AN HYPOTHESIS CONCERNING TURBULENT DIFFUSION

1960 ◽  
Vol 38 (5) ◽  
pp. 665-676 ◽  
Author(s):  
R. Bourret
Keyword(s):  
Differential Equation ◽  
Stochastic Model ◽  
Autocorrelation Function ◽  
Concentration Gradient ◽  
Turbulent Diffusion ◽  
Irreversible Thermodynamic ◽  
Integro Differential Equation ◽  
History Of ◽  
Hereditary Function ◽  
Thermodynamic Processes

It is shown that the Goldstein equation for turbulent diffusion implies diffusion currents dependent upon the history of the concentration gradient. An analysis of the stochastic model upon which the Goldstein equation is based reveals that the hereditary function, by which the history is weighted, is the ensemble autocorrelation function of velocity. Heuristic arguments and an appeal to the theory of irreversible thermodynamic processes lead to the postulation of an integro-differential equation for turbulent diffusion involving the velocity autocorrelations of the diffusate particles.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

Stochastic Modelling of Particle Segregation in a Horizontal Drum Mixer

1992 ◽  
Vol 57 (10) ◽  
pp. 2100-2112 ◽  
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Andrzej Rochowiecki
Keyword(s):  
Differential Equation ◽  
Diffusion Coefficient ◽  
Stochastic Model ◽  
Diffusion Process ◽  
Stochastic Modelling ◽  
Solid Particles ◽  
Kolmogorov Equation ◽  
Particle Segregation ◽  
Drum Mixer ◽  
Horizontal Drum

A process of segregation of two distinct fractions of solid particles in a rotating horizontal drum mixer was described by stochastic model assuming the segregation to be a diffusion process with varying diffusion coefficient. The model is based on description of motion of particles inside the mixer by means of a stochastic differential equation. Results of stochastic modelling were compared to the solution of the corresponding Kolmogorov equation and to results of earlier carried out experiments.

THE FORWARD PDE FOR EUROPEAN OPTIONS ON STOCKS WITH FIXED FRACTIONAL JUMPS

2005 ◽  
Vol 08 (02) ◽  
pp. 239-253 ◽  
Author(s):  
PETER CARR ◽  
ALIREZA JAVAHERI
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Stock Price ◽  
Arrival Rate ◽  
European Options ◽  
Standard Assumption ◽  
Integro Differential Equation ◽  
Local Variance ◽  
Calendar Dates

We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward local default arrival rate. We then specialize to the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-jump value. This is a standard assumption when valuing an option written on a stock which can default. We discuss novel strategies for calibrating to a term and strike structure of European options prices. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

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