scholarly journals A Boltzmann-type kinetic model for misorientation distribution functions in two-dimensional fiber-texture polycrystalline grain growth

2016 ◽  
Vol 109 ◽  
pp. 230-247 ◽  
Author(s):  
I. Yegorov ◽  
C.E. Torres ◽  
M. Emelianenko
Keyword(s):  
Kinetic Model ◽  
Grain Growth ◽  
Fiber Texture ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Misorientation Distribution

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

scholarly journals Self-Similar Solutions to a Kinetic Model for Grain Growth

2012 ◽  
Vol 22 (3) ◽  
pp. 399-427 ◽  
Author(s):  
Michael Herrmann ◽  
Philippe Laurençot ◽  
Barbara Niethammer
Keyword(s):  
Kinetic Model ◽  
Grain Growth ◽  
Self Similar ◽  
Similar Solutions

Impact of non-thermal electrons on spatial damping: a kinetic model for the parallel propagating modes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhammad Sarfraz ◽  
Gohar Abbas ◽  
Hashim Farooq ◽  
I. Zeba
Keyword(s):  
Kinetic Model ◽  
Wave Spectrum ◽  
Field Approximation ◽  
Weak Field ◽  
Distribution Functions ◽  
Global Perspective ◽  
Energetic Electrons ◽  
Thermal Anisotropy ◽  
Spatial Damping

Abstract A sequence of in situ measurements points the presence of non-thermal species in the profile of particle distributions. This study highlights the role of such energetic electrons on the wave-spectrum. Using Vlasov–Maxwell’s model, the dispersion relations of the parallel propagating modes along with the space scale of damping are discussed using non-relativistic bi-Maxwellian and bi-Kappa distribution functions under the weak field approximation, i.e., ω − k . v > Ω 0 $\left\vert \omega -\mathbf{k}.\mathbf{v}\right\vert { >}{{\Omega}}_{0}$ . Power series and asymptotic expansions of plasma dispersion functions are performed to derive the modes and spatial damping of waves, respectively. The role of these highly energetic electrons is illustrated on real frequency and anomalous damping of R and L-modes which is in fact controlled by the parameter κ in the dispersion. Further, we uncovered the effect of external magnetic field and thermal anisotropy on such spatial attenuation. In global perspective of the kinetic model, it may be another step.

Applications of PNC in Numerical Methods

2017 ◽  
pp. 235-268
Keyword(s):  
Probability Distribution ◽  
Shape Representation ◽  
Mathematical Problem ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Key Points ◽  
Characteristic Points ◽  
Curve Modeling ◽  
Curve Contour ◽  
Dimensional Object

Nodes are treated as characteristic points of data for modeling and analyzing. The model of data can be built by choice of probability distribution function and nodes combination. Two-dimensional object is extrapolated and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function. Curve interpolation represents one of the most important problems in mathematics and computer science: how to model the curve via discrete set of two-dimensional points? Also the matter of shape representation (as closed curve - contour) and curve parameterization is still opened. For example pattern recognition, signature verification or handwriting identification problems are based on curve modeling via the choice of key points. So interpolation is not only a pure mathematical problem but important task in computer vision and artificial intelligence.

scholarly journals Quasiparton distribution functions: Two-dimensional scalar and spinor QCD

2019 ◽  
Vol 99 (5) ◽  
Author(s):  
Xiangdong Ji ◽  
Yizhuang Liu ◽  
Ismail Zahed
Keyword(s):  
Distribution Functions ◽  
Two Dimensional
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