Magnetic field generated resistivity maximum in graphite

In zero magnetic field, B, the electrical resistivity, rho(O,T) of highly oriented pyrolytic (polycrystalline) graphite drops smoothly with decreasing T, becoming constant below 4 K. However, in a fixed applied magnetic field B, the resistivity rho(B,T) goes through a maximum as a function of T, with larger maximum for larger B. The temperature of the maximum increases with B, but saturates to a constant value near 25 K (exact T depends on sample) at high B. In single crystal graphite a maximum in rho(B,T) as a function of T is also present, but has the effects of Landau level quantization superimposed. Several possible explanations for the rho(B,T) maximum are proposed, but a complete explanation awaits detailed calculations involving the energy band structure of graphite, and the particular scattering mechanisms involved

Universality in two-dimensional Kardar-Parisi-Zhang growth

We analyze simulations results of a model proposed for etching of a crystalline solid and results of other discrete models in the 2+1-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of orders n=2,3,4 of the heights distribution are estimated. Results for the etching model, the ballistic deposition (BD) model and the temperature-dependent body-centered restricted solid-on-solid model (BCSOS) suggest the universality of the absolute value of the skewness S = W_3 / (W_2)^(3/2) and of the value of the kurtosis Q = W_4 / (W_2)^2 - 3. The sign of the skewness is the same of the parameter \lambda of the KPZ equation which represents the process in the continuum limit. The best numerical estimates, obtained from the etching model, are |S| = 0.26 +- 0.01 and Q = 0.134 +- 0.015. For this model, the roughness exponent \alpha = 0.383 +- 0.008 is obtained, accounting for a constant correction term (intrinsic width) in the scaling of the squared interface width. This value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value \alpha=2/5. The conclusion is supported by results for the ballistic deposition model. Independent estimates of the dynamical exponent and of the growth exponent are 1.605 <= z <= 1.64 and \beta = 0.229 +- 0.005, respectively, which are consistent with the relations \alpha + z = 2 and z = \alpha / \beta.Comment: 8 pages, 9 figures, to be published in Phys. Rev.

The Parallel Complexity of Growth Models

This paper investigates the parallel complexity of several non-equilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solid-on-solid growth are all seemingly highly sequential processes that yield self-similar or self-affine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these clusters. The running times of the algorithms scale as $O(\log^2 N)$, where $N$ is the system size, and the number of processors required scale as a polynomial in $N$. The algorithms are based on fast parallel procedures for finding minimum weight paths; they illuminate the close connection between growth models and self-avoiding paths in random environments. In addition to their potential practical value, our algorithms serve to classify these growth models as less complex than other growth models, such as diffusion-limited aggregation, for which fast parallel algorithms probably do not exist.Comment: 20 pages, latex, submitted to J. Stat. Phys., UNH-TR94-0

Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient of the nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma = 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-4) ~ p^(-8), in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.Comment: 16 pages, 7 figures; to appear in Phys. Rev.

Effect of Long-Range Interactions in the Conserved Kardar-Parisi-Zhang Equation

The conserved Kardar-Parisi-Zhang equation in the presence of long-range nonlinear interactions is studied by the dynamic renormalization group method. The long-range effect produces new fixed points with continuously varying exponents and gives distinct phase transitions, depending on both the long-range interaction strength and the substrate dimension $d$. The long-range interaction makes the surface width less rough than that of the short-range interaction. In particular, the surface becomes a smooth one with a negative roughness exponent at the physical dimension d=2.Comment: 4 pages(LaTex), 1 figure(Postscript

An Anisotropic Ballistic Deposition Model with Links to the Ulam Problem and the Tracy-Widom Distribution

We compute exactly the asymptotic distribution of scaled height in a (1+1)--dimensional anisotropic ballistic deposition model by mapping it to the Ulam problem of finding the longest nondecreasing subsequence in a random sequence of integers. Using the known results for the Ulam problem, we show that the scaled height in our model has the Tracy-Widom distribution appearing in the theory of random matrices near the edges of the spectrum. Our result supports the hypothesis that various growth models in $(1+1)$ dimensions that belong to the Kardar-Parisi-Zhang universality class perhaps all share the same universal Tracy-Widom distribution for the suitably scaled height variables.Comment: 5 pages Revtex, 3 .eps figures included, new references adde

Scaling Behavior of Cyclical Surface Growth

The scaling behavior of cyclical surface growth (e.g. deposition/desorption), with the number of cycles n, is investigated. The roughness of surfaces grown by two linear primary processes follows a scaling behavior with asymptotic exponents inherited from the dominant process while the effective amplitudes are determined by both. Relevant non-linear effects in the primary processes may remain so or be rendered irrelevant. Numerical simulations for several pairs of generic primary processes confirm these conclusions. Experimental results for the surface roughness during cyclical electrodeposition/dissolution of silver show a power-law dependence on n, consistent with the scaling description.Comment: 2 figures adde

Growth model with restricted surface relaxation

We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson linear model, but only within a distance s. If the local minimum is out from this distance, the particle evaporates through a refuse mechanism similar to the Kim-Kosterlitz nonlinear model. In d=1, the growth exponent beta, measured from the temporal behavior of roughness, indicates that in the coarse-grained limit, the linear term of the Kardar-Parisi-Zhang equation dominates in short times (low-roughness) and, in asymptotic times, the nonlinear term prevails. The crossover between linear and nonlinear behaviors occurs in a characteristic time t_c which only depends on the magnitude of the parameter s, related to the nonlinear term. In d=2, we find indications of a similar crossover, that is, logarithmic temporal behavior of roughness in short times and power law behavior in asymptotic times

Abrupt grain boundary melting in ice

The effect of impurities on the grain boundary melting of ice is investigated through an extension of Derjaguin-Landau-Verwey-Overbeek theory, in which we include retarded potential effects in a calculation of the full frequency dependent van der Waals and Coulombic interactions within a grain boundary. At high dopant concentrations the classical solutal effect dominates the melting behavior. However, depending on the amount of impurity and the surface charge density, as temperature decreases, the attractive tail of the dispersion force interaction begins to compete effectively with the repulsive screened Coulomb interaction. This leads to a film-thickness/temperature curve that changes depending on the relative strengths of these interactions and exhibits a decrease in the film thickness with increasing impurity level. More striking is the fact that at very large film thicknesses, the repulsive Coulomb interaction can be effectively screened leading to an abrupt reduction to zero film thickness.Comment: 8 pages, 1 figur

A simulational and theoretical study of the spherical electrical double layer for a size-asymmetric electrolyte: the case of big coions

Monte Carlo simulations of a spherical macroion, surrounded by a size-asymmetric electrolyte in the primitive model, were performed. We considered 1:1 and 2:2 salts with a size ratio of 2 (i.e., with coions twice the size of counterions), for several surface charge densities of the macrosphere. The radial distribution functions, electrostatic potential at the Helmholtz surfaces, and integrated charge are reported. We compare these simulational data with original results obtained from the Ornstein-Zernike integral equation, supplemented by the hypernetted chain/hypernetted chain (HNC/HNC) and hypernetted chain/mean spherical approximation (HNC/MSA) closures, and with the corresponding calculations using the modified Gouy-Chapman and unequal-radius modified Gouy-Chapman theories. The HNC/HNC and HNC/MSA integral equations formalisms show good concordance with Monte Carlo "experiments", whereas the notable limitations of point-ion approaches are evidenced. Most importantly, the simulations confirm our previous theoretical predictions of the non-dominance of the counterions in the size-asymmetric spherical electrical double layer [J. Chem. Phys. 123, 034703 (2005)], the appearance of anomalous curvatures at the outer Helmholtz plane and the enhancement of charge reversal and screening at high colloidal surface charge densities due to the ionic size asymmetry.Comment: 11 pages, 7 figure