33 research outputs found
Probability distribution of the sizes of largest erased-loops in loop-erased random walks
We have studied the probability distribution of the perimeter and the area of
the k-th largest erased-loop in loop-erased random walks in two-dimensions for
k = 1 to 3. For a random walk of N steps, for large N, the average value of the
k-th largest perimeter and area scales as N^{5/8} and N respectively. The
behavior of the scaled distribution functions is determined for very large and
very small arguments. We have used exact enumeration for N <= 20 to determine
the probability that no loop of size greater than l (ell) is erased. We show
that correlations between loops have to be taken into account to describe the
average size of the k-th largest erased-loops. We propose a one-dimensional
Levy walk model which takes care of these correlations. The simulations of this
simpler model compare very well with the simulations of the original problem.Comment: 11 pages, 1 table, 10 included figures, revte
Delocalization in harmonic chains with long-range correlated random masses
We study the nature of collective excitations in harmonic chains with masses
exhibiting long-range correlated disorder with power spectrum proportional to
, where is the wave-vector of the modulations on the random
masses landscape. Using a transfer matrix method and exact diagonalization, we
compute the localization length and participation ratio of eigenmodes within
the band of allowed energies. We find extended vibrational modes in the
low-energy region for . In order to study the time evolution of an
initially localized energy input, we calculate the second moment of
the energy spatial distribution. We show that , besides being dependent
of the specific initial excitation and exhibiting an anomalous diffusion for
weakly correlated disorder, assumes a ballistic spread in the regime
due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure
Renormalization Scheme Dependence and the Problem of Theoretical Uncertainties in Next-Next-to-Leading Order QCD Predictions
Renormalization scheme uncertainties in the next-next-to-leading order QCD
predictions are discussed. To obtain an estimate of these uncertainties it is
proposed to compare predictions in all schemes that do not have unnaturally
large expansion coefficients. A concrete prescription for eliminating the
unnatural schemes is given, based on the requirement that large cancellations
in the expression for the characteristic renormalization scheme invariant
should be avoided. As an example the QCD corrections to the Bjorken sum rule
are considered. The importance of the next-next-to-leading order corrections
for a proper evaluation of perturbative QCD predictions is emphasized.Comment: 15 pages, 3 figures,Late
Scale-free network on a vertical plane
A scale-free network is grown in the Euclidean space with a global
directional bias. On a vertical plane, nodes are introduced at unit rate at
randomly selected points and a node is allowed to be connected only to the
subset of nodes which are below it using the attachment probability: . Our numerical results indicate that the directed
scale-free network for belongs to a different universality class
compared to the isotropic scale-free network. For the
degree distribution is stretched exponential in general which takes a pure
exponential form in the limit of . The link length
distribution is calculated analytically for all values of .Comment: 4 pages, 4 figure
Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles
We examine the effect of spatial bias on a nonequilibrium system in which
masses on a lattice evolve through the elementary moves of diffusion,
coagulation and fragmentation. When there is no preferred directionality in the
motion of the masses, the model is known to exhibit a nonequilibrium phase
transition between two different types of steady states, in all dimensions. We
show analytically that introducing a preferred direction in the motion of the
masses inhibits the occurrence of the phase transition in one dimension, in the
thermodynamic limit. A finite size system, however, continues to show a
signature of the original transition, and we characterize the finite size
scaling implications of this. Our analysis is supported by numerical
simulations. In two dimensions, bias is shown to be irrelevant.Comment: 7 pages, 7 figures, revte
Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
We consider the problem of `discrete-time persistence', which deals with the
zero-crossings of a continuous stochastic process, X(T), measured at discrete
times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no
crossing) probability decays as exp(-\theta_D T) = [\rho(a)]^n for large n,
where a = \exp[-(\Delta T)/2], and the discrete persistence exponent, \theta_D,
is given by \theta_D = \ln(\rho)/2\ln(a). Using the `Independent Interval
Approximation', we show how \theta_D varies with (\Delta T) for small (\Delta
T) and conclude that experimental measurements of persistence for smooth
processes, such as diffusion, are less sensitive to the effects of discrete
sampling than measurements of a randomly accelerated particle or random walker.
We extend the matrix method developed by us previously [Phys. Rev. E 64,
015151(R) (2001)] to determine \rho(a) for a two-dimensional random walk and
the one-dimensional random acceleration problem. We also consider `alternating
persistence', which corresponds to a < 0, and calculate \rho(a) for this case.Comment: 14 pages plus 8 figure
Persistence in a Stationary Time-series
We study the persistence in a class of continuous stochastic processes that
are stationary only under integer shifts of time. We show that under certain
conditions, the persistence of such a continuous process reduces to the
persistence of a corresponding discrete sequence obtained from the measurement
of the process only at integer times. We then construct a specific sequence for
which the persistence can be computed even though the sequence is
non-Markovian. We show that this may be considered as a limiting case of
persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte
Semileptonic decay constants of octet baryons in the chiral quark-soliton model
Based on the recent study of the magnetic moments and axial constants within
the framework of the chiral quark-soliton model, we investigate the baryon
semileptonic decay constants and . Employing the
relations between the diagonal transition matrix elements and off-diagonal ones
in the vector and axial-vector channels, we obtain the ratios of baryon
semileptonic decay constants and . The ratio is also
discussed and found that the value predicted by the present model naturally
lies between that of the Skyrme model and that of the nonrelativistic quark
model. The singlet axial constant can be expressed in terms of the
ratio and in the present model and turns out to be small. The
results are compared with available experimental data and found to be in good
agreement with them. In addition, the induced pseudotensor coupling constants
are calculated, the SU(3) symmetry breaking being considered. The
results indicate that the effect of SU(3) symmetry breaking might play an
important role for some decay modes in hyperon semileptonic decay.Comment: 16 pages, RevTeX is used. No figure. Accepted for publication in
Phys. Rev.