In single phase flow of a passive tracer through heterogeneous porous media, a mixing layer develops between the tagged and untagged regions of the fluid. The mixing region expands as the time evolves. We have developed a multilength scale theory for the growth of the mixing region induced by a general random velocity field (multi-fractal field). The theory relates the statistics of the mixing ...

For a compact manifold, which has part isometric to cylinder of finite length, we consider an adiabatic limit procedure, in the length tends infinity. We study asymptotic spectrum Hodge-Laplacian and $L^2$-metric on de Rham cohomology. As application, give pure analytic proof gluing formula for torsion.

Abstract—This paper considers the problem of variable-length coding over a discrete memoryless channel (DMC) with noiseless feedback. The paper provides a stochastic control view of the problem whose solution is analyzed via a newly proposed symmetrized divergence, termed extrinsic Jensen–Shannon (EJS) divergence. It is shown that strictly positive lower bounds on EJS divergence provide non-asy...

Fracture of quasibrittle materials such as concrete, rock, ice, tough ceramics and various fibrous or particulate composites, exhibits complex size effects. An asymptotic theory of scaling governing these size effects is presented, while its extension to fractal cracks is left to a companion paper [1] which follows. The energy release from the structure is assumed to depend on its size D, on th...

We analysed growth of nestling Chilean Swallows (Tachycineta meyeni) over four consecutive breeding seasons and determined the factors that explain variation in growth rate, asymptotic body mass and length of the nestling period. As the breeding season advanced nestlings grew more slowly and attained lower asymptotic mass, but the length of the nestling period and nestling survival did not show...

We obtain an asymptotic formula in q for the number of MDS codes of length n and dimension k over a finite field with q elements.

in this paper we discuss on the fixed points of asymptotic contractions and boyd-wong type contractions in uniform spaces equipped with an e-distance. a new version ofkirk's fixed point theorem is given for asymptotic contractions and boyd-wong type contractions is investigated in uniform spaces.

We present a new CuSum chart for monitoring shifts in the mean of autocorrelated data. The monitoring statistic is the plain cumulative sum of differences between the observations and the target value, and the control limits are a function of the asymptotic variance constant and target in-control average run length. Our method uses a variety of non-parametric techniques that are popular in the ...

We address the issue of fluctuations, about an exponential line shape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of...