Kinetics of a diffusive capture process: lamb besieged by a pride of lions
نویسندگان
چکیده
The survival probability, SN(t), of a diffusing prey (‘lamb’) in the proximity of N diffusing predators (a ‘pride of lions’) in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, SN(t) ∝ t−βN , with the decay exponent βN proportional to ln N . The crossover behaviour as a function of the relative diffusivities of the lions and the lamb is also discussed. When N → ∞, the lamb survival probability exhibits a log-normal decay, S∞(t) ∝ exp(− ln2 t).
منابع مشابه
ar X iv : c on d - m at / 9 60 31 76 v 1 2 8 M ar 1 99 6 Kinetics of a Diffusive Capture Process : Lamb Besieged by a Pride of Lions
The survival probability, S N (t), of a diffusing prey (" lamb ") in the proximity of N diffusing predators (a " pride of lions ") in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S N (t) ∝ t −β N , with the decay exponent β N proportional to ln N. The crossover behavior as a function of the relative ...
متن کاملKinetics of a Di usive Capture Process: Lamb Besieged by a Pride of Lions
The survival probability, S N (t), of a diiusing prey (\lamb") in the proximity of N diiusing predators (a \pride of lions") in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S N (t) / t ? N , with the decay exponent N proportional to ln N. The crossover behavior as a function of the relative diiusivit...
متن کاملCapture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
What is the survival probability of a diffusing lamb which is hunted by N hungry lions? Although this capture process is appealingly simple to define ~see Fig. 1!, its long-time behavior poses a theoretical challenge because of the delicate interplay between the positions of the lamb and the closest lion. This model also illustrates a general feature of nonequilibrium statistical mechanics: lif...
متن کاملCan a lamb reach a haven before being eaten by diffusing lions?
We study the survival of a single diffusing lamb on the positive half line in the presence of N diffusing lions to the right of the lamb and a haven at x = 0. If the lamb reaches this haven before meeting any lion, the lamb survives. We investigate the survival probability of the lamb, SN (x,L), as a function of N and the respective initial positions of the lamb and the lions, x and L. We deter...
متن کاملMultiple predator based capture process on complex networks
Abstract. The predator/prey (capture) problem is a prototype of many networkrelated applications. We study the capture process on complex networks by considering multiple predators from multiple sources. In our model, some lions start from multiple sources simultaneously to capture the lamb by biased random walks, which are controlled with a free parameter α. We derive the distribution of the l...
متن کامل