arXiv subjects

Oleg Zaboronski

Publications and source records attributed to Oleg Zaboronski.

41 records · Page 3Linked to original sources

arXiv2004

Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda_c and annihilation at rate lambda_a. The test particle dies at rate lambda' on coming into contact with the other particles. The survival probability decays algebraically with time as t^{-theta}. The exponent theta in d<2 is calculated using the perturbative renormalization group formalism as an expansion in epsilon=2-d. It is shown to be universal, independent of lambda', and to depend only on delta, the ratio of the diffusion constant of test particles to that of the other particles, and on the ratio lambda_a/lambda_c. In two dimensions we calculate the logarithmic corrections to the power law decay of the survival probability. Surprisingly, the log corrections are non-universal. The one loop answer for theta in one dimension obtained by setting epsilon=1 is compared with existing exact solutions for special values of delta and lambda_a/lambda_c. The analytical results for the logarithmic corrections are verified by Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2003

Persistence properties of a system of coagulating and annihilating random walkers

We study a d-dimensional system of diffusing particles that on contact either annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1). In 1-dimension, the system models the zero temperature Glauber dynamics of domain walls in the q-state Potts model. We calculate P(m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly (m-1) coagulations. Using perturbative renormalization group analysis for d < 2, we show that, if the number of coagulations m is much less than the typical number M(t), then P(m,t) ~ m^(z/d) t^(-theta), with theta=d Q + Q(Q-1/2) epsilon + O(epsilon^2), z=(2Q-1) epsilon + (2 Q-1) (Q-1)(1/2+A Q) epsilon^2 +O(epsilon^3), where Q=(q-1)/q, epsilon =2-d and A =-0.006. M(t) is shown to scale as t^(d/2-delta), where delta = d (1 -Q)+(Q-1)(Q-1/2) epsilon+ O(epsilon^2). In two dimensions, we show that P(m,t) ~ ln(t)^(Q(3-2Q)) ln(m)^((2Q-1)^2) t^(-2Q) for m << t^(2 Q-1). The 1-dimensional results corresponding to epsilon=1 are compared with results from Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2002

Kang-Redner Anomaly in Cluster-Cluster Aggregation

The large time, small mass, asymptotic behavior of the average mass distribution $\pb$ is studied in a $d$-dimensional system of diffusing aggregating particles for $1\leq d \leq 2$. By means of both a renormalization group computation as well as a direct re-summation of leading terms in the small reaction-rate expansion of the average mass distribution, it is shown that $\pb \sim \frac{1}{t^d} (\frac{m^{1/d}}{\sqrt{t}})^{e_{KR}}$ for $m \ll t^{d/2}$, where $e_{KR}=ε+O(ε^2)$ and $ε=2-d$. In two dimensions, it is shown that $\pb \sim \frac{\ln(m) \ln(t)}{t^2}$ for $ m \ll t/ \ln(t)$. Numerical simulations in two dimensions supporting the analytical results are also presented.

cond-mat.stat-mech↗

arXiv2000

Stochastic Aggregation of Point Particles Revisited

In the present letter we employ the method of the dynamical renormalisation group to compute the average mass distribution of aggregating point particles in 2 dimensions in the regime when the effects of local mass distribution fluctuations are essential

cond-mat.stat-mech↗

arXiv2000

On the large time asymptotics of decaying Burgers turbulence

The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and velocity differences are computed exactly, together with the "time-like" structure functions . The analysis of the answers reveals both well known features of Burgers turbulence, such as the presence of dissipative anomaly, the extreme anomalous scaling of the velocity structure functions and self similarity of the statistics of the velocity field, and new features such as the extreme anomalous scaling of the "time-like" structure functions and the non-existence of a global inertial scale due to multiscaling of the Burgers velocity field. We also observe that all the results can be recovered using the one point probability distribution function of the shock strength and discuss the implications of this fact for Burgers turbulence in general.

chao-dyn↗