8,905 research outputs found
Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time
Consider a branching random walk in which the offspring distribution and the
moving law both depend on an independent and identically distributed random
environment indexed by the time.For the normalised counting measure of the
number of particles of generation in a given region, we give the second and
third orders asymptotic expansions of the central limit theorem under rather
weak assumptions on the moments of the underlying branching and moving laws.
The obtained results and the developed approaches shed light on higher order
expansions. In the proofs, the Edgeworth expansion of central limit theorems
for sums of independent random variables, truncating arguments and martingale
approximation play key roles. In particular, we introduce a new martingale,
show its rate of convergence, as well as the rates of convergence of some known
martingales, which are of independent interest.Comment: Accepted by Bernoull
A differential cluster variation method for analysis of spiniodal decomposition in alloys
A differential cluster variation method (DCVM) is proposed for analysis of
spinoidal decomposition in alloys. In this method, lattice symmetry operations
in the presence of an infinitesimal composition gradient are utilized to deduce
the connection equations for the correlation functions and to reduce the number
of independent variables in the cluster variation analysis.
Application of the method is made to calculate the gradient energy
coefficient in the Cahn-Hilliard free energy function and the fastest growing
wavelength for spinodal decomposition in Al-Li alloys. It is shown that the
gradient coefficient of congruently ordered Al-Li alloys is much larger than
that of the disordered system. In such an alloy system, the calculated fastest
growing wavelength is approximately 10 nm, which is an order of magnitude
larger than the experimentally observed domain size. This may provide a
theoretical explanation why spinodal decomposition after a congruent ordering
is dominated by the antiphase boundaries.Comment: 15 pages, 7 figure
A method for getting a finite in the IR region from an all-order beta function
The analytical method of QCD running coupling constant is extended to a model
with an all-order beta function which is inspired by the famous
Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric
gau\-g\-e theories. In the approach presented here, the running coupling is
determined by a transcendental equation with non-elementary integral of the
running scale . In our approach , which reads 0.30642,
does not rely on any dimensional parameters. This is in accordance with results
in the literature on the analytical method of QCD running coupling constant.
The new "analytically im\-p\-roved" running coupling constant is also
compatible with the property of asymptotic freedom.Comment: 5 pages, 3 figure
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