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

Pulmonary artery resuscitation for isolated ductal origin of a pulmonary artery

ObjectiveDuctal origin of a pulmonary artery (DOPA) is commonly misdiagnosed as agenesis of a pulmonary artery (PA), which may result in inadequate treatment. The objective is to describe the results of resuscitation of unilateral DOPA.MethodsThis study is a retrospective review of all patients with unilateral DOPA who underwent PA resuscitation at Texas Children's Hospital from 1993 to 2012. Patients with other cardiac or contralateral lung anomalies were excluded.ResultsTen patients, median age 2 years (range, 3 days to 9 years), with unilateral DOPA were included. Symptoms were present in 6 patients. Cardiac catheterization was performed in all and showed a patent duct or a ductal stump in most patients and a small PA on wedge angiography of the pulmonary veins. Two patients underwent single-stage centralization. The other 8 underwent ductal stenting (n = 2) or a systemic-to-PA shunt (n = 6) as the first stage before centralization. The 2 patients with ductal stenting developed pulmonary edema. The 2 patients with a cryopreserved vein shunt developed early thrombosis requiring reintervention. Nine patients have undergone centralization. Six patients have required further interventional procedures. There have been no deaths. Symptoms and lung hypoplasia have improved in all patients. Median relative lung perfusion at follow-up was 26% (range, 12%-46%) with significant improvement in the size of the affected PA.ConclusionsPA resuscitation is effective at restoring flow to the affected lung resulting in improved diameter of the PA, lung growth, and resolution of symptoms. PA resuscitation should be considered in all children with DOPA, including those beyond infancy

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.Comment: 12 pages, revtex, 5 figure

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 $e_{KR}=\epsilon +O(\epsilon ^2)$ and $\epsilon =2-d$. 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.Comment: 11 pages, 6 figures, Revtex