Motion of a random walker in a quenched power law correlated velocity field

We study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model, with long-range velocity correlation. For a velocity correlation function, dependent on transverse co-ordinates y as 1/(a+|{y_1 - y_2}|)^alpha, we analytically calculate the two-time correlation function of the x-coordinate. We find that the motion of the x-coordinate is a fractional Brownian motion (fBm), with a Hurst exponent H = max [1/2, (1- alpha/4), (1-d/4)]. From this and known properties of fBM, we calculate the disorder averaged persistence probability of x(t) up to time t. We also find the lines in the parameter space of d and alpha along which there is marginal behaviour. We present results of simulations which support our analytical calculation.Comment: 8 pages, 4 figures. To appear in Physical Review

Suppressive activity of a macrolide antibiotic, roxithromycin on co-stimulatory molecule expression on mouse splenocytes in vivo.

The influence of roxithromycin (RXM) on the expression of co-stimulatory molecules, CD40, CD80 and CD86, was examined in vivo. When BALB/c mice were immunized intraperitoneally with two doses of dinitrophenylated ovalbumin (DNP-OVA) at 1 week intervals, intraperitoneal administration of RXM at 250 microg/kg once a day for 14 days strongly suppressed IgE contents in sera obtained from mice 22 days after the first immunization. In addition, RXM treatment of mice suppressed endogenous IL-4 contents in aqueous spleen extracts, which were enhanced by DNP-OVA immunization. We next examined the influence of RXM on co-stimulatory molecule expression on splenic lymphocytes. RXM treatment of the immunized mice caused suppression of CD40 expression, but this treatment did not affect CD80 and CD86 expression

Suppressive effects of anti-allergic agent suplatast tosilate (IPD-1151T) on the expression of co-stimulatory molecules on mouse splenocytes in vivo.

The effects of IPD-1151T on the expression of co-stimulatory molecules, CD40, CD80 and CD86, were investigated in vivo using mice with allergic disorders. BALB/c mice were immunized intraperitoneally with two doses of dinitrophenylated ovalbumin (DNP-OVA) at 1-week intervals. These mice then were treated intraperitoneally with 100 microg/kg of IPD-1151T once a day for 14 days, starting 7 days after the first immunization. On day 21, some mice were challenged intraperitoneally with DNP-OVA and the other mice were not challenged. All mice were autopsied on day 22 and assayed for immunoglobulin E, interleuken (IL)-4 and IL-5 productions following DNP-OVA immunization. The intraperitoneal treatment with IPD-1151T strongly suppressed immunoglobulin E contents in serum, which were enhanced by DNA-OVA immunization. IPD-1151T also caused a decrease in both IL-4 and IL-5 levels in splenic lymphocytes. We next examined the influence of IPD-1151T on co-stimulatory molecule expression on splenic lymphocytes. IPD-1151T caused suppression of CD40 and CD86 expression; however, the treatments did not affect CD80 expression

Box-ball system: soliton and tree decomposition of excursions

We review combinatorial properties of solitons of the Box-Ball system introduced by Takahashi and Satsuma in 1990. Starting with several definitions of the system, we describe ways to identify solitons and review a proof of the conservation of the solitons under the dynamics. Ferrari, Nguyen, Rolla and Wang 2018 proposed a soliton decomposition of a configuration into a family of vectors, one for each soliton size. Based on this decompositions, the authors have proposed a family of measures on the set of excursions which induces invariant distributions for the Box-Ball System. In this paper, we propose a new soliton decomposition which is equivalent to a branch decomposition of the tree associated to the excursion, see Le Gall 2005. A ball configuration distributed as independent Bernoulli variables of parameter $\lambda<1/2$ is in correspondence with a simple random walk with negative drift $2\lambda-1$ and infinitely many excursions over the local minima. In this case the authors have proven that the soliton decomposition of the walk consists on independent double-infinite vectors of iid geometric random variables. We show that this property is shared by the branch decomposition of the excursion trees of the random walk and discuss a corresponding construction of a Geometric branching process with independent but not identically distributed Geometric random variables.Comment: 47 pages, 33 figures. This is the revised version after addressing referee reports. This version will be published in the special volume of the XIII Simposio de Probabilidad y Procesos Estoc\'asticos, UNAM Mexico, by Birkhause

Short Communication Functional characterization of carrier-mediated transport of pravastatin across the blood-retinal barrier in rats

Abstract: 248 words Introduction: 432 word

Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift

We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the energy spectrum of a single particle quantum Hamiltonian, which can be subsequently found. Our method allows us analytical access to arbitrary values of the drift (bias), thus going beyond the previous methods which provide results only in the limit of vanishing drift. We show that on varying the drift, the persistence displays a variety of rich asymptotic behaviors including, in particular, interesting qualitative changes at some special values of the drift.Comment: 17 pages, two eps figures (included

Persistence of a particle in the Matheron-de Marsily velocity field

We show that the longitudinal position $x(t)$ of a particle in a $(d+1)$-dimensional layered random velocity field (the Matheron-de Marsily model) can be identified as a fractional Brownian motion (fBm) characterized by a variable Hurst exponent $H(d)=1-d/4$ for $d2$. The fBm becomes marginal at $d=2$. Moreover, using the known first-passage properties of fBm we prove analytically that the disorder averaged persistence (the probability of no zero crossing of the process $x(t)$ upto time $t$) has a power law decay for large $t$ with an exponent $\theta=d/4$ for $d<2$ and $\theta=1/2$ for $d\geq 2$ (with logarithmic correction at $d=2$), results that were earlier derived by Redner based on heuristic arguments and supported by numerical simulations (S. Redner, Phys. Rev. E {\bf 56}, 4967 (1997)).Comment: 4 pages Revtex, 1 .eps figure included, to appear in PRE Rapid Communicatio

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page