Numerical simulation of soliton gas within the Korteweg-de Vries type equations

2019 ◽  
pp. 52-66
Author(s):  
Екатерина Геннадьевна Диденкулова ◽  
Анна Витальевна Кокорина ◽  
Алексей Викторович Слюняев
Keyword(s):  
Numerical Scheme ◽  
Initial Conditions ◽  
Probability Distributions ◽  
Scattering Problem ◽  
Spectral Composition ◽  
Computation Time ◽  
Qualitative Description ◽  
Statistical Characteristics ◽  
De Vries ◽  
Pseudo Spectral Method

Приведены детали численной схемы и способа задания начальных условий для моделирования нерегулярной динамики ансамблей солитонов в рамках уравнений типа Кортевега-де Вриза на примере модифицированного уравнения Кортевега-де Вриза с фокусирующим типом нелинейности. Дано качественное описание эволюции статистических характеристик для ансамблей солитонов одной и разных полярностей. Обсуждаются результаты тестовых экспериментов по столкновению большого числа солитонов. The details of the numerical scheme and the method of specifying the initial conditions for the simulation of the irregular dynamics of soliton ensembles within the framework of equations of the Korteweg - de Vries type are given using the example of the modified Korteweg - de Vries equation with a focusing type of nonlinearity. The numerical algorithm is based on a pseudo-spectral method with implicit integration over time and uses the Crank-Nicholson scheme for improving the stability property. The aims of the research are to determine the relationship between the spectral composition of the waves (the Fourier spectrum or the spectrum of the associated scattering problem) and their probabilistic properties, to describe transient processes and the equilibrium states. The paper gives a qualitative description of the evolution of statistical characteristics for ensembles of solitons of the same and different polarities, obtained as a result of numerical simulations; the probability distributions for wave amplitudes are also provided. The results of test experiments on the collision of a large number of solitons are discussed: the choice of optimal conditions and the manifestation of numerical artifacts caused by insufficient accuracy of the discretization. The numerical scheme used turned out to be extremely suitable for the class of the problems studied, since it ensures good accuracy in describing collisions of solitons with a short computation time.

scholarly journals An Efficient Method of Image Encryption Using Rossler Chaotic System

2021 ◽  
Vol 10 (2) ◽  
pp. 11
Author(s):  
Yasir Ahmed Hamza ◽  
Marwan Dahar Omer
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Initial Conditions ◽  
Computation Time ◽  
Encryption Algorithm ◽  
Brute Force ◽  
Symmetric Encryption ◽  
New Approach ◽  
System Parameters ◽  
Plain Image

In this study, a new approach of image encryption has been proposed. This method is depends on the symmetric encryption algorithm RC4 and Rossler chaotic system. Firstly, the encryption key is employed to ciphering a plain image using RC4 and obtains a ciphered-image. Then, the same key is used to generate the initial conditions of the Rossler system. The system parameters and the initial conditions are used as the inputs for Rossler chaotic system to generate the 2-dimensional array of random values. The resulted array is XORed with the ciphered-image to obtain the final encrypted-image. Based on the experimental results, the proposed method has achieved high security and less computation time. Also, the proposed method can be resisted attacks like (statistical, brute-force, and differential).

Statistical characteristics for the defect occurrence of raw silk

2019 ◽  
Vol 90 (3-4) ◽  
pp. 302-312
Author(s):  
Jian-mei Xu ◽  
Ying Zhou ◽  
Jiantao Niu ◽  
Dongping Wu ◽  
Lun Bai
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Capacitive Sensor ◽  
Test Method ◽  
International Organization ◽  
Statistical Characteristics ◽  
Goodness Of Fit Test ◽  
Polya Distribution ◽  
Silk Filament ◽  
Better Than

In order to consider different defects that occur during the computer simulation of raw silk size series, it is necessary to find out the statistical characteristics for the defect occurrence of raw silk. Under the newest International Organization for Standardization standard for electronic testing of raw silk, the defects are classified into small slubs, big slubs, thick places, thin places, and small imperfection elements. By analyzing some probability distributions that happen during the silk reeling process and the formation of the defects, the study proposed that Pólya distribution may fit better than Poisson distribution in describing the number of defects formed in a certain length of silk filament. To verify this theoretical deduction experimentally, the defects for 15 lots of raw silk were tested every 1000 meters using an electronic tester for raw silk; each time 12 skeins were tested together and each test was repeated from 13 to 17 times. A goodness-of-fit test method for Poisson and Pólya distributions was deduced, which was used to analyze the statistical characteristics for the defects except for small imperfection elements. The results showed that when using the capacitive sensor, the defects of big slubs, small slubs, and thick places had a Pólya distribution with a weak spreading characteristic; the thin places were a combination of independent Pólya distributions, and each subclass of thin places took Pólya distribution; when using the optical sensor, all the defects had a Pólya distribution, which was in line with the theoretical deduction.

An Investigation Into Nonlinear Growth Rate of Two-Dimensional and Three-Dimensional Single-Mode Richtmyer–Meshkov Instability Using an Arbitrary-Lagrangian–Eulerian Algorithm

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Mike Probyn ◽  
Ben Thornber ◽  
Dimitris Drikakis ◽  
David Youngs ◽  
Robin Williams
Keyword(s):  
Growth Rate ◽  
Numerical Scheme ◽  
Initial Conditions ◽  
Numerical Study ◽  
Three Dimensional ◽  
Single Mode ◽  
Computational Time ◽  
Initial Growth ◽  
Arbitrary Lagrangian Eulerian ◽  
Layer Width

This paper presents an investigation into the use of a moving mesh algorithm for solving unsteady turbulent mixing problems. The growth of a shock induced mixing zone following reshock, using an initial setup comparable to that of existing experimental work, is used to evaluate the behavior of the numerical scheme for single-mode Richtmyer–Meshkov instability (SM-RMI). Subsequently the code is used to evaluate the growth rate for a range of different initial conditions. The initial growth rate for three-dimensional (3D) SM Richtmyer–Meshkov is also presented for a number of different initial conditions. This numerical study details the development of the mixing layer width both prior to and after reshock. The numerical scheme used includes an arbitrary Lagrangian–Eulerian grid motion which is successfully used to reduce the mesh size and computational time while retaining the accuracy of the simulation results. Varying initial conditions shows that the growth rate after reshock is independent of the initial conditions for a SM provided that the initial growth remains in the linear regime.

Resonance Analysis of Train–Track–Bridge Interaction Systems with Correlated Uncertainties

2019 ◽  
Vol 20 (01) ◽  
pp. 2050008 ◽  
Author(s):  
Lifeng Xin ◽  
Xiaozhen Li ◽  
Jiaxin Zhang ◽  
Yan Zhu ◽  
Lin Xiao
Keyword(s):  
Probability Distributions ◽  
Three Dimensional ◽  
Estimation Method ◽  
Interaction Model ◽  
Point Estimation ◽  
Statistical Characteristics ◽  
Resonance Analysis ◽  
Track Bridge ◽  
Point Estimation Method ◽  
Nataf Transformation

Over the last decades, the resonance-related dynamics for bridge systems subjected to a moving train has been researched and discussed from mechanics, physics and mathematics. In the current work, new perspectives of train-induced resonance analysis are investigated through introducing random propagation process into the train–bridge dynamic interactions. Besides, the Nataf-transformation-based point estimation method is applied to generate pseudorandom variables following arbitrarily correlated probability distributions. A three-dimensional (3D) nonlinear train-ballasted track–bridge interaction model founded on fundamental physical and mechanical principles is employed to convey and depict train–bridge interactions with random properties considered. After that, extensive applications are illustrated in detail for revealing the statistical characteristics of the so-called “random resonance”. Numerical results show that the critical train speeds associated with resonance and cancelation are random in essence owing to the variability of system parameters; the correlation between parameters exerts obvious influences on system dynamic behaviors; the last vehicle of a train will be in more violent vibrations compared to the front vehicles; the influences of track irregularities on the wheel–rail interactions are significantly greater than those of resonance.

scholarly journals Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

2018 ◽  
Vol 25 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Cosmo ◽  
Domenico Felice ◽  
Stefano Mancini ◽  
Giuseppe Marmo ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Geometric Structure ◽  
Initial Conditions ◽  
Probability Distributions ◽  
End Points ◽  
Quantum Properties ◽  
Statistical Manifolds ◽  
Classical Setting ◽  
Qualitative Effect

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method

2016 ◽  
Vol 26 (1) ◽  
pp. 284-306 ◽  
Author(s):  
Mehdi Jamei ◽  
H Ghafouri
Keyword(s):  
Porous Media ◽  
Discontinuous Galerkin ◽  
Numerical Scheme ◽  
Two Phase Flow ◽  
Weighted Average ◽  
Computation Time ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Content Type

Purpose – The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme. Design/methodology/approach – The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method. Findings – Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media. Research limitations/implications – The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible. Practical implications – The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers. Originality/value – The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

scholarly journals DYNAMICS OF THE LINKAGE DISEQUILIBRIUM FUNCTION UNDER MODELS OF GENE-FREQUENCY HITCHHIKING

Genetics ◽  
1981 ◽  
Vol 99 (2) ◽  
pp. 337-356
Author(s):  
Marjorie A Asmussen ◽  
Michael T Clegg
Keyword(s):  
Linkage Disequilibrium ◽  
Gene Frequency ◽  
Initial Conditions ◽  
Recombination Fraction ◽  
Qualitative Description ◽  
Selection Intensity ◽  
Gene Frequencies ◽  
Dependent Behavior ◽  
Wide Range ◽  
Over Time

ABSTRACT The dynamic behavior of the linkage disequilibrium (D) between a neutral and a selected locus is analyzed for a variety of deterministic selection models. The time-dependent behavior of D is governed by the gene frequency at the selected locus (p) and by the selection (s) and recombination (r) parameters. Thomson (1977) showed numerically that D may increase under certain initial conditions. We give exact conditions for D to increase in time, which require that the selection intensity exceed the recombination fraction (s > r) and that p be near zero or one. We conclude from this result that gene frequency hitchhiking is most likely to be important when a new favorable mutant enters a population. We also show that, for what can be a wide range of gene frequencies, D will decay at a faster rate than the neutral rate. Consequently, the hitchhiking effect may quickly diminish as the selected gene becomes more common.—The method of analysis allows a complete qualitative description of the dynamics of D as a function of s and r. Two major findings concern the range of gene frequencies at the selected locus for which D either increases over time or decays at a faster rate than under neutrality. For all models considered, the region where D increases (i) first enlarges then shrinks as selection intensifies, and (ii) steadily shrinks as r increases. In contrast, the region of accelerated decay constantly enlarges as the selection intensity increases. This region will either shrink or enlarge as r increases, depending upon the form of selection in force.

Can we forecast the arrival of ICMEs for the whole Solar Systems?

2020 ◽  
Author(s):  
Dario Del Moro ◽  
Gianluca Napoletano ◽  
Francesco Berrilli ◽  
Luca Giovannelli ◽  
Ermanno Pietropaolo ◽  
...  
Keyword(s):  
Space Weather ◽  
Weather Forecasting ◽  
Probability Distributions ◽  
Computation Time ◽  
Space Mission ◽  
Interplanetary Coronal Mass Ejections ◽  
Solar Systems ◽  
Transit Times ◽  
Solar System Bodies ◽  
Using Data

<p>Solar wind transients, i.e. interplanetary coronal mass ejections (ICMEs) drive Space Weather throughout the heliosphere and the prediction of their impact on different solar system bodies is one of the primary goals of the Planetary Space Weather forecasting. We realized a procedure based on the Drag-Based Model (Vrsnak et al., 2013, Napoletano et al. 2018) which uses probability distributions for the input parameters, and allows the evaluation of the uncertainty on the forecast. This approach has been tested against a set of ICMEs whose transit times are known, obtaining extremely promising results.</p><p>We apply this model to propagate a sample of ICMEs from their sources on the solar surface into the heliosphere. We made use of the seminal works by Prise et al. (2015), Winslow et al. (2015) and Witasse et al. (2017) who tracked the ICMEs through their journeys using data from several spacecraft.</p><p>Considering the extremely short computation time needed by the model to propagate ICMEs, this approach is a promising candidate to forecast ICME arrival to planetary bodies and spacecraft in the whole heliosphere, with relevant application to space-mission short-term planning.</p>

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