scholarly journals Random walk analysis of cave maps for exemplary gypsum caves-mazes of Western Ukraine

2018 ◽  
Vol 36 ◽  
pp. 3-8
Author(s):  
Tomasz Błachowicz ◽  
Viacheslav Andreychouk ◽  
Krzysztof Domino
Keyword(s):  
Random Walk ◽  
Hurst Exponent ◽  
New Method ◽  
Western Ukraine ◽  
Random Walk Analysis

The paper presents a new method of quantitative parameterization of net geomorphological structures with the use of random walk formalism and an analysis of Hurst exponent distribution derived from random walk experiments. As examples, horizontally developed gypsum caves were elaborated. The provided methodology is able to uniquely characterize cave systems.

Schramm–Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes

2018 ◽  
Vol 29 (01) ◽  
pp. 1850008 ◽  
Author(s):  
N. Posé ◽  
K. J. Schrenk ◽  
N. A. M. Araújo ◽  
H. J. Herrmann
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Long Range ◽  
Hurst Exponent ◽  
Diffusion Constant ◽  
Strongly Correlated ◽  
Loewner Evolution ◽  
Positive Formula ◽  
Practical Implications ◽  
Negative Formula

Real landscapes exhibit long-range height–height correlations, which are quantified by the Hurst exponent [Formula: see text]. We give evidence that for negative [Formula: see text], in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm–Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for [Formula: see text] and [Formula: see text] and a conjecture is proposed for the values in between. By contrast, for positive [Formula: see text], we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.

Numerical simulation of contaminant dispersion in estuary flows

1982 ◽  
Vol 381 (1780) ◽  
pp. 179-194 ◽  
Keyword(s):  
Numerical Simulation ◽  
Random Walk ◽  
Shear Flow ◽  
Diffusion Equation ◽  
New Method ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Turbulent Shear Flow ◽  
Oscillatory Flows ◽  
Contaminant Dispersion

The paper examines in detail the dispersion of a passive contaminant in steady and oscillatory turbulent shear flow in a two-dimensional channel. The aim of this examination is to understand dispersion in estuaries. A new method of analysing and predicting concentration distributions has been developed from work of Sullivan ( J. Fluid Mech . 49, 551–576 (1971)). A random walk technique is used, the contaminant being represented by a large number of marked particles whose paths are tracked as they move through the fluid. The technique seeks to model the physics of dispersion more realistically than the standard diffusion equation, and results from the simulation, with input based on data taken in the Mersey, show it to be a useful and versatile method of studying dispersion in oscillatory flows.

scholarly journals Limit profiles for reversible Markov chains

2021 ◽  
Author(s):  
Evita Nestoridi ◽  
Sam Olesker-Taylor
Keyword(s):  
Random Walk ◽  
Markov Chains ◽  
Random Walks ◽  
Gibbs Sampler ◽  
Statistical Physics ◽  
Homogeneous Spaces ◽  
New Method ◽  
Reversible Markov Chains ◽  
Similar Approximation ◽  
Random Transpositions

AbstractIn a recent breakthrough, Teyssier (Ann Probab 48(5):2323–2343, 2020) introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacy-invariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous spaces and for general reversible Markov chains. We illustrate applications of these lemmas to some famous problems: the k-cycle shuffle, sharpening results of Hough (Probab Theory Relat Fields 165(1–2):447–482, 2016) and Berestycki, Schramm and Zeitouni (Ann Probab 39(5):1815–1843, 2011), the Ehrenfest urn diffusion with many urns, sharpening results of Ceccherini-Silberstein, Scarabotti and Tolli  (J Math Sci 141(2):1182–1229, 2007), a Gibbs sampler, which is a fundamental tool in statistical physics, with Binomial prior and hypergeometric posterior, sharpening results of Diaconis, Khare and Saloff-Coste (Stat Sci 23(2):151–178, 2008).

scholarly journals The response of human neutrophils to a chemotactic tripeptide (N-formyl- methionyl-leucyl-phenylalanine) studied by microcinematography

Blood ◽  
1984 ◽  
Vol 64 (1) ◽  
pp. 221-228 ◽  
Author(s):  
J Maher ◽  
JV Martell ◽  
BA Brantley ◽  
EB Cox ◽  
JE Niedel ◽  
...  
Keyword(s):  
Random Walk ◽  
Cell Surface ◽  
Linear Displacement ◽  
Human Neutrophils ◽  
Human Granulocytes ◽  
Stimulation Of ◽  
Random Walk Analysis ◽  
Cellular Motion

A quantitative microcinematographic technique for the measurement of cellular motion in response to chemical influences is described. The data are analyzed by using a magnetic digitizer connected to a computer, permitting comparison of several characteristics of such motion. When human granulocytes are placed in a gradient of formyl- methionyl-leucyl-phenylalanine (fMLP) (concentration 10(-6)-10(-8) mol/L) against buffer, the motion of the cells is increased in velocity (chemokinesis) and is directed toward the chemoattractant, as measured by the orientation of the vector of motion. This directionality is confirmed by positive values for the McCutcheon index and analysis of directed linear displacement. Concentrations of fMLP below 10(-9) mol/L did not result in chemokinesis or chemotaxis, presumably due to insufficient stimulus. Concentrations of 10(-6) mol/L fMLP and greater resulted in marked stimulation of the cell surface but reduced directionality and velocity of motion compared with cells in a more optimal gradient. Motion of the unstimulated cells tended to be ortholinear , and this was not increased by the presence of a gradient of fMLP. Hence, as previously shown, the Random Walk analysis, which does not give weight to the direction of motion, is not useful in the analysis of the response of these cells to a chemotaxin in this system.

scholarly journals Effect of colloids on non-Fickian transport of strontium in sediments elucidated by continuous-time random walk analysis

2019 ◽  
Vol 252 ◽  
pp. 1491-1499 ◽  
Author(s):  
Dong-Xu Liu ◽  
Rui Zuo ◽  
Andrey P. Jivkov ◽  
Jin-Sheng Wang ◽  
Li-Tang Hu ◽  
...  
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Random Walk Analysis

Random walk analysis of time-resolved transmittance measurements

2003 ◽  
Author(s):  
Ines Delfino ◽  
Maria Lepore ◽  
Pietro L. Indovina
Keyword(s):  
Random Walk ◽  
Time Resolved ◽  
Random Walk Analysis
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