scholarly journals Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric

2015 ◽  
Vol 18 (2) ◽  
pp. 14-20
Author(s):  
Dung Anh Tran ◽  
Hang Thi Chu ◽  
Long Ta Bui
Keyword(s):  
Differential Equation ◽  
Bessel Function ◽  
Bessel Functions ◽  
Analytic Solutions ◽  
Air Pollutant ◽  
Spherical Coordinates ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Bessel Differential Equation ◽  
Separation Of Variable

The Bessel differential equation with the Bessel function of solution has been applied. Bessel functions are the canonical solutions of Bessel's differential equation. Bessel's equation arises when finding separable solutions to Laplace's equation in cylindrical or spherical coordinates. Bessel functions are important for many problems of advection–diffusion progress and wave propagation. In this paper, authors present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation of variable method and Bessel’s equation.

scholarly journals Starlikeness of Normalized Bessel Functions with Symmetric Points

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Maryam Nazir ◽  
Syed Zakar Hussain Bukhari ◽  
Imtiaz Ahmad ◽  
Muhammad Ashfaq ◽  
Malik Ali Raza
Keyword(s):  
Differential Equation ◽  
Bessel Functions ◽  
Starlike Functions ◽  
Radius Of Starlikeness ◽  
Bessel Differential Equation ◽  
Symmetric Points

Bessel functions are related with the known Bessel differential equation. In this paper, we determine the radius of starlikeness for starlike functions with symmetric points involving Bessel functions of the first kind for some kinds of normalized conditions. Our prime tool in these investigations is the Mittag-Leffler representation of Bessel functions of the first kind.

scholarly journals Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Y. Z. Povstenko
Keyword(s):  
Diffusion Equation ◽  
Half Plane ◽  
Bessel Functions ◽  
Fourier Transforms ◽  
Integral Transform ◽  
Fundamental Solutions ◽  
Numerical Results ◽  
Dirichlet Problems ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

The fundamental solutions to time-fractional advection diffusion equation in a plane and a half-plane are obtained using the Laplace integral transform with respect to timetand the Fourier transforms with respect to the space coordinatesxandy. The Cauchy, source, and Dirichlet problems are investigated. The solutions are expressed in terms of integrals of Bessel functions combined with Mittag-Leffler functions. Numerical results are illustrated graphically.

scholarly journals Aplikasi Persamaan Bessel Orde Nol Pada Persamaan Panas Dua Dimensi

2013 ◽  
Vol 2 (2) ◽  
pp. 113
Author(s):  
Annisa Eki Mulyati ◽  
Sugiyanto Sugiyanto
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equations ◽  
Bessel Function ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Two Dimensional ◽  
Modified Bessel Function ◽  
Order Zero ◽  
Bessel Differential Equation

Bessel differential equation is one of the applied equation in physics is about heat transfer. Application of modified Bessel function of order zero on heat transfer process of two-dimensional objects which can be modelled in the form of a two-order partial differential equations as follows, ..... With the obtained solutions of Bessel's differential equation application of circular fin, ....   two-dimensional temperature stated on the point .....  against time t

scholarly journals On nabla discrete fractional calculus operator for a modified Bessel equation

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 203-209 ◽  
Author(s):  
Resat Yilmazer ◽  
Okkes Ozturk
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Bessel Functions ◽  
Discrete Fractional Calculus ◽  
Bessel Beams ◽  
Bessel Equation ◽  
Bessel Differential Equation ◽  
Thermal Sciences

In thermal sciences, it is possible to encounter topics such as Bessel beams, Bessel functions or Bessel equations. In this work, we also present new discrete fractional solutions of the modified Bessel differential equation by means of the nabla-discrete fractional calculus operator. We consider homogeneous and non-homogeneous modified Bessel differential equation. So, we acquire four new solutions of these equations in the discrete fractional forms via a newly developed method

scholarly journals The Bessel function J 0 in fractional differential equations

2021 ◽  
Vol 2090 (1) ◽  
pp. 012093
Author(s):  
Jorge Olivares Funes ◽  
Elvis Valero Kari ◽  
Pablo Martin
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Bessel Function ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Bessel Functions ◽  
Error Function ◽  
Fractional Differential

Abstract Spherical Bessel functions have many important applications in engineering, optic and science. In this work, wich is a continuation of the error function in fractional differential equations, it is shown how solve the fractional differential equation d α y d x α = j 0 ( x ) , y ( k ) ( 0 ) = 0 , k = 0 , … m − 1 ,   with m − 1 < α ≤ m , m ∈ Ν , where the nonhomogenous part is the function Bessel spherical J 0(x).

scholarly journals Global heat balance and heat uptake in potential temperature coordinates

2021 ◽  
Author(s):  
Antoine Hochet ◽  
Rémi Tailleux ◽  
Till Kuhlbrodt ◽  
David Ferreira
Keyword(s):  
Global Warming ◽  
Water Mass ◽  
Potential Temperature ◽  
Effective Diffusion ◽  
Mitigation Strategies ◽  
Ocean Heat Uptake ◽  
Cold Temperatures ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Heat Uptake

AbstractThe representation of ocean heat uptake in Simple Climate Models used for policy advice on climate change mitigation strategies is often based on variants of the one-dimensional Vertical Advection/Diffusion equation (VAD) for some averaged form of potential temperature. In such models, the effective advection and turbulent diffusion are usually tuned to emulate the behaviour of a given target climate model. However, because the statistical nature of such a “behavioural” calibration usually obscures the exact dependence of the effective diffusion and advection on the actual physical processes responsible for ocean heat uptake, it is difficult to understand its limitations and how to go about improving VADs. This paper proposes a physical calibration of the VAD that aims to provide explicit traceability of effective diffusion and advection to the processes responsible for ocean heat uptake. This construction relies on the coarse-graining of the full three-dimensional advection diffusion for potential temperature using potential temperature coordinates. The main advantage of this formulation is that the temporal evolution of the reference temperature profile is entirely due to the competition between effective diffusivity that is always positive definite, and the water mass transformation taking place at the surface, as in classical water mass analyses literature. These quantities are evaluated in numerical simulations of present day climate and global warming experiments. In this framework, the heat uptake in the global warming experiment is attributed to the increase of surface heat flux at low latitudes, its decrease at high latitudes and to the redistribution of heat toward cold temperatures made by diffusive flux.

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