Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = middle-τ Cantor sets

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
12 pages, 520 KB  
Article
Statistical Mechanics Involving Fractal Temperature
by Alireza Khalili Golmankhaneh
Fractal Fract. 2019, 3(2), 20; https://doi.org/10.3390/fractalfract3020020 - 17 Apr 2019
Cited by 13 | Viewed by 4017
Abstract
In this paper, the Schrödinger equation involving a fractal time derivative is solved and corresponding eigenvalues and eigenfunctions are given. A partition function for fractal eigenvalues is defined. For generalizing thermodynamics, fractal temperature is considered, and adapted equations are defined. As an application, [...] Read more.
In this paper, the Schrödinger equation involving a fractal time derivative is solved and corresponding eigenvalues and eigenfunctions are given. A partition function for fractal eigenvalues is defined. For generalizing thermodynamics, fractal temperature is considered, and adapted equations are defined. As an application, we present fractal Dulong-Petit, Debye, and Einstein solid models and corresponding fractal heat capacity. Furthermore, the density of states for fractal spaces with fractional dimension is obtained. Graphs and examples are given to show details. Full article
Show Figures

Figure 1

9 pages, 364 KB  
Article
On the Fractal Langevin Equation
by Alireza Khalili Golmankhaneh
Fractal Fract. 2019, 3(1), 11; https://doi.org/10.3390/fractalfract3010011 - 13 Mar 2019
Cited by 17 | Viewed by 3318
Abstract
In this paper, fractal stochastic Langevin equations are suggested, providing a mathematical model for random walks on the middle- τ Cantor set. The fractal mean square displacement of different random walks on the middle- τ Cantor set are presented. Fractal under-damped and over-damped [...] Read more.
In this paper, fractal stochastic Langevin equations are suggested, providing a mathematical model for random walks on the middle- τ Cantor set. The fractal mean square displacement of different random walks on the middle- τ Cantor set are presented. Fractal under-damped and over-damped Langevin equations, fractal scaled Brownian motion, and ultra-slow fractal scaled Brownian motion are suggested and the corresponding fractal mean square displacements are obtained. The results are plotted to show the details. Full article
Show Figures

Figure 1

Back to TopTop