相关论文: Growth Laws for Phase Ordering
We show how the continuity equations expressing conservation of topological point or string defect charge can be used to determine the order-parameter correlation function for the phase-ordering kinetics of the O(n) model in the special…
The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lema\^\i tre & H. Chat\'e, {\em Phys. Rev. Lett.} {\bf 82}, 1140 (1999)) are revisited with the help of detailed investigations of interface…
The dynamics of phase separation for a binary fluid subjected to a uniform shear are solved exactly for a model in which the order parameter is generalized to an n-component vector and the large-n limit taken. Characteristic length scales…
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting…
We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the…
A consistent perturbation theory expansion is presented for phase ordering kinetics in the case of a nonconserved scalar order parameter. At lowest order in this formal expansion one obtains the theory due to Ohta, Jasnow and Kawasaki…
Globally conserved phase ordering dynamics is investigated in systems with short range correlations in the initial condition. A Ginzburg-Landau equation with a global conservation law is employed as the phase field model. The conditions are…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $\phi^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles (SP) on a fluctuating surface and…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
The leading correction to scaling associated with departures of the initial condition from the scaling morphology is determined for some soluble models of phase-ordering kinetics. The result for the pair correlation function has the form…
The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) approach. Results show the simultaneous existence of domains of two characteristic scales.…
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density,…
The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in…
We study the long-range order in two dimensions where an order parameter is advected by laminar flows such as rotational, shear, and elongational flows. Under these flows, we analyze an ordered state of the $O(N)$ scalar model in the…
Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…