scholarly journals DNA Nano Devices as a Biased Random Walk Process: A Case Study of Isothermal Ratchet?

2015 ◽  
Vol 06 (05) ◽  
pp. 401-419
Author(s):  
Jean-Pierre Aimé ◽  
Juan Elezgaray
Keyword(s):  
Random Walk ◽  
Random Walk Process ◽  
Biased Random Walk

scholarly journals The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree

10.37236/8327 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Tony Johansson
Keyword(s):  
Random Walk ◽  
Regular Graph ◽  
Vertex Cover ◽  
Random Walk Process ◽  
Cover Time ◽  
Edge Cover ◽  
Biased Random Walk ◽  
Random Regular Graph ◽  
Odd Degree ◽  
Leading Term

We consider a random walk process on graphs introduced by Orenshtein and Shinkar (2014). At any time, the random walk moves from its current position along a previously unvisited edge chosen uniformly at random, if such an edge exists. Otherwise, it walks along a previously visited edge chosen uniformly at random. For the random $r$-regular graph, with $r$ a constant odd integer, we show that this random walk process has asymptotic vertex and edge cover times $\frac{1}{r-2}n\log n$ and $\frac{r}{2(r-2)}n\log n$, respectively, generalizing a result of Cooper, Frieze and the author (2018) from $r = 3$ to any odd $r\geqslant 3$. The leading term of the asymptotic vertex cover time is now known for all fixed $r\geqslant 3$, with Berenbrink, Cooper and Friedetzky (2015) having shown that $G_r$ has vertex cover time asymptotic to $\frac{rn}{2}$ when $r\geqslant 4$ is even.

One-step random-walk process of nanoparticles in cement-based materials

2021 ◽  
Vol 28 (6) ◽  
pp. 1679-1691
Author(s):  
Ali Bahari ◽  
Aref Sadeghi-Nik ◽  
Elena Cerro-Prada ◽  
Adel Sadeghi-Nik ◽  
Mandana Roodbari ◽  
...  
Keyword(s):  
Random Walk ◽  
Random Walk Process ◽  
Cement Based Materials ◽  
One Step

A Biased Random Walk with Symmetry

1992 ◽  
Vol 65 (5) ◽  
pp. 330
Author(s):  
J. N. Boyd ◽  
P. N. Raychowdhury
Keyword(s):  
Random Walk ◽  
Biased Random Walk

COMPUTATIONAL INVESTIGATION OF THE EFFECTS OF SPHERICAL FILLER MORPHOLOGY AND LOADING ON DIFFUSION TORTUOSITY AND RUBBER PERMEABILITY

2013 ◽  
Vol 86 (2) ◽  
pp. 175-189 ◽  
Author(s):  
T. C. Gruber ◽  
S. D. Crossley ◽  
A. P. Smith
Keyword(s):  
Random Walk ◽  
Rolling Resistance ◽  
Diffusion Path ◽  
Filler Loading ◽  
Pressure Losses ◽  
Biased Random Walk ◽  
Gas Molecule ◽  
Path Lengths ◽  
Path Tortuosity ◽  
Spherical Filler

ABSTRACT Inflation pressure loss in tires degrades performance, raises rolling resistance, and reduces fuel economy. The incorporation of solid fillers, such as carbon black, at relatively high loadings in tire innerliners helps minimize these pressure losses by reducing innerliner permeability due to increases in average gas molecule diffusion path lengths (tortuosity), as well as reductions in diffusion pathway density (capacity). The effects of filler morphology and loading on diffusion path tortuosity can be explored by modeling biased random-walk diffusion through impermeable sphere-filled matrices. Modeled diffusion rate was found to decrease with increased filler loading, reduced filler sphere sizes, increased random-walk step sizes, and the aggregation of filler spheres. Initial correlations with limited empirical permeability measurements are used to validate the model approach.

A Biased Random Walk with Symmetry

1992 ◽  
Vol 65 (5) ◽  
pp. 330-333
Author(s):  
J. N. Boyd ◽  
P. N. Raychowdhury
Keyword(s):  
Random Walk ◽  
Biased Random Walk
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