Influence of Disorder Strength on Phase Field Models of Interfacial Growth

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.Comment: Accepted for publication in PR

Ionic current inversion in pressure-driven polymer translocation through nanopores

We predict streaming current inversion with multivalent counterions in hydrodynamically driven polymer translocation events from a correlation-corrected charge transport theory including charge fluctuations around mean-field electrostatics. In the presence of multivalent counterions, electrostatic many-body effects result in the reversal of the DNA charge. The attraction of anions to the charge-inverted DNA molecule reverses the sign of the ionic current through the pore. Our theory allows for a comprehensive understanding of the complex features of the resulting streaming currents. The underlying mechanism is an efficient way to detect DNA charge reversal in pressure-driven translocation experiments with multivalent cations.Comment: This version is accepted for publication in Physical Review Letter

Bit Level Correlations in Some Pseudorandom Number Generators

We present results of extensive bit level tests on some pseudorandom number generators which are commonly used in physics applications. The generators have first been tested with an extended version of the $d$-tuple test. Second, we have developed a novel {\it cluster test} where a physical analogy of the binary numbers with the two dimensional Ising model has been utilized. We demonstrate that the new test is rather powerful in finding periodic correlations on bit level. Results of both test methods are presented for each bit of the output of the generators. Some generators exhibit clear bit level correlations but we find no evidence of discernible correlations for generators, which have recently produced systematic errors in Monte Carlo simulations.Comment: University of Helsinki preprint HU-TFT-93-4

Long wavelength properties of phase field crystal models with second order dynamics

The phase field crystal (PFC) approach extends the notion of phase field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.Comment: 10 pages, 7 figure

Instability and wavelength selection during step flow growth of metal surfaces vicinal to fcc(001)

We study the onset and development of ledge instabilities during growth of vicinal metal surfaces using kinetic Monte Carlo simulations. We observe the formation of periodic patterns at [110] close packed step edges on surfaces vicinal to fcc(001) under realistic molecular beam epitaxy conditions. The corresponding wavelength and its temperature dependence are studied by monitoring the autocorrelation function for step edge position. Simulations suggest that the ledge instability on fcc(1,1,m) vicinal surfaces is controlled by the strong kink Ehrlich-Schwoebel barrier, with the wavelength determined by dimer nucleation at the step edge. Our results are in agreement with recent continuum theoretical predictions, and experiments on Cu(1,1,17) vicinal surfaces.Comment: 4 pages, 4 figures, RevTe

Dipolar depletion effect on the differential capacitance of carbon based materials

The remarkably low experimental values of the capacitance data of carbon based materials in contact with water solvent needs to be explained from a microscopic theory in order to optimize the efficiency of these materials. We show that this experimental result can be explained by the dielectric screening deficiency of the electrostatic potential, which in turn results from the interfacial solvent depletion effect driven by image dipole interactions. We show this by deriving from the microscopic system Hamiltonian a non-mean-field dipolar Poisson-Boltzmann equation. This can account for the interaction of solvent molecules with their electrostatic image resulting from the dielectric discontinuity between the solvent medium and the substrate. The predictions of the extended dipolar Poisson-Boltzmann equation for the differential capacitance are compared with experimental data and good agreement is found without any fitting parameters

Dynamics of Chainlike Molecules on Surfaces

We consider the diffusion and spreading of chainlike molecules on solid surfaces. We first show that the steep spherical cap shape density profiles, observed in some submonolayer experiments on spreading polymer films, imply that the collective diffusion coefficient $D_C(\theta)$ must be an increasing function of the surface coverage $\theta$ for small and intermediate coverages. Through simulations of a discrete model of interacting chainlike molecules, we demonstrate that this is caused by an entropy-induced repulsive interaction. Excellent agreement is found between experimental and numerically obtained density profiles in this case, demonstrating that steep submonolayer film edges naturally arise due to the diffusive properties of chainlike molecules. When the entropic repulsion dominates over interchain attractions, $D_C(\theta)$ first increases as a function of $\theta$ but then eventually approaches zero for $\theta \to 1$. The maximum value of $D_C(\theta)$ decreases for increasing attractive interactions, leading to density profiles that are in between spherical cap and Gaussian shapes. We also develop an analytic mean field approach to explain the diffusive behavior of chainlike molecules. The thermodynamic factor in $D_C(\theta)$ is evaluated using effective free energy arguments, and the chain mobility is calculated numerically using the recently developed dynamic mean field theory. Good agreement is obtained between theory and simulations.Comment: 16 pages, 13 Postscript figure