7,883 research outputs found
Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence
We study analytically the statistics of multiple sign changes in a discrete
non-Markovian sequence ,\psi_i=\phi_i+\phi_{i-1} (i=1,2....,n) where \phi_i's
are independent and identically distributed random variables each drawn from a
symmetric and continuous distribution \rho(\phi). We show that the probability
P_m(n) of m sign changes upto n steps is universal, i.e., independent of the
distribution \rho(\phi). The mean and variance of the number of sign changes
are computed exactly for all n>0. We show that the generating function {\tilde
P}(p,n)=\sum_{m=0}^{\infty}P_m(n)p^m\sim \exp[-\theta_d(p)n] for large n where
the `discrete' partial survival exponent \theta_d(p) is given by a nontrivial
formula, \theta_d(p)=\log[{{\sin}^{-1}(\sqrt{1-p^2})}/{\sqrt{1-p^2}}] for 0\le
p\le 1. We also show that in the natural scaling limit when m is large, n is
large but but keeping x=m/n fixed, P_m(n)\sim \exp[-n \Phi(x)] where the large
deviation function \Phi(x) is computed. The implications of these results for
Ising spin glasses are discussed.Comment: 4 pages revtex, 1 eps figur
Effect of Surface Roughness on Hydrodynamic Bearings
A theoretical analysis on the performance of hydrodynamic oil bearings is made considering surface roughness effect. The hydrodynamic as well as asperity contact load is found. The contact pressure was calculated with the assumption that the surface height distribution was Gaussian. The average Reynolds equation of partially lubricated surface was used to calculate hydrodynamic load. An analytical expression for average gap was found and was introduced to modify the average Reynolds equation. The resulting boundary value problem was then solved numerically by finite difference methods using the method of successive over relaxation. The pressure distribution and hydrodynamic load capacity of plane slider and journal bearings were calculated for various design data. The effects of attitude and roughness of surface on the bearing performance were shown. The results are compared with similar available solution of rough surface bearings. It is shown that: (1) the contribution of contact load is not significant; and (2) the hydrodynamic and contact load increase with surface roughness
Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics
We obtain \theta_p(q) = 2\theta_s(q) for one-dimensional q-state
ferromagnetic Potts models evolving under parallel dynamics at zero temperature
from an initially disordered state, where \theta_p(q) is the persistence
exponent for parallel dynamics and \theta_s(q) = -{1/8}+
\frac{2}{\pi^2}[cos^{-1}{(2-q)/q\sqrt{2}}]^2 [PRL, {\bf 75}, 751, (1995)], the
persistence exponent under serial dynamics. This result is a consequence of an
exact, albeit non-trivial, mapping of the evolution of configurations of Potts
spins under parallel dynamics to the dynamics of two decoupled reaction
diffusion systems.Comment: 13 pages Latex file, 5 postscript figure
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