Power Levy motion. I. Diffusion

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2025, Volume and Issue: 35(3)

Published: March 1, 2025

Recently introduced and explored, power Brownian motion (PBM) is a versatile generalization of motion: it Markovian on the one hand displays variety anomalous-diffusion behaviors other hand. universal scaling-limit finite-variance random walks. Shifting from realm to infinite-variance realm, counterpart Levy stable symmetric process. This pair papers introduces explores (PLM), which what PBM motion. first part constructs PLM explains its emergence rationale. Taking “diffusion perspective,” this addresses following facets features PLM: increments their Fourier structure, selfsimilarity Hurst exponent, sub-diffusion super-diffusion, aging anti-aging, Holder exponent. an “evolution second will continue investigation PLM.

Language: Английский

---

Concentration-dependent anomalous diffusion of crystal violet dye in agar gel: application of the continuous time random walk model

Physical Chemistry Chemical Physics, Journal Year: 2025, Volume and Issue: unknown

Published: Jan. 1, 2025

The transport of materials is fundamental importance, with studies on diffusion being at the forefront. Diffusion in a simple matrix typically considered Fickian. However, anomalous various media dominant process. It well documented that results from medium heterogeneity, extreme events, phase transitions, surface dynamics, and other factors. present work demonstrated cationic dye (crystal violet, CV) an agar gel was anomalous, as shown by spatial time-series data movement. We estimated classical coefficients using Einstein-Smoluchowski solution to Fick's law, but these did not yield consistent Gaussianity, stationarity, or non-seasonality. confirmed modelling experimental data. exponent values (α) ranged 0.468 ± 0.027 0.883 0.107, indicating sub-diffusion depended concentration CV same medium. then evaluated time- ensemble-averaged mean squared displacement dye-spreading via image processing. discrepancy distribution functions over long period highlighted non-ergodic nature stochastic dimensionless ergodicity-breaking parameter evaluated, confirming found continuous time random walk (CTRW) model well-suited for describing this system. attributed violations assumptions Brownian motion particles diffusing

Language: Английский

---

Power Brownian motion

Journal of Physics A Mathematical and Theoretical, Journal Year: 2023, Volume and Issue: 57(3), P. 03LT01 - 03LT01

Published: Dec. 19, 2023

Abstract Brownian motion (BM) is the archetypal model of regular diffusion. BM a Gaussian and Markov process, whose increments are stationary, non-overlapping independent. Elevating from diffusion to anomalous diffusion, fractional (FBM) scaled (SBM) arguably two most popular anomalous-diffusion models. Each these models maintains some properties, abandons other, displays certain behaviors. This paper explores model— Power Motion (PBM)—that attained by coupled amplitudal temporal ‘tinkering’ with BM. The PBM combines ‘the better FBM SBM’. Indeed, as FBM, behaviors persistence anti-persistence. And, SBM, process that aging anti-aging. On their own, neither nor SBM can provide ‘features package’ provides. on one hand, its simple construction other render compelling model.

Language: Английский

---

Designing selfsimilar diffusions

Physica A Statistical Mechanics and its Applications, Journal Year: 2024, Volume and Issue: 658, P. 130270 - 130270

Published: Dec. 11, 2024

---