Displacement of Transport Processes on Networked Topologies

Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and ...

[1]  Frank Spitzer,et al.  Some theorems concerning 2-dimensional Brownian motion , 1958 .

[2]  L. Gallos.  Random walk and trapping processes on scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Random walks on the Menger sponge , 1997 .

[4]  Random walk on the Bethe lattice and hyperbolic Brownian motion , 1995, cond-mat/9509067.

[5]  M. Welte,et al.  Bidirectional Transport along Microtubules , 2004, Current Biology.

[6]  Bhattacharya.  Random walk for interacting particles on a Sierpínski gasket. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  H. Cho,et al.  Translational and rotational diffusion of a single nanorod in unentangled polymer melts. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Karl-Heinz Hoffmann,et al.  Resistance scaling and random walk dimensions for finitely ramified Sierpinski carpets , 2000, SIGS.

[9]  Ralf Metzler,et al.  Boundary value problems for fractional diffusion equations , 2000 .

[10]  A. Comtet,et al.  Winding of planar Brownian curves , 1990 .

[11]  Roger L. Hughes,et al.  A continuum theory for the flow of pedestrians , 2002 .

[12]  S. Jonathan Chapman,et al.  Effective Transport Properties of Lattices , 2017, SIAM J. Appl. Math..

[13]  S. Redner,et al.  A Kinetic View of Statistical Physics , 2010 .

[14]  C. Hoogenraad,et al.  Microtubule-based transport – basic mechanisms, traffic rules and role in neurological pathogenesis , 2013, Journal of Cell Science.

[15]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[16]  O. B'enichou,et al.  Propagators of random walks on comb lattices of arbitrary dimension , 2016, 1602.03477.

[17]  S. Majumdar,et al.  Winding statistics of a Brownian particle on a ring , 2014, 1406.0419.

[18]  R. Guyer.  Diffusion on the Sierpiński gaskets: A random walker on a fractally structured object , 1984 .

[19]  Zhi-Xi Wu,et al.  Walks on Apollonian networks , 2006, cond-mat/0601357.

[20]  Marijonas Bogdevičius,et al.  Mathematical modelling of network traffic flow , 2009 .

[21]  R. Goldstein,et al.  Cytoplasmic streaming in Drosophila oocytes varies with kinesin activity and correlates with the microtubule cytoskeleton architecture , 2012, Proceedings of the National Academy of Sciences.

[22]  S. Redner.  A guide to first-passage processes , 2001 .

[23]  A. Aman,et al.  Cell migration during morphogenesis. , 2010, Developmental biology.

[24]  Yuan Jin,et al.  Modeling and Simulation of Mucus Flow in Human Bronchial Epithelial Cell Cultures – Part I: Idealized Axisymmetric Swirling Flow , 2016, PLoS Comput. Biol..

[25]  Elena Agliari,et al.  Two-particle problem in comblike structures. , 2016, Physical review. E.

[26]  O Bénichou,et al.  Diffusion and Subdiffusion of Interacting Particles on Comblike Structures. , 2015, Physical review letters.

[27]  Anomalous diffusion and Hall effect on comb lattices. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Nelson,et al.  Vortex entanglement in high-Tc superconductors. , 1988, Physical review letters.

[29]  P. Bressloff,et al.  Stochastic models of intracellular transport , 2013 .

[30]  Hilfer,et al.  Fractional master equations and fractal time random walks. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  K. Hoffmann,et al.  Random walks of oriented particles on fractals , 2014 .

[32]  Jim Pitman,et al.  On Walsh's Brownian motions , 1989 .

[33]  Karthik K. Srinivasan,et al.  Study of traffic flow characteristics using different vehicle-following models under mixed traffic conditions , 2018 .

[34]  R. Granek,et al.  Active transport on disordered microtubule networks: the generalized random velocity model. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  J. Rudnick,et al.  The winding angle distribution of an ordinary random walk , 1987 .

[36]  Benoit B. Mandelbrot,et al.  Critical Phenomena on Fractal Lattices , 1980 .