Sound energy decay in coupled spaces using a parametric analytical solution of a diffusion equation

2014 ◽  
Vol 135 (5) ◽  
pp. 2765-2776 ◽  
Author(s):  
Paul Luizard ◽  
Jean-Dominique Polack ◽  
Brian F. G. Katz
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Energy Decay ◽  
Sound Energy

Anomalous diffusion equation using a new general fractional derivative within the Miller–Ross kernel

2020 ◽  
Vol 34 (27) ◽  
pp. 2050289
Author(s):  
Yiying Feng ◽  
Jiangen Liu
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Anomalous Diffusion ◽  
Fractional Integral ◽  
Liouville Type

In view of the generalization of Miller–Ross kernel in the sense of Riemann–Liouville type, we propose the new definitions of the general fractional integral (GFI) and general fractional derivative (GFD) to discuss the anomalous diffusion equation, which is distinct from those classic calculus operators. The obtained analytical solution of the application described in the graph is effective and accurate making the use of Laplace transform.

An Analytical Methodology to Air Pollution Modelling in Atmosphere

2019 ◽  
Vol 396 ◽  
pp. 91-98 ◽  
Author(s):  
Régis S. Quadros ◽  
Glênio A. Gonçalves ◽  
Daniela Buske ◽  
Guilherme J. Weymar
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Numerical Inversion ◽  
Analytical Methodology ◽  
Air Pollution Modelling ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Using Data

This work presents an analytical solution for the transient three-dimensional advection-diffusion equation to simulate the dispersion of pollutants in the atmosphere. The solution of the advection-diffusion equation is obtained analytically using a combination of the methods of separation of variables and GILTT. The main advantage is that the presented solution avoids a numerical inversion carried out in previous works of the literature, being by this way a totally analytical solution, less than a summation truncation. Initial numerical simulations and statistical comparisons using data from the Copenhagen experiment are presented and prove the good performance of the model.

scholarly journals P-Fuzzy Diffusion Equation Using Rules Base

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jefferson Leite ◽  
R. C. Bassanezi ◽  
Jackellyne Leite ◽  
Moiseis Cecconello
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Fuzzy System ◽  
Classical Diffusion

We propose a fuzzy system that simulates dispersion of individuals whose movements are described by diffusion. We will use only the position of the population as an input variable for describing the process. We emphasize that the classical diffusion equation along with its analytical solution in no time was used for obtaining our solution.

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