scholarly journals Numerical Solution to Anomalous Diffusion Equations for Levy Walks

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3219
Author(s):  
Viacheslav V. Saenko ◽  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Yuri E. Chamchiyan
Keyword(s):  
Monte Carlo ◽  
Asymptotic Behavior ◽  
Kinetic Equation ◽  
Constant Velocity ◽  
Solution Algorithm ◽  
Diffusion Equations ◽  
Advantages And Disadvantages ◽  
Lévy Walks ◽  
The Monte Carlo Method ◽  
Fractional Differential

The process of Levy random walks is considered in view of the constant velocity of a particle. A kinetic equation is obtained that describes the process of walks, and fractional differential equations are obtained that describe the asymptotic behavior of the process. It is shown that, in the case of finite and infinite mathematical expectation of paths, these equations have a completely different form. To solve the obtained equations, the method of local estimation of the Monte Carlo method is described. The solution algorithm is described and the advantages and disadvantages of the considered method are indicated.

scholarly journals Распределение кислородных вакансий во внешнем электрическом поле и кислородная проводимость в акцепторно допированных ионных проводниках флюоритной структуры

2021 ◽  
Vol 63 (6) ◽  
pp. 735
Author(s):  
М.З. Урицкий
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Monte Carlo Method ◽  
Dopant Concentration ◽  
Impurity Content ◽  
Fluorite Structure ◽  
Impurity Effect ◽  
The Monte Carlo Method ◽  
Carrier Redistribution ◽  
Stationary Conditions

The distribution of current carriers over the lattice sites in the fluorite structure of (AO₂)₁₋ₓ(BO₁.₅)ₓ oxides for the region of not too large values of the dopant concentration in an external electric field has been calculated by solving the basic kinetic equation under stationary conditions. The influence of carrier redistribution in the external field on the value of ionic conductivity and the position of the maximum of its dependence on the impurity content has been studied. The conductivity is considered in the framework of a model in which the impurity effect on transport is reduced to blocking jumps of current carriers along the edges of the oxygen lattice closest to the dopant ions. The analytical results are confirmed by numerical calculations using the Monte Carlo method and can be used to explain the position of experimentally observed maxima of the dependence of conductivity on the dopant concentration in such structures.

UGR CALCULATION BASED ON THE LUMINANCE SPATIAL-ANGULAR DISTRIBUTION

2020 ◽  
Vol 2020 (4) ◽  
pp. 25-32
Author(s):  
Viktor Zheltov ◽  
Viktor Chembaev
Keyword(s):  
Monte Carlo ◽  
Angular Distribution ◽  
Monte Carlo Method ◽  
Visual Task ◽  
New Method ◽  
Lighting System ◽  
Preliminary Assessment ◽  
System A ◽  
The Monte Carlo Method

The article has considered the calculation of the unified glare rating (UGR) based on the luminance spatial-angular distribution (LSAD). The method of local estimations of the Monte Carlo method is proposed as a method for modeling LSAD. On the basis of LSAD, it becomes possible to evaluate the quality of lighting by many criteria, including the generally accepted UGR. UGR allows preliminary assessment of the level of comfort for performing a visual task in a lighting system. A new method of "pixel-by-pixel" calculation of UGR based on LSAD is proposed.

PSHA software review based on the Monte Carlo method

2020 ◽  
pp. 14-24
Author(s):  
V.A. Mironov ◽  
S.A. Peretokin ◽  
K.V. Simonov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Seismic Hazard ◽  
Hazard Analysis ◽  
Software Review ◽  
Seismic Hazard Analysis ◽  
Probabilistic Seismic Hazard ◽  
Test Calculation ◽  
Seismic Surveys ◽  
The Monte Carlo Method

The article is a continuation of the software research to perform probabilistic seismic hazard analysis (PSHA) as one of the main stages in engineering seismic surveys. The article provides an overview of modern software for PSHA based on the Monte Carlo method, describes in detail the work of foreign programs OpenQuake Engine and EqHaz. A test calculation of seismic hazard was carried out to compare the functionality of domestic and foreign software.

Application of the Monte Carlo Method for the Prediction of Behavior of Peptides

2019 ◽  
Vol 20 (12) ◽  
pp. 1151-1157 ◽  
Author(s):  
Alla P. Toropova ◽  
Andrey A. Toropov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Natural Sciences ◽  
Monte Carlo Technique ◽  
Quantitative Structure ◽  
Structure Property ◽  
The Monte Carlo Method ◽  
Modern Natural

Prediction of physicochemical and biochemical behavior of peptides is an important and attractive task of the modern natural sciences, since these substances have a key role in life processes. The Monte Carlo technique is a possible way to solve the above task. The Monte Carlo method is a tool with different applications relative to the study of peptides: (i) analysis of the 3D configurations (conformers); (ii) establishment of quantitative structure – property / activity relationships (QSPRs/QSARs); and (iii) development of databases on the biopolymers. Current ideas related to application of the Monte Carlo technique for studying peptides and biopolymers have been discussed in this review.

scholarly journals A Novel Kinetic Modeling Framework for the Polycondensation of Sugars Using Monte Carlo and the Method of Moments

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 745
Author(s):  
Dimitrios Meimaroglou ◽  
Sandrine Hoppe ◽  
Baptiste Boit
Keyword(s):  
Monte Carlo ◽  
Kinetic Modeling ◽  
Method Of Moments ◽  
Kinetic Monte Carlo ◽  
Kinetic Scheme ◽  
Modeling Framework ◽  
Industrial Sectors ◽  
The Monte Carlo Method ◽  
Reacting Systems ◽  
High Degree

The kinetics of the hydrolysis and polycondensation reactions of saccharides have made the subject of numerous studies, due to their importance in several industrial sectors. The present work, presents a novel kinetic modeling framework that is specifically well-suited to reacting systems under strict moisture control that favor the polycondensation reactions towards the formation of high-degree polysaccharides. The proposed model is based on an extended and generalized kinetic scheme, including also the presence of polyols, and is formulated using two different numerical approaches, namely a deterministic one in terms of the method of moments and a stochastic kinetic Monte Carlo approach. Accordingly, the most significant advantages and drawbacks of each technique are clearly demonstrated and the most fitted one (i.e., the Monte Carlo method) is implemented for the modeling of the system under different conditions, for which experimental data were available. Through these comparisons it is shown that the model can successfully follow the evolution of the reactions up to the formation of polysaccharides of very high degrees of polymerization.

scholarly journals Innovative aerodynamic grain separation system for plant harvesting in sloped areas: problems, research and optimization of parameters

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Jerzy Bienek ◽  
Piotr Komarnicki ◽  
Jerzy Detyna
Keyword(s):  
Monte Carlo ◽  
Separation System ◽  
Indicator Values ◽  
Negative Effects ◽  
The Monte Carlo Method ◽  
Longitudinal Slope ◽  
Combine Harvester ◽  
The Given ◽  
Transverse Slope ◽  
Plant Harvesting

AbstractThis article presents the main problems associated with cereal harvesting in sloping areas. The presented innovative aerodynamic system supporting the separating unit of combine harvester can be one of the ways to counteract the negative effects of harvesting machines work on slopes. The Monte Carlo numerical method, presented in this article, was applied in the optimization of an aerodynamic sieve separation process on an inclined terrain. The given variables are the transverse slope of separator α (of the sieve), longitudinal slope β and the output of the main and side fans. The Monte Carlo method makes it possible to determine an optimized set of parameters (α = 10°, β = 2.8°, δ = 9°), the output of the main fan (0.67 m3 s−1) and the output of the side fan (1.86 m3 s−1), allowing to obtain the best indicator values of 2.1% grain loss and 97.5% grain purity.

Sign in / Sign up

Export Citation Format

Share Document