scholarly journals A fractional generalization of the dirichlet distribution and related distributions

2021 ◽  
Vol 24 (1) ◽  
pp. 112-136
Author(s):  
Elvira Di Nardo ◽  
Federico Polito ◽  
Enrico Scalas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Dirichlet Distribution ◽  
One Dimensional ◽  
Reasonable Approximation ◽  
Generalized Dirichlet Distribution ◽  
The One ◽  
Generalized Dirichlet

Abstract This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

scholarly journals Averaging and the Shape of the Correlation Function

Universe ◽  
2019 ◽  
Vol 5 (6) ◽  
pp. 148 ◽  
Author(s):  
Boris Tomášik ◽  
Jakub Cimerman ◽  
Christopher Plumberg
Keyword(s):  
Monte Carlo ◽  
Correlation Function ◽  
Monte Carlo Simulations ◽  
Blast Wave ◽  
Stable Distribution ◽  
Wave Model ◽  
Gaussian Form ◽  
One Dimensional ◽  
The One

A brief pedagogical introduction to correlation femtoscopy is given. We then focus on the shape of the correlation function and discuss the possible reasons for its departure from the Gaussian form and better reproduction with a Lévy stable distribution. With the help of Monte Carlo simulations based on asymmetric extension of the Blast-Wave model with resonances we demonstrate possible influence of averaging over many events and integrating over wide momentum bins on the shape of the correlation function. We also show that the shape is strongly influenced by the use of the one-dimensional parametrisation in the q i n v variable.

Simulation of the Variability in Next-Generation Microelectronic Capacitors with Polycrystalline Dielectrics

2001 ◽  
Vol 688 ◽  
Author(s):  
Jesse L. Cousins ◽  
David E. Kotecki
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Area Distribution ◽  
The Mean ◽  
Polycrystalline Microstructure ◽  
Probability Density Function Pdf ◽  
Lognormal Probability

AbstractMonte Carlo simulations of capacitors with polycrystalline (Bax, Sr1−x)TiO3 (BST) dielectrics were performed. The variation in capacitors due to the polycrystalline microstructure of the dielectric was investigated, as well as the effects of varying the distribution of crystal sizes. When a lognormal probability density function (pdf) was used to approximate the crystal area pdf and the average number of crystals per capacitor was near 100, it was found that the minimum capacitance value was nearly independent of the standard deviation of crystal area distribution. Both the mean and maximum capacitance values were found to increase as the width of the standard deviation increased.

One-dimensional nanofiller induced crystallization in random copolymers studied by dynamic Monte Carlo simulations

2018 ◽  
Vol 46 (9) ◽  
pp. 669-677 ◽  
Author(s):  
Rongjuan Liu ◽  
Luyao Yang ◽  
Xiaoyan Qiu ◽  
Haitao Wu ◽  
Yongqiang Zhang ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Random Copolymers ◽  
One Dimensional ◽  
Dynamic Monte Carlo ◽  
Induced Crystallization

Topological defects in nematic films between planar degenerate surfaces. A Monte Carlo study

2021 ◽  
pp. 2250016
Author(s):  
Cesare Chiccoli ◽  
Paolo Pasini ◽  
Luiz Roberto Evangelista ◽  
Rodolfo Teixeira de Souza ◽  
Claudio Zannoni
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Defect Structure ◽  
Topological Defects ◽  
Monte Carlo Study ◽  
Geometric Parameters ◽  
Molecular Organization ◽  
The One

The molecular organization of a nematic film sandwiched between two planar randomly aligned surfaces is studied by means of detailed Monte Carlo simulations. The formation as well as the evolution of topological defects induced by these particular boundary conditions are investigated. The resulting defect structure is compared with the one induced by hybrid aligned surfaces. The observation of such defects and some features of their structures can be associated with geometric parameters of the film and with properties of the confining surfaces.

Monte Carlo Probability Density Function Method for Gas Turbine Combustor Flowfield Predictions

1997 ◽  
Vol 13 (2) ◽  
pp. 218-225 ◽  
Author(s):  
Anil K. Tolpadi ◽  
Sanjay M. Correa ◽  
David L. Burrus ◽  
Hukam C. Mongia
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Gas Turbine ◽  
Density Function ◽  
Function Method ◽  
Gas Turbine Combustor

Interdiffusion in Short-Wavelength Modulated Materials Studied by Monte-Carlo Simulations

1987 ◽  
Vol 103 ◽  
Author(s):  
M. Atzmon
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Interdiffusion Coefficient ◽  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
One Dimensional ◽  
Interdiffusion Process ◽  
Limiting Value ◽  
Modulation Wavelength

ABSTRACTInterdiffusion in a two-dimensional compositionally modulated lattice has been studied by Monte-Carlo simulations. In the initial stages, the interdiffusion coefficient has been observed to change with time due to the development of short-range order simultaneously with the interdiffusion process. When the short-range order parameter approached its limiting value, the diffusion coefficient approached a constant value. The dependence of the interdiffusion coefficient on the modulation wavelength does not agree with the prediction of one-dimensional theories. For ordering alloy systems, the effective interdiffusion coefficient is positive, i.e., an initially present modulation decays in time, for all wavelengths.

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