transition. The ABC model, a three species model defined on a chain characterized by non-symmetric exchanges between particles, is known to possess a non-equilibrium phase transition. This model exhibits anomalous slow dynamics that we investigate in some detail using two-time quantities. In addition we discuss an extension of this model to a case where this single lane is coupled to a one-dimensional particle bath. This coupling yields an additional phase transition that we discuss in some detail. [Preview Abstract] |
Saturday, October 22, 2011 12:09PM - 12:21PM |
PB.00008: Degree-based graph construction and sampling Hyunju Kim Network representation and modeling has been one of the most comprehensive ways to study many complex systems. However, the network describing the system frequently has to be built from incomplete connectivity data, a typical case being degree-based graph construction, when only the sequence of node degrees is available. In this presentation I will introduce problems and results related to the construction of all the possible graphs and sampling from the class of graphs with fixed degree-sequence. Firstly, for graph construction, I will present necessary and sufficient conditions for a sequence of integers to be realized as a simple graph's degree sequence under the condition that a specific set of connections from an arbitrary node are avoided. Secondly, by using this result, I will show how to provide an efficient, polynomial time algorithm that generates graph samples with a given degree sequence. Unlike other existing algorithms, this method always produces statistically independent samples, without back-tracking or rejections. Also, the algorithm provides the weight associated with each sample, allowing graph observables to be measured uniformly over the graph ensemble. [Preview Abstract] |
Saturday, October 22, 2011 12:21PM - 12:33PM |
PB.00009: A simple model for studying interacting networks Wenjia Liu, Shivakumar Jolad, Beate Schmittmann, R.K.P. Zia The characteristics of single networks, whether physical, biological or socia, are well known. However, many of these networks function not only in isolation, but also coupled to each other. So far, little is known about such ``interacting networks.'' Here, we consider two coupled systems, modeling social networks with a preferred number of friends. We first report on the (statistical) properties of the stationary state of a single network, which consists of a fixed set of nodes and a stochastically varying set of links (generated according to a preferred degree, $\kappa$). Next, we investigate the effects of coupling two such networks (with different $\kappa$s) by various means. Findings using both analytic and simulation techniques will be presented and potential consequences for real networks will be discussed. [Preview Abstract] |
Saturday, October 22, 2011 12:33PM - 12:45PM |
PB.00010: Image Charge Optimization for the Reaction Field by Matching to an Electrostatic Force Tensor Wei Song, Donald Jacobs A new image charge solvation model has recently been developed, which consists of a spherical cavity of explicit solvent embedded in a continuum dielectric medium. Inside the cavity, the dielectric constant is 1 and outside the cavity is set to 80. Although the discontinuity from 1 to 80 at the cavity interface creates large artifacts near the boundary, MD simulation using this model yields accurate results by incorporating a buffer layer containing imaged water. We generalized the model to reflect a continuously changing dielectric profile at the boundary, and optimized image charges for the reaction field based on electrostatic forces to minimize the buffer layer volume and reproduce the electrostatic force field associated with the dielectric properties of the model solvent. However, MD simulation suggests that the new model is unstable. Previously, we also showed that the reaction field has an order of magnitude stronger influence on the electrostatic torque compared to force on solvent water molecules. Therefore, we optimize the image charges in a different way, using a force tensor defined by a grid of dipoles, which places more constraints on the system. [Preview Abstract] |
Saturday, October 22, 2011 12:45PM - 12:57PM |
PB.00011: Unusual criticality in a generalized XY model Yifei Shi We study the generalized XY model in two dimension, which has a term proportional to cos(2$\theta$) in addition to the normal XY Hamiltonian. This corresponds to having half vortices connected by solitons, as well as integer vortices. From both renormalization group analysis and Monte Carlo simulation using the worm algorithm, we find that the phase diagram includes Kosterlitz-Thouless transitions of half and integer vortices, together with an Ising transition. Remarkably, part of the Ising line is a direct transition from the quasi-long-ranged ordered state to the disordered state. [Preview Abstract] |
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