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Fractal Brownian Motion of Colloidal Particles in Plasma
AbstractExperimental data on the motion of a single colloidal particle in a trap in the near-electrode layer of an RF-discharge plasma are analyzed....
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Fractal-view analysis of local fractional Fokker–Planck equation occurring in modelling of particle’s Brownian motion
In this paper, the solution and behaviour of local fractional Fokker–Planck equation (LFFPE) is investigated in fractal media. For this purpose, the...
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Hot Brownian Motion
The chapter deals with hot Brownian particles and swimmers as two examples for Brownian motion very far from equilibrium. Thanks to the strong scale...
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Self-Organization of Clusters of Active Brownian Particles in a Colloidal Plasma under the Action of Laser Radiation
AbstractClusters of active Brownian particles in gas-discharge plasma are considered as open systems with energy exchange with the environment. The...
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Random Walks on Mated-CRT Planar Maps and Liouville Brownian Motion
We prove a scaling limit result for random walk on certain random planar maps with its natural time parametrization. In particular, we show that for
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Modeling of the Processes of Formation of Dust Fractal Clusters in a Protoplanetary Cloud
AbstractProceeding from the concept of the fractal nature of dust clusters, we develop an evolutionary hydrodynamic model of the formation and growth...
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Interrelation Between the Fractional Dimensions of Measurands and Fractal Dimensions
The article examines the possibility of an informal relationship between the two concepts of dimensions — dimension of the measurand and the fractal...
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Analysis of the Fractal Structure of Rough Friction Surfaces to Establish Transient Regimes of Frictional Contact
AbstractIt is shown that friction fracture surfaces can be self-affine with a local fractal dimension. However, the intersection of such a...
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Regularities of the Formation of Fractal Structures on the Surface of Metallic Films of Different Thicknesses
AbstractThe surface morphology of nanosized copper and nickel films on mica has been studied on a scanning tunneling microscope. The height...
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The Brownian loop soup stress-energy tensor
The Brownian loop soup (BLS) is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity λ > 0....
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Comparative analysis of fractal dimension of CdS, CdZnS and CdZnS:Ce thin films
CdS, CdZnS, and CdZnS:Ce thin films are prepared by using the chemical bath deposition (CBD) technique. Thin films were prepared on glass substrates....
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Laplace equations on the fractal cubes and Casimir effect
In this paper, we have generalized fractal calculus on fractal Cantor cubes. The mass function on fractal Cantor cubes is defined. Then, we use the...
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Energy Spectrum of 3D Velocity Field Generated by Ensemble of Semi-fractal Vortex Loops
AbstractThe energy spectra E(k) of a three-dimensional velocity field induced by a set of vortex loops of different sizes and semi-fractal structure...
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The concept of velocity in the history of Brownian motion
Interest in Brownian motion was shared by different communities: this phenomenon was first observed by the botanist Robert Brown in 1827, then...
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Scalar Conformal Primary Fields in the Brownian Loop Soup
The Brownian loop soup is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity
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Effective de Sitter space, quantum behaviour and large-scale spectral dimension (3+1)
De Sitter space-time, essentially our own universe, is plagued by problems at the quantum level. Here we propose that Lorentzian de Sitter space-time...
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Introduction
Owing to their small size, advanced position detection possibilities, and accurate theoretical description, optically trapped microspheres have...