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Register a new userComputing the crystal growth rate by the interface pinning method
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An essential parameter for crystal growth is the kinetic coefficient given by the proportionality between super-cooling and average growth velocity. Here we show that this coefficient can be computed in a single equilibrium simulation using the interface pinning method where two-phase configurations are stabilized by adding an spring-like bias field coupling to an order-parameter that discriminates between the two phases. Crystal growth is a Smoluchowski process and the crystal growth rate can therefore be computed from the terminal exponential relaxation of the order parameter. The approach is investigated in detail for the Lennard-Jones model. We find that the kinetic coefficient scales as the inverse square-root of temperature along the high temperature part of the melting line. The practical usability of the method is demonstrated by computing the kinetic coefficient of the elements Na, Mg, Al and Si from first principles. It is briefly discussed how a generalized version of the method is an alternative to forward flux sampling methods for computing rates along trajectories of rare events.
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We study pattern formation, fluctuations and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy consuming proteins embedded in the plasma membrane, responsible for membrane deformation and cell movement. In our model, the active particle overturns local valleys of the interface into hills, simulating growth, while itself sliding and seeking new valleys. In 1D, this overturn-slide-search dynamics of the active particle causes it to move superdiffusively in the transverse direction while pulling the immobile interface upwards. Using Monte Carlo simulations, we find an emerging tent-like mean profile developing with time, despite large fluctuations. The roughness of the interface follows scaling with the growth, dynamic and roughness exponents, derived using simple arguments as $beta=2/3, z=3/2, alpha=1/2$ respectively, implying a breakdown of the usual scaling law $beta = alpha/z$, owing to very local growth of the interface. The transverse displacement of the puller on the interface scales as $sim t^{2/3}$ and the probability distribution of its displacement is bimodal, with an unusual linear cusp at the origin. Both the mean interface pattern and probability distribution display scaling. A puller on a static 2D interface also displays aspects of scaling in the mean profile and probability distribution. We also show that a pusher on a fluctuating interface moves subdiffusively leading to a separation of time scale in pusher motion and interface response.
The effect of geometry in the statistics of textit{nonlinear} universality classes for interface growth has been widely investigated in recent years and it is well known to yield a split of them into subclasses. In this work, we investigate this for the textit{linear} classes of Edwards-Wilkinson (EW) and of Mullins-Herring (MH) in one- and two-dimensions. From comparison of analytical results with extensive numerical simulations of several discrete models belonging to these classes, as well as numerical integrations of the growth equations on substrates of fixed size (flat geometry) or expanding linearly in time (radial geometry), we verify that the height distributions (HDs), the spatial and the temporal covariances are universal, but geometry-dependent. In fact, the HDs are always Gaussian and, when defined in terms of the so-called KPZ ansatz $[h simeq v_{infty} t + (Gamma t)^{beta} chi]$, their probability density functions $P(chi)$ have mean null, so that all their cumulants are null, except by their variances, which assume different values in the flat and radial cases. The shape of the (rescaled) covariance curves is analyzed in detail and compared with some existing analytical results for them. Overall, these results demonstrate that the splitting of such university classes is quite general, being not restricted to the nonlinear ones.
A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions are identified in the deterministic limit. The polygon solutions, of relevance to on-lattice Eden growth from a seed in the zero-noise limit, are unstable in the continuum in favour of the symmetric solutions. The asymptotic surface width scaling for stochastic radial interface growth is investigated through numerical simulations and found to be characterized by the same scaling exponent as that for stochastic growth on a substrate.
We propose a general method (based on the Wang-Landau algorithm) to compute numerically free energies that are obtained from the logarithm of the ratio of suitable partition functions. As an application, we determine with high accuracy the order-order interface tension of the four-state Potts model in three dimensions on cubic lattices of linear extension up to L=56. The infinite volume interface tension is then extracted at each beta from a fit of the finite volume interface tension to a known universal behavior. A comparison of the order-order and order-disorder interface tension at the critical value of beta provides a clear numerical evidence of perfect wetting.
The original perturbative Kramers method (starting from the phase space coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion equation for Newtonian particles with separable and additive Hamiltonians is generalized to yield the energy-controlled diffusion equation and thus the very low damping (VLD) escape rate including spin-transfer torque for classical giant magnetic spins with two degrees of freedom. These have dynamics governed by the magnetic Langevin and Fokker-Planck equations and thus are generally based on non-separable and non-additive Hamiltonians. The derivation of the VLD escape rate directly from the (magnetic) Fokker-Planck equation for the surface distribution of magnetization orientations in the configuration space of the polar and azimuthal angles $(vartheta, varphi)$ is much simpler than those previously used.
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