Stochastic modelling of fractal diffusion and dimension estimation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00359821" target="_blank" >RIV/68407700:21340/22:00359821 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.physa.2022.127624" target="_blank" >https://doi.org/10.1016/j.physa.2022.127624</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.physa.2022.127624" target="_blank" >10.1016/j.physa.2022.127624</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Stochastic modelling of fractal diffusion and dimension estimation

Popis výsledku v původním jazyce

The revision of classical methods for spectral and walk dimension estimates is the main aim of the paper. Being focused on the unbiased estimation of the walk and spectral dimensions, we aim to construct the estimates with the minimal mean square error. Accompanied simulation experiments are performed on finite substrates, spacial structures serving as a good model of both continuum and fractal sets. We compare the classical approach based on the log-log transform of asymptotic models of returning probabilities and the second moments, and we also develop a weighted approach to improve the statistical properties of dimension estimates. The other discussed aspect is whether to simulate diffusion using the classical graph diffusion model with zero probability of staying in the same vertex or to prefer the physically motivated model of diffusion over edges with the optimal value of jump probability. Finally, we present the results of simulation experiments on two-dimensional finite substrates which approximate the continuum and selected Sierpinski gaskets and carpets. The paper also summarises general suggestions based on the obtained results from the simulation experiments.

Název v anglickém jazyce

Stochastic modelling of fractal diffusion and dimension estimation

Popis výsledku anglicky

The revision of classical methods for spectral and walk dimension estimates is the main aim of the paper. Being focused on the unbiased estimation of the walk and spectral dimensions, we aim to construct the estimates with the minimal mean square error. Accompanied simulation experiments are performed on finite substrates, spacial structures serving as a good model of both continuum and fractal sets. We compare the classical approach based on the log-log transform of asymptotic models of returning probabilities and the second moments, and we also develop a weighted approach to improve the statistical properties of dimension estimates. The other discussed aspect is whether to simulate diffusion using the classical graph diffusion model with zero probability of staying in the same vertex or to prefer the physically motivated model of diffusion over edges with the optimal value of jump probability. Finally, we present the results of simulation experiments on two-dimensional finite substrates which approximate the continuum and selected Sierpinski gaskets and carpets. The paper also summarises general suggestions based on the obtained results from the simulation experiments.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Výzkumné centrum informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Physica A: Statistical Mechanics and Its Applications

ISSN

0378-4371

e-ISSN

1873-2119

Svazek periodika

602

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

—

Kód UT WoS článku

000830512800005

EID výsledku v databázi Scopus

2-s2.0-85131450048