7,695 research outputs found
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 () interactions with ,
``Energy-Scaling'' arguments predict a growth-law of the average domain size for all . Numerical results for ,
, and 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 , 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, , 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
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 model with nonconserved order
parameter, in spatial dimension and spin dimension .
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 model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
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