On the Behavior of the Invariant Measure of a Diffusion Process with Small Diffusion on a Circle

1964 ◽  
Vol 9 (1) ◽  
pp. 125-131 ◽  
Author(s):  
M. B. Nevel’son
Keyword(s):  
Invariant Measure ◽  
Diffusion Process ◽  
Small Diffusion

scholarly journals On recurrent properties of Fisher--Wright's diffusion on (0,1) with mutation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Roman Sineokiy ◽  
Alexander Veretennikov
Keyword(s):  
Population Genetics ◽  
Invariant Measure ◽  
Diffusion Process ◽  
Rate Of Convergence ◽  
Exponential Rate ◽  
One Dimensional ◽  
Exponential Rate Of Convergence

Abstract A one-dimensional Fisher–Wright diffusion process on the interval ( 0 , 1 ) {(0,1)} with mutations is considered. This is a widely known model in population genetics. The goal of this paper is an exponential recurrence of the process, which also implies an exponential rate of convergence towards the invariant measure.

scholarly journals Asymptotic dissipativity of the diffusion process in the asymptotic small diffusion scheme

2015 ◽  
Vol 14 (4) ◽  
pp. 93-103
Author(s):  
Anastasiia Kinash ◽  
◽  
Yaroslav Chabanyuk ◽  
Uliana Khimka ◽  
◽  
...  
Keyword(s):  
Diffusion Process ◽  
Small Diffusion ◽  
Diffusion Scheme

Dopant Diffusion in TiSi2

1986 ◽  
Vol 77 ◽  
Author(s):  
F. M. d'Heurle ◽  
A. E. Michel ◽  
F. K. LeGoues ◽  
G. Scilla ◽  
J. T. Wetzel ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Diffusion Process ◽  
Diffusion Coefficients ◽  
Boundary Diffusion ◽  
Radioactive Tracer ◽  
Lattice Diffusion ◽  
The Other ◽  
Small Diffusion ◽  
Secondary Ion ◽  
Thick Layers

ABSTRACTDopant elements, B and Ga, P, As and Sb, and Ge as well, have been implanted into thick (350–400 nm) layers of TiSi2 prepared by Ti-Si reaction. Both B and Sb appear to be immobile, this behavior is thought to result from very small solid solubilities, rather than from very small diffusion coefficients. The other elements display about the same behavior, with detectable grain boundary diffusion at temperatures as low as 600°C, and lattice diffusion becoming considerable at 750°C, so that with the cooperation of both phenomena almost complete homogenisation of these relatively thick layers occurs in 30 minutes at 800°C. Germanium is used in lieu of a Si radioactive tracer because it can be analyzed by Secondary Ion Mass Spectroscopy. Its behavior is thought to imply that there is little equilibrium adsorption of the dopant elements at the Si/TiSi2 interface. The comparable values of the diffusion coefficients for the mobile elements confirm the anticipation that the dopants move as substitutional atoms on the Si sublattice. Results obtained with some samples implanted with both dopant and Ti indicate that in these silicon-saturated suicide layers the diffusion process is not significantly affected by small changes in stoichiometry.

scholarly journals CHAOTIC CRYPTOGRAPHIC SCHEME BASED ON COMPOSITION MAPS

2008 ◽  
Vol 18 (01) ◽  
pp. 251-261 ◽  
Author(s):  
SOHRAB BEHNIA ◽  
AFSHIN AKHSHANI ◽  
HADI MAHMODI ◽  
AMIR AKHAVAN
Keyword(s):  
Invariant Measure ◽  
Diffusion Process ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Control Parameters ◽  
Chaotic Region ◽  
Key Space ◽  
Image Pixels ◽  
High Level ◽  
Cryptographic Scheme

In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them have encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on Composition of Trigonometric Chaotic Maps is proposed. These maps which are defined as ratios of polynomials of degree N, have interesting properties such as invariant measure, ergodicity, variable chaotic region with respect to the control parameters and ability to construct composition form of maps. We have used a composition of chaotic map to shuffle the position of image pixels. Another composition of chaotic map is used in diffusion process. According to the performed analysis, the introduced algorithm can satisfy the required performances such as high level security, large key space and the acceptable encryption speed.

Burgers fluid flow in perspective of Buongiorno’s model with improved heat and mass flux theory for stretching cylinder

2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed
Keyword(s):  
Diffusion Process ◽  
Mathematical Formulation ◽  
Thermal Relaxation ◽  
Mass Diffusion ◽  
Stretching Cylinder ◽  
Discussion Section ◽  
Buongiorno’S Model ◽  
Homotopy Analysis ◽  
Burgers Fluid ◽  
Diffusion Phenomena

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

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