Simulated magnetization reversal in Fe nanopillar.
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Biomedical subjects
P A Rikvold
Publications and source records attributed to P A Rikvold.
Scaling analysis of polyacrylamide gel surfaces synthesized in the presence of surfactants.
Surfaces of polyacrylamide hydrogels synthesized in the presence of surfactants were imaged by atomic force microscopy (AFM), and the surface morphology was studied by numerical scaling analysis. The gels were formed by polymerizing acrylamide plus a cross-linker in the presence of surfactants, which were then removed by soaking in distilled water. Gels formed in the presence of over 20% surfactant (by weight) formed clear, but became opaque upon removal of the surfactants. Other gels formed and remained clear. The surface morphology of the gels was studied by several one- and two-dimensional numerical scaling methods. The surfaces were found to be self-affine on short length scales, with a roughness (Hurst) exponent in the range from 0.85 to 1, crossing over to a constant root-mean-square surface width at long scales. Both the crossover length between these two regimes and the saturation value of the surface width increased significantly with increasing surfactant concentration, coincident with the increase in opacity. We propose that the changes in the surface morphology are due to a percolation transition in the system of voids formed upon removal of the surfactants from the bulk.
Acrylic Resins↗
Suppressing roughness of virtual times in parallel discrete-event simulations.
In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs) whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang equation from the theory of nonequilibrium surface growth. Although the simulated (virtual) times of the PEs progress at a nonzero rate, their standard deviation (spread) diverges with the number of PEs, hindering efficient data collection. We show that weak random interactions among the PEs can make this spread nondivergent. The PEs then progress at a nonzero, near-uniform rate without requiring global synchronizations.
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Absence of first-order transition and tricritical point in the dynamic phase diagram of a spatially extended bistable system in an oscillating field.
It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is of the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit, the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures.
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Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures.
We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to d-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches [H]/J=2 at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approach zero under these conditions. Near [H]/J=2 and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for [H]/J>2 and one for [H]/J<2.
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Surface scaling analysis of a frustrated spring-network model for surfactant-templated hydrogels.
We propose and study a statistical-mechanical model, inspired by recent atomic force microscopy studies of the surface structures of crosslinked polymer gels into which voids are introduced through templating by surfactant micelles [M. Chakrapani et al., e-print cond-mat/0112255]. The gel is represented by a frustrated, triangular network of nodes connected by springs of random equilibrium lengths. The nodes represent crosslinkers, and the springs correspond to polymer chains. The boundaries are fixed at the bottom, free at the top, and periodic in the lateral direction. Voids are introduced by deleting a proportion of the nodes and their associated springs. The model is numerically relaxed to a representative local energy minimum, resulting in an inhomogeneous, "clumpy" bulk structure. The free top surface is defined at evenly spaced points in the lateral (x) direction by the height of the topmost spring, measured from the bottom layer, h(x). Its scaling properties are studied by calculating the root-mean-square surface width and the generalized increment correlation functions C(q)(x)=<|h(x(0)+x)-h(x(0))|(q)>. The surface is found to have a nontrivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales. As the vacancy concentration approaches the site-percolation limit, both the crossover length and the saturation value of the surface width diverge in a manner that appears to be proportional to the bulk connectivity length. This suggests that a percolation transition in the bulk also drives a similar divergence observed in surfactant templated polyacrylamide gels at high surfactant concentrations.
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Halide adsorption on single-crystal silver substrates: dynamic simulations and ab initio density functional theory.
We investigate the static and dynamic behaviors of a Br adlayer electrochemically deposited onto single-crystal Ag(100) using an off-lattice model of the adlayer. Unlike previous studies using a lattice-gas model, the off-lattice model allows adparticles to be located at any position within a two-dimensional approximation to the substrate. Interactions with the substrate are approximated by a corrugation potential. Using density functional theory (DFT) to calculate surface binding energies, a sinusoidal approximation to the corrugation potential is constructed. A variety of techniques, including Monte Carlo and Langevin simulations, are used to study the behavior of the adlayer. The lateral root-mean-square (rms) deviation of the adparticles from the binding sites is presented along with equilibrium coverage isotherms, and the thermally activated Arrhenius barrier-hopping model used in previous dynamic Monte Carlo simulations is tested.
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Dynamic phase transition in a time-dependent Ginzburg-Landau model in an oscillating field.
The Ginzburg-Landau model below its critical temperature in a temporally oscillating external field is studied both theoretically and numerically. As the frequency or the amplitude of the external field is changed, a nonequilibrium phase transition is observed. This transition separates spatially uniform, symmetry-restoring oscillations from symmetry-breaking oscillations. Near the transition a perturbation theory is developed, and a switching phenomenon is found in the symmetry-broken phase. Our results confirm the equivalence of the present transition to that found in Monte Carlo simulations of kinetic Ising systems in oscillating fields, demonstrating that the nonequilibrium phase transition in both cases belongs to the universality class of the equilibrium Ising model in zero field. This conclusion is in agreement with symmetry arguments [G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985)] and recent numerical results [G. Korniss, C. J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E 63, 016120 (2001)]. Furthermore, a theoretical result for the structure function of the local magnetization with thermal noise, based on the Ornstein-Zernike approximation, agrees well with numerical results in one dimension.
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Dynamic phase transition, universality, and finite-size scaling in the two-dimensional kinetic Ising model in an oscillating field.
We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multidroplet regime, where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine nonequilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations, employing finite-size scaling techniques adopted from equilibrium critical phenomena. The critical exponents, the fixed-point value of the fourth-order cumulant, and the critical order-parameter distribution all are consistent with the universality class of the two-dimensional equilibrium Ising model. We also study the cross-over from the multidroplet regime to the strong-field regime, where the transition disappears.
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Evolution of speckle during spinodal decomposition.
Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time tau as R=[Btau](n) with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector k can be collapsed onto a scaling function Cov(deltat,t), where deltat=k(1/n)B(tau(2)-tau(1)) and t=k(1/n)B(tau(1)+tau(2))/2. Both analytically and numerically, the covariance is found to depend on deltat only through deltat/t in the small-t limit and deltat/t (1-n) in the large-t limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large t. In addition, the two-time, two-point order-parameter correlation function is found to scale as C(r/(B(n)sqaureroot[tau1(2n)+tau2(2n)]),tau1/tau2), even for quite large distances r. The asymptotic power-law exponent for the autocorrelation function is found to be lambda approximately 4.47, violating an upper bound conjectured by Fisher and Huse.
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