• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Doctoral Thesis
DOI
10.11606/T.59.2008.tde-18122009-153031
Document
Author
Full name
César Augusto Sangaletti Terçariol
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Ribeirão Preto, 2008
Supervisor
Committee
Martinez, Alexandre Souto (President)
Mendes, Tereza Cristina da Rocha
Mitrowsky, Rafael Andres Rosales
Rosa, Reinaldo Roberto
Silva, Marco Antonio Alves da
Title in Portuguese
Caminhadas deterministas parcialmente auto-repulsivas: resultados analíticos para o efeito da memória do turista na exploração de meios desordenados
Keywords in Portuguese
caminhada com memória
caminhada determinista
caminhada do turista
distribuição conjunta
distribuição de período de atratores
distribuição de tempos de transiente
meios aleatórios
memória crítica
modelo de distâncias aleatórias
modelo de mapeamento aleatório
Abstract in Portuguese
Considere um meio desordenado constituído por $N$ pontos cujas coordenadas são geradas aleatoriamente de maneira uniforme e independente nas arestas unitárias de um hipercubo $d$-dimensional. As probabilidades de vizinhança entre os pares de pontos deste meio são expressas através da fórmula de Cox. Um caminhante parte de um dado ponto deste meio desordenado e se movimenta obedecendo à regra determinista de ir para o ponto mais próximo que não tenha sido visitado nos últimos $\mu$ passos. Este processo foi denominado de caminhada determinista do turista. Cada trajetória gerada por esta dinâmica possui uma parte inicial não-periódica de $t$ passos (transiente) e uma parte final periódica de $p$ passos (atrator). Neste trabalho, obtemos analiticamente algumas distribuições estatísticas para a caminhada determinista do turista com memória $\mu$ arbitrária em sistemas unidimensionais e com memória $\mu=2$ no modelo Random Link (que corresponde ao limite $d ightarrow 1$). Estes resultados nos permitiram compreender o papel da memória no comportamento exploratório do turista e explicar a equivalência não-trivial entre o modelo Random Link e o modelo Random Map (que é um caso limite das redes de Kauffman). Enfatizamos que o número de pontos explorados pelo turista é a grandeza fundamental nos problemas considerados. As distribuições analíticas obtidas foram validadas através de experimentos numéricos. Também obtivemos uma dedução alternativa para a fórmula de Cox, apresentando os resultados finais em termos de distribuições estatísticas elementares.
Title in English
Deterministic partially self-avoiding walks: analytical results for the effect of tourist's memory in the exploration of disordered media
Keywords in English
attractor period distribution
critical memory
deterministic walk
joint distribution
random distance model
random map model.
random media
tourist walk
transient time distribution
walk with memory
Abstract in English
Consider a medium characterized by $N$ points whose coordinates are randomly and independently generated by a uniform distribution along the unitary edges of a $d$-dimensional hypercube. The neighborhood probabilities between any pair of points in this medium are given by the Cox formula. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go the nearest point which has not been visited in the preceding $\mu$ steps. This process has been called the deterministic tourist walk. Each trajectory generated by this dynamics has an initial non-periodic part of $t$ steps (transient) and a final periodic part of $p$ steps (attractor). In this work, we obtain analytically some statistical distributions for the deterministic tourist walk with arbitrary memory $\mu$ in one-dimensional systems and with memory $\mu=2$ in the random link model (which corresponds to $d ightarrow 1$ limit). These results enable us to understand the main role played by the memory on the tourist's exploratory behavior and explain the non-trivial equivalence between the random link model and the random map model (which is a limiting case of the Kauffman model). We stress that the number of explored points is the fundamental quantity in the considered problems. The obtained distributions have been validated by numerical experiments. We also obtain an alternative derivation for the Cox formula, writing the final results in terms of known statistical distributions.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
TeseP.pdf (1.28 Mbytes)
Publishing Date
2010-01-06
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • TERçARIOL, César Augusto Sangaletti, KIIPPER, Felipe de Moura, and MARTINEZ, Alexandre Souto. An analytical calculation of neighbourhood order probabilities for high dimensional Poissonian processes and mean field models [doi:10.1088/1751-8113/40/9/005]. Journal of Physics A: Mathematical and Theoretical [online], 2007, vol. 40, n. 9, p. 1981-1989.
  • TERçARIOL, César, and MARTINEZ, Alexandre. Influence of memory in deterministic walks in random media : Analytical calculation within a mean-field approximation [doi:10.1103/PhysRevE.78.031111]. Physical Review E [online], 2008, vol. 78, n. 3.
  • ARRUDA, T. J., et al. Arithmetical and geometrical means of generalized logarithmic and exponential functions: Generalized sum and product operators [doi:10.1016/j.physleta.2007.12.020]. Physics Letters. A [online], 2008, vol. 372, p. 2578-2582.
  • GONZÁLEZ, R. S., et al. Deterministic tourist walk. Journal of Computational Interdisciplinary Sciences, 2009, vol. 1, p. 119-125.
  • MARTINEZ, A. S., GONZÁLEZ, R. S., and TERÇARIOL, C. A. S. Continuous growth models in terms of generalized logarithm and exponential functions [doi:10.1016/j.physa.2008.06.015]. Physica. A [online], 2008, vol. 387, p. 5679-5687.
  • MARTINEZ, A. S., GONZÁLEZ, R. S., and TERÇARIOL, C. A. S. Generalized Probability Functions [doi:10.1155/2009/206176]. Advances in Mathematical Physics [online], 2009, vol. 2009, p. 1-14.
  • TERÇARIOL, C. A. S., et al. Deterministic and random partially self-avoiding walks in random media [doi:10.1016/j.physa.2007.07.019]. Physica. A [online], 2007, vol. 386, p. 678-680.
  • TERÇARIOL, C. A. S., and MARTINEZ, A. S. Analytical calculation for the percolation crossover in deterministic partially self-avoiding walks in one-dimensional random media [doi:10.1103/PhysRevE.75.061117]. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics [online], 2007, vol. 75, p. 061117.
  • TERÇARIOL, C. A. S., and MARTINEZ, A. S. Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation [doi:10.1103/PhysRevE.78.031111]. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics [online], 2008, vol. 78, p. 031111.
  • TERÇARIOL, C. A. S., KIIPPER, F. M., and MARTINEZ, A. S. An analytical calculation of neighbourhood order probabilities for high dimensional Poissonian processes and mean field models [doi:10.1088/1751-8113/40/9/005]. Journal of Physics. A, Mathematical and Theoretical [online], 2007, vol. 40, p. 1981-1989.
  • TERÇARIOL, C. A. S., GONZÁLEZ, R. S., and MARTINEZ, A. S. Exploring random media with partially self-avoiding walks. In 31st Conference of the Middle European Cooperation (MECO 31), Primo ten , Croatia, 2006. Livro de resumos., 2006. Abstract.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2021. All rights reserved.