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Random walks on uniform and non-uniform combs and brushes

Alex V Plyukhin, Dan Plyukhin
2017 Journal of Statistical Mechanics: Theory and Experiment  
We consider random walks on comb- and brush-like graphs consisting of a base (of fractal dimension D) decorated with attached side-groups.  ...  the Sierpinski brush (with the base and anchor set built on the same Sierpinski gasket).  ...  CONCLUSION We have studied random walks on two groups of comb-and brush-like graphs.  ... 
doi:10.1088/1742-5468/aa79b4 fatcat:urjadjyoivfjjg2fn4a5hagk44

Dynamics of continuous-time quantum walks in restricted geometries

E Agliari, A Blumen, O Mülken
2008 Journal of Physics A: Mathematical and Theoretical  
A direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time.  ...  Indeed, a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms.  ...  Support from the Deutsche Forschungsgemeinschaft (DFG), the Fonds der Chemischen Industrie and the Ministry of Science, Research and the Arts of Baden-Württemberg (AZ: 24-7532.23-11-11/1) is gratefully  ... 
doi:10.1088/1751-8113/41/44/445301 fatcat:i2fswtgeorct5ad767q5hkxtfu

First-passage properties of mortal random walks: ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs [article]

V. Balakrishnan, E. Abad, T. Abil, J.J. Kozak
2019 arXiv   pre-print
We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites.  ...  The properties of the map then determine, in each case, the behavior of the trapping probability, the mean time to trapping, the temporal scaling factor governing the random walk dimension on the graph  ...  Random walk on a graph with traps Turning now to Markovian random walks on graphs in discrete time in the presence of trap sites, it is helpful to begin with the standard case (q = 1), in order to bring  ... 
arXiv:1901.10226v1 fatcat:ebbpt3iezvg4hkyuwzmzpyq57i

Loop-erased random walk on the Sierpinski gasket [article]

Kumiko Hattori, Michiaki Mizuno
2012 arXiv   pre-print
We consider a model of loop-erased random walks on the finite pre-Sierpinski gasket which permits rigorous analysis.  ...  We prove the existence of the scaling limit and show that the path of the limiting process is almost surely self-avoiding, while having Hausdorff dimension strictly greater than 1.  ...  Theorem 5 suggests that the displacement exponent for the loop-erased random walk on the pre-Sierpiński gasket is log λ/ log 2, in the sense that the average number of steps it takes to cover the distance  ... 
arXiv:1209.4959v1 fatcat:j42vwoiumbfevbsqvcqbjeqjmi

Meaningful Interpretation of Subdiffusive Measurements in Living Cells (Crowded Environment) by Fluorescence Fluctuation Microscopy

Gerd Baumann, Robert F. Place, Zeno Foldes-Papp
2010 Current Pharmaceutical Biotechnology  
In order to separate both processes, we introduce anomalous random walks on fractals that represented crowded environments.  ...  The less the anomalous exponent the higher the geometric crowding of the underlying structure of motion that is quantified by the ratio of the Hausdorff dimension and the walk exponent w f d d / and specific  ...  University in Cairo, the University of Ulm (Germany) as well as the bwGRiD Cluster Ulm that is part of the high performance computing facilities of the Federal State of Baden-Wuerttemberg (Germany), where  ... 
doi:10.2174/138920110791591454 pmid:20553227 pmcid:PMC3583073 fatcat:64y74gpkpzhszi2mlmflk3alxu

Multifractal Measures Characterized by the Iterative Map with Two Control Parameters [article]

Kyungsik Kim, G. H. Kim, Y. S. Kong
2000 arXiv   pre-print
and reflection on a two - dimensional Sierpinski gasket.  ...  Especially, based on the Monte Carlo simulation, the normalized first passage time to arrive at the absorbing barrier after starting from an arbitrary site is mainly obtained in the presence of both absorption  ...  Acknowledgments This work is supported in part by the Academic Research Fund of Pukyong National Univ. of Korea.  ... 
arXiv:cond-mat/0009074v1 fatcat:wwivr24gxvhllmtkeyjr6kc5f4

Log-periodic modulation in one-dimensional random walks

L. Padilla, H. O. Mártin, J. L. Iguain
2009 Europhysics letters  
Both the random walk exponent and the period of the modulation are analytically calculated and confirmed by Monte Carlo simulations.  ...  We have studied the diffusion of a single particle on a one-dimensional lattice.  ...  A proof of the fluctuating behaviour of the n-step probabilities for a simple RW on a Sierpiński graph was given in ref.  ... 
doi:10.1209/0295-5075/85/20008 fatcat:4nfur7yuy5et5glwhk5yys6kyq

Random walks on graphs: ideas, techniques and results

R Burioni, D Cassi
2005 Journal of Physics A: Mathematical and General  
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology.  ...  Here we aim at giving a brief but comprehensive perspective of these progresses, with a particular emphasis on physical aspects.  ...  One can then define the generalized Laplacian The random walk problem Let us now introduce the so-called simple random walk on a graph G.  ... 
doi:10.1088/0305-4470/38/8/r01 fatcat:awdt755e3zbctlmpqxxczarny4

Anomalous Subdiffusive Measurements by Fluorescence Correlations Spectroscopy and Simulations of Translational Diffusive Behavior in Live Cells

Gerd Baumann, Masataka Kinjo, Zeno Földes-Papp
2014 Journal of Biological Methods  
The GFP-tagged glucocorticoid receptor α was either a homodimer or a monomer in the nucleoplasm depending on the presence or absence of the stimulus dexamethasone.  ...  The first one was the Inverse Gamma distribution and the second class was a stable Levy distribution.  ...  Due to space limit, we apologize for the many omissions of the pioneering work of other researchers, and mainly focus on our contributions to the field that are related to the reliable measurements of  ... 
doi:10.14440/jbm.2014.17 fatcat:ndkt24x2zjg7ziifhelrd65xja

Cutting-decimation renormalization for diffusive and vibrational dynamics on fractals

Raffaella Burioni, Davide Cassi, Sofia Regina
1999 Physica A: Statistical Mechanics and its Applications  
In this paper we study in detail the dynamical dimension splitting on these fractals analyzing the mathematical properties of the cutting-decimation transform.  ...  Our results clarify how the splitting arises from the cutting transform and show that the dynamical dimension degeneracy is a very peculiar consequence of exact decimability.  ...  A relation between the random walk probabilities P ii (t) andd V does indeed exist but it involves the average of the P ii (t) over all points of the graph [3] : P(t) = lim N →∞ 1 N N i=1 P ii (t) ∼ t  ... 
doi:10.1016/s0378-4371(98)00477-4 fatcat:dzut5cy2yjh4tosxuvjgdzimja

Cutting-Decimation Renormalization for diffusive and vibrational dynamics on fractals [article]

Raffaella Burioni, Davide Cassi, Sofia Regina
1997 arXiv   pre-print
In this paper we study in details the dynamical dimension splitting on these fractals analyzing the mathematical properties of the cutting-decimation transform.  ...  Our results clarify how the splitting arises from the cutting transform and show that the dynamical dimension degeneration is a very peculiar consequence of exact decimability.  ...  A relation between the random walk probabilities P ii (t) and d V does indeed exist but it involves the average of the P ii (t) over all points of the graph [3] :P (t) = lim N →∞ 1 N N i=1 P ii (t) ∼  ... 
arXiv:cond-mat/9710273v1 fatcat:zla73sjlifhnjdchzvutylqbq4

Scaling Concepts in Graph Thoery: Self-Avoiding Walk on Fractal Complex Networks [article]

Yoshihito Hotta
2014 arXiv   pre-print
We find that the exponent ν is equal to the exponent of displacement, which describes the speed of diffusion in terms of the shortest distance.  ...  We here study the self-avoiding walk on complex fractal networks through the mapping of the self-avoiding walk to the n-vector model by a generating function formalism.  ...  The self-avoiding walk on this tree is identical with the random walk with an immediate return being forbidden (namely, the non-reversal random walk) [31, 32] .  ... 
arXiv:1402.0953v1 fatcat:fozheibxavhzxbqcq6pfmycdym

Random walks with fractally correlated traps: Stretched exponential and power-law survival kinetics

Dan Plyukhin, Alex V. Plyukhin
2016 Physical review. E  
We consider the survival probability f(t) of a random walk with a constant hopping rate w on a host lattice of fractal dimension d and spectral dimension d_s< 2, with spatially correlated traps.  ...  The traps form a sublattice with fractal dimension d_aw, including the limit of perfect traps w_a→∞, the stretched exponential regime is absent and the decay of f(t) follows, after a short transient, the  ...  Parodi for discussions and interest, and the anonymous referees for their insightful comments and suggestions.  ... 
doi:10.1103/physreve.94.042132 pmid:27841519 fatcat:za2hzt5zpreh3kcxfbvale5zha

On the influence of reflective boundary conditions on the statistics of Poisson–Kac diffusion processes

Massimiliano Giona, Antonio Brasiello, Silvestro Crescitelli
2016 Physica A: Statistical Mechanics and its Applications  
We analyze the influence of reflective boundary conditions on the statistics of Poisson-Kac diffusion processes, and specifically how they modify the Poissonian switching-time statistics.  ...  After addressing simple cases such as diffusion in a channel, and the switching statistics in the presence of a polarization potential, we thoroughly study Poisson-Kac diffusion in fractal domains.  ...  27 lyze anomalous transport properties in fractal media, alternative to the more classical analysis of the scaling of the mean square displacement r 2 (t) , just using a single particle trajectory.  ... 
doi:10.1016/j.physa.2015.12.142 fatcat:eagty52mdnbhlhnyxybdrzolre

On the occurrence of oscillatory modulations in the power law behavior of dynamic and kinetic processes in fractals

M. A. Bab, G. Fabricius, E. V. Albano
2007 Europhysics letters  
The conjecture is tested numerically for random walks, and representative systems of broad universality classes in the fields of irreversible and equilibrium critical phenomena.  ...  So, we conjecture that the interplay between the physical process and the symmetry properties of the fractal leads to the occurrence of time DSI evidenced by soft log-periodic modulations of physical observables  ...  GF acknowledge the ICTP for working facilities.  ... 
doi:10.1209/0295-5075/81/10003 fatcat:gqxk5yzqvvautga5y7dmbzb7gu
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