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Previous issue date: 2013-02-07 / CNPq / Nesta Dissertac¸ ˜ao estudamos a dinˆamica energ´etica das buscas aleat ´orias aplicadas ao
problema de foraging, em que animais buscam por comida ou parceiros em ambientes
escassos. Discutiremos, inicialmente, um modelo estat´ıstico de caminhadas aleat ´orias
utilizando as distribuic¸ ˜oes de L´evy para os tamanhos dos passos de busca, as quais tˆem
sido reportadas na literatura como estrat´egias de eficiˆencia ´otima para o problema. Em
seguida vamos incluir no modelo ganhos e perdas de energia na caminhada aleat ´ oria de
busca, e abordaremos a dinˆamica energ´etica do processo de busca unidimensional com
extremos absorventes. Vamos discutir a transic¸ ˜ao de fase que o buscador experimenta
de um estado ativo (“vivo”), t´ıpico de ambientes com abundˆancia de recursos, para um
estado est´atico absorvente (“morto”), onde a busca ´e encerrada pela falta de energia
oriunda do encontro de recursos. Obteremos os expoentes cr´ıticos relativos a essa
transic¸ ˜ao atrav´es de abordagens te ´ oricas, tais como o m´etodo de primeira passagem
para o estado de energia nula, e num´ericas, baseadas na hip´otese de escala. Mostraremos
a independˆencia destes expoentes com a forma funcional da func¸ ˜ao gasto de energia. Por
fim, faremos uma breve revis˜ao da literatura sobre a equac¸ ˜ao de Fokker-Planck canˆonica
e tamb´em sobre as suas vers˜oes utilizando derivadas fracion´arias, numa prepararac¸ ˜ao
para uma futura abordagem, durante o programa de Doutorado, do problema da busca
aleat´oria envolvendo difus˜oes anˆomalas (por exemplo, superdifus˜ao) via equac¸ ˜oes
diferenciais. / In this work we study the energy dynamics of random searches applied to the foraging
problem, in which animals search for food or mates in scarce environments. Firstly, we
discuss a statistical model of random search walks using the L´evy distribution of step
lengths, which has been reported in the literature as an optimal solution to the problem.
In the sequence we include in the model energy gains and losses during the search walk,
and discuss the energy dynamics of the search process in a one dimensional space with
absorbing boundaries. We discuss the phase transition that the searcher experiences
from an active (“alive”) state, typical of environments abundant in resources, to a
static absorbed (“dead”) one, in which the search is terminated due to the lack of
energy obtained from the encounters.We obtain the critical exponents for this transition
through both theoretical (such as the first-passage method to the state of zero energy)
and numerical approaches, based on the scale hypothesis.We show the independence
of the exponents with the functional form of the energy cost. Finally, we provide a
brief review of the literature on the canonical Fokker-Planck equation and also on
its version using fractional derivatives, in a preparation for a future approach of the
random search problem involving anomalous diffusion (e.g., superdiffusion) through
differential equations during the Ph.D. program.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufpe.br:123456789/17100 |
| Date | 07 February 2013 |
| Creators | ARAÚJO, Hugo de Andrade |
| Contributors | http://lattes.cnpq.br/4321118621178584, RAPOSO, Ernesto Carneiro Pessoa |
| Publisher | Universidade Federal de Pernambuco, Programa de Pos Graduacao em Fisica, UFPE, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Breton |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UFPE, instname:Universidade Federal de Pernambuco, instacron:UFPE |
| Rights | Attribution-NonCommercial-NoDerivs 3.0 Brazil, http://creativecommons.org/licenses/by-nc-nd/3.0/br/, info:eu-repo/semantics/openAccess |
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