Erratum: “Boundary conditions and trajectories of diffusion processes” [J. Chem. Phys. 117, 2469 (2002)]

2002 ◽  
Vol 117 (16) ◽  
pp. 7815-7815
Author(s):  
Mark F. Schumaker
Keyword(s):  
Boundary Conditions ◽  
Diffusion Processes ◽  
Chem Phys

Calculations of Phase Transformations in Welding Simulations

2014 ◽  
Vol 611 ◽  
pp. 46-53 ◽  
Author(s):  
Ladislav Novotný ◽  
Vladimír Ivančo
Keyword(s):  
Heat Flux ◽  
Phase Transformation ◽  
Boundary Conditions ◽  
Phase Transformations ◽  
Diffusion Processes ◽  
Transient Solution ◽  
Welding Simulation

In the paper the principle of welding simulation is presented and the methods of solution of phase transformation are described. The first part characterizes elementary equations of heat transient solution, boundary conditions during welding simulation (prescribing moving heat flux, convection, radiation). The methods of phase transformations’ solution are described for diffusion processes as well as diffusionless processes.

scholarly journals Integrated Time-Fractional Diffusion Processes for Fractional-Order Chaos-Based Image Encryption

Sensors ◽  
2021 ◽  
Vol 21 (20) ◽  
pp. 6838
Author(s):  
Fudong Ge ◽  
Zufa Qin ◽  
YangQuan Chen
Keyword(s):  
Boundary Conditions ◽  
Image Encryption ◽  
Fractional Order ◽  
Diffusion Processes ◽  
Fractional Diffusion ◽  
Spatiotemporal Chaos ◽  
Diffusion System ◽  
Encryption Algorithm ◽  
Secret Key ◽  
Image Encryption Algorithm

The purpose of this paper is to explore a novel image encryption algorithm that is developed by combining the fractional-order Chua’s system and the 1D time-fractional diffusion system of order α∈(0,1]. To this end, we first discuss basic properties of the fractional-order Chua’s system and the 1D time-fractional diffusion system. After these, a new spatiotemporal chaos-based cryptosystem is proposed by designing the chaotic sequence of the fractional-order Chua’s system as the initial condition and the boundary conditions of the studied time-fractional diffusion system. It is shown that the proposed image encryption algorithm can gain excellent encryption performance with the properties of larger secret key space, higher sensitivity to initial-boundary conditions, better random-like sequence and faster encryption speed. Efficiency and reliability of the given encryption algorithm are finally illustrated by a computer experiment with detailed security analysis.

scholarly journals The First Passage Time and the Dividend Value Function for One-Dimensional Diffusion Processes between Two Reflecting Barriers

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Chuancun Yin ◽  
Huiqing Wang
Keyword(s):  
Boundary Conditions ◽  
Value Function ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
The Laplace Transform ◽  
The Value Function ◽  
Reflecting Barriers

We consider the general one-dimensional time-homogeneous regular diffusion process between two reflecting barriers. An approach based on the Itô formula with corresponding boundary conditions allows us to derive the differential equations with boundary conditions for the Laplace transform of the first passage time and the value function. As examples, the explicit solutions of them for several popular diffusions are obtained. In addition, some applications to risk theory are considered.

Diffusion processes with boundary conditions

1971 ◽  
Vol 24 (2) ◽  
pp. 147-225 ◽  
Author(s):  
Daniel W. Stroock ◽  
S. R. S. Varadhan
Keyword(s):  
Boundary Conditions ◽  
Diffusion Processes

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Formulation of Boundary Conditions in Flow Systems

1994 ◽  
Vol 59 (2) ◽  
pp. 345-358
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Libor Vejmola
Keyword(s):  
Boundary Conditions ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Dispersion Model ◽  
Point Of View ◽  
General Point ◽  
Engineering Systems ◽  
Boundary Conditions For Diffusion ◽  
Flow Through ◽  
The One

Problems associated with the formulation of the boundary conditions for diffusion equations describing flow-through chemical-engineering systems from the point of view of stochastic process theory are discussed. An approach to modelling such systems is presented, allowing the one-dimensional diffusion (dispersion) model of a continuous flow mixer, commonly used in chemical engineering, to be reassessed from a rather general point of view.

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