A Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation

We develop a biased Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels. Given a trajectory with a fixed number of collisions, the algorithm modifies both the waiting times between collisions, as well as the sequence of collisions, using local moves. We show that the algorithm is ergodic by giving a protocol that transforms an arbitrary trajectory to a standard trajectory using valid Monte Carlo moves. The algorithm can sample rare events with probabilities of the order of $10^{-40}$ and lower. The algorithm's effectiveness in sampling low-probability events is established by showing that the numerical results for the large deviation function of constant-kernel aggregation reproduce the exact results. It is shown that the algorithm can obtain the large deviation functions for other kernels, including gelling ones, as well as the instanton trajectories for atypical times. The dependence of the autocorrelation times, both temporal and configurational, on the different parameters of the algorithm is also characterized.Comment: 26 pages, 10 figure

An Insight to Micropropagation of Freshwater Aquatic Medicinal Plants

Freshwater aquatic plants include medicinal and ornamental species: have limited demand and rarely micropropagated. Most of them are found in Southeast Asian environments as amphibians or fully submerged or floating in lakes, streams, and watercourses that are ignored as weeds. These plants have never been central focuses and were not looked for characteristic proliferation. It is difficult to multiply these plants using traditional techniques through seeds or natural proliferation of rhizomes or cuttings by maintaining quality. Rare and fragmented but important information about micropropagation of these neglected plants has been discussed in this chapter. There are certain aquatic or semiaquatic medicinal plants for which no effort has been made to propagate in vitro. Contrarily, plants like water hyssop have extensive in vitro regeneration protocols due to its high demand. This study compares methodologies used by researchers to micropropagate these plants. It is concluded that this study will help in understanding and establishing systems for scientific propagation of these plants. © Springer Nature Switzerland AG 2019