Corrections to Scaling in Phase-Ordering Kinetics

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 C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a characteristic length scale extracted from the energy. The correction-to-scaling exponent \omega has the value \omega=4 for the d=1 Glauber model, the n-vector model with n=\infty, and the approximate theory of Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st

Spin-resolved electron-impact ionization of lithium

Electron-impact ionization of lithium is studied using the convergent close-coupling (CCC) method at 25.4 and 54.4 eV. Particular attention is paid to the spin-dependence of the ionization cross sections. Convergence is found to be more rapid for the spin asymmetries, which are in good agreement with experiment, than for the underlying cross sections. Comparison with the recent measured and DS3C-calculated data of Streun et al (1999) is most intriguing. Excellent agreement is found with the measured and calculated spin asymmetries, yet the discrepancy between the CCC and DS3C cross sections is very large

Corrections to Scaling in the Phase-Ordering Dynamics of a Vector Order Parameter

Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to scaling, the equal-time pair correlation function has the form C(r,t) = f_0(r/L) + L^{-omega} f_1(r/L) + ..., where L is the coarsening length scale. The correction-to-scaling exponent, omega, and the correction-to-scaling function, f_1(x), are calculated for both nonconserved and conserved order parameter systems using the approximate Gaussian closure theory of Mazenko. In general, omega is a non-trivial exponent which depends on both the dimensionality, d, of the system and the number of components, n, of the order parameter. Corrections to scaling are also calculated for the nonconserved 1-d XY model, where an exact solution is possible.Comment: REVTeX, 20 pages, 2 figure

Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\sigma)}$) interactions with $\sigma>0$, ``Energy-Scaling'' arguments predict a growth-law of the average domain size $L \sim t^{1/(1+\sigma)}$ for all $\sigma >0$. Numerical results for $\sigma=0.5$, $1.0$, and $1.5$ demonstrate both scaling and the predicted growth laws. For purely short-range interactions, an approach of Nagai and Kawasaki is asymptotically exact. For this case, the equal-time correlations scale, but the time-derivative correlations break scaling. The short-range solution also applies to systems with long-range interactions when $\sigma \rightarrow \infty$, and in that limit the amplitude of the growth law is exactly calculated.Comment: 19 pages, RevTex 3.0, 8 FIGURES UPON REQUEST, 1549

Coupling of Two Motor Proteins: a New Motor Can Move Faster

We study the effect of a coupling between two motor domains in highly-processive motor protein complexes. A simple stochastic discrete model, in which the two parts of the protein molecule interact through some energy potential, is presented. The exact analytical solutions for the dynamic properties of the combined motor species, such as the velocity and dispersion, are derived in terms of the properties of free individual motor domains and the interaction potential. It is shown that the coupling between the motor domains can create a more efficient motor protein that can move faster than individual particles. The results are applied to analyze the motion of helicase RecBCD molecules

A Remark on Boundary Effects in Static Vacuum Initial Data sets

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that the boundary of (M, g) has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that the boundary has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the area and mean curvature of the boundary. Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit

A counter-example to a recent version of the Penrose conjecture

By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.Comment: 12 pages. Appendix added with technical details. To appear in Classical and Quantum Gravit

Growth Laws for Phase Ordering

We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by comparing the global rate of energy change to the energy dissipation from the local evolution of the order parameter. We derive growth laws for O(n) models, and our results can be applied to other systems with similar defect structures.Comment: 12 pages, LaTeX, second tr

Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2