Higher Order Solitary Wave Solutions of the Standard KdV Equations

Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.

Boundary Value Problems for Burgers Equations, through Nonstandard Analysis

In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-COLE transformation to linearize the problems and explicitly solve them. Next we study the Burgers equation and solve the initial value problem for it. We study the asymptotic behavior of solutions and we show that the exact solution of boundary value problem for viscid Burgers equation as viscosity parameter is sufficiently small approach the shock type solution of boundary value problem for inviscid Burgers equation. We discuss both confluence and interacting shocks. In this article a new approach has been developed to find the exact solutions. The results are formulated in classical mathematics and proved with infinitesimal technique of non standard analysis.

Applicability of standard forward column/row recurrence equations for ALFs

Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.

Solution of Self-similar Equations of the k-ε Model in the Shear Turbulent Mixing Problem and Its Numerical Simulation

The paper presents the k-ε model equations of turbulence with a single set of constants chosen by the authors, which is appropriate to simulate a wide range of turbulent flows. The model validation has been performed for a number of flows and its main results are given in the paper. The turbulent mixing of flow with shear in the tangential velocity component is discussed in details. An analytical solution to the system of ordinary differential equations of the k-ε model of turbulent mixing has been found for the self-similar regime of flow. The model coefficients were chosen using simulation results for some simplest turbulent flows. The solution can be used for the verification of codes. The numerical simulation of the problem has been performed by the 2D code EGAK using this model. A good agreement of the numerical simulation results with the self-similar solution, 3D DNS results and known experimental data has been achieved. This allows stating that the k-ε model constants chosen by the authors are acceptable for the considered flow.

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Optimal convergence rates for three-dimensional turbulent flow equations

In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the LP-norm of the perturbation is bounded for some p ε [1, 6）.

不可压湍流流动K-ε两方程模型参数辨识

本文提出了不可压湍流流动情况下标准 K -ε两方程模型的参数辨识方法 ,并对轴对称管道流动、二维后向台阶流动、轴对称突扩管道流动下的模型参数进行了参数辨识与分析 ,得到了一些初步结论 :( 1)参数辨识方法是确定湍流模型经验参数值的一种有效方法 ;( 2 )参数辨识结果受数值计算精度和流动特性影响很大 ;( 3)由于标准 K -ε两方程模型本身还有缺陷 。

A New Two-Parameter Heteromorphic Elliptic Equation: Properties and Applications

The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient θ = b/a = 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts.

Validation of general linear modeling for identifying factors associated with Quality of Life: A comparison with structural equation modeling

Purpose: General linear modeling (GLM) is usually applied to investigate factors associated with the domains of Quality of Life (QOL). A summation score in a specific sub-domain is regressed by a statistical model including factors that are associated with the sub-domain. However, using the summation score ignores the influence of individual questions. Structural equation modeling (SEM) can account for the influence of each question’s score by compositing a latent variable from each question of a sub-domain. The objective of this study is to determine whether a conventional approach such as GLM, with its use of the summation score, is valid from the standpoint of the SEM approach. Method: We used the Japanese version of the Maugeri Foundation Respiratory Failure Questionnaire, a QOL measure, on 94 patients with heart failure. The daily activity sub-domain of the questionnaire was selected together with its four accompanying factors, namely, living together, occupation, gender, and the New York Heart Association’s cardiac function scale (NYHA). The association level between individual factors and the daily activity sub-domain was estimated using SEM?and GLM, respectively. The standard partial regression coefficients of GLM and standardized path coefficients of SEM were compared. If?these coefficients were similar (absolute value of the difference -0.06 and -0.07 for the GLM and SEM. Likewise, the estimates of occupation, gender, and NYHA were -0.18 and -0.20, -0.08 and -0.08, 0.51 and 0.54, respectively. The absolute values of the difference for each factor were 0.01, 0.02, 0.00, and 0.03, respectively. All differences were less than 0.05. This means that these two approaches lead to similar conclusions. Conclusion: GLM is a valid method for exploring association factors with a domain in QOL.

ERROR ESTIMATES OF GALERKIN METHOD FOR HIGH DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

Error estimates of Galerkin method for Kuramoto-Sivashingsky (K-S) equation in space dimension ≥3 are derived in the paper. These results furnish strong evidence for the computation of the solutions.

REMARK ON GALERKIN METHOD FOR TWO-DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

In this paper, the convergence and L 2 estimate of the Galerkin method are given for the steady state Kuramoto-Sivashinsky (K-S) equation.

Interpretation of Dark Matter and Quark-Gluon Plasma: The Generation of the Periodic Table Elements and Its Phase Diagram: A Novel Millennium Power Plant

This paper presents a novel physical interpretation of the state of matter of the quark-gluon as the most fundamental building blocks in nature. Such a model is derived based on the assumption that dark matter and dark energy behave as a perfect ideal fluid at extremely high temperature. By the virtue of Boltzmann constant of the ideal gas law and NASA’s Cosmic Microwave Background Explorer (CMB) which estimate that the space has an average temperature close to 2.7251 Kelvin, then the equivalent mass-energy of the fundamental particle of the dark matter/dark energy is determined. Moreover, assuming a uniform space dark energy/dark matter density, then the critical temperature at which the dark matter has a unity entity per volume is identified as 64 × 1012 K. The calculated critical temperature of the quark-gluon plasma is found to be proportional to the temperature generated by colliding heavy ions at the Relativistic Heavy Ion Collider (RHIC) and European Organization for Nuclear Research (CERN). Moreover, the individual critical temperatures of the quark-gluon plasma matter at which the elements of the Periodic Table are generated are explicitly determined. The generation temperature trend of the elements of the Periodic Table groups and Periods is then demonstrated. Accordingly, the phase diagram of the quark-gluon state matter is proposed. Finally, a new model of quark-gluon power generation plant is proposed and aims to serve humanity with new energy sources in the new millennium.

Semiclassical Method to Schroedinger Equation with Position-Dependent Effective Mass

In this paper, two novel semiclassical methods including the standard and supersymmetric WKB quantization conditions are suggested to discuss the Schroedinger equation with position-dependent effective mass. From a proper coordinate transformation, the formalism of the Schroedinger equation with position-dependent effective mass is mapped into isospectral one with constant mass and therefore for a given mass distribution and physical potential function the bound state energy spectrum can be determined easily by above method associated with a simple integral formula. It is shown that our method can give the analytical results for some exactly-solvable quantum systems.

Group Geometric Algebra and the Standard Model

We show how to generalize the Weyl equation to include the Standard Model fermions and a dark matter fermion. The 2 × 2 complex matrices are a matrix ring R. A finite group G can be used to define a group algebra G[R] which is a generalization of the ring. For a group of size N, this defines N Weyl equations coupled by the group operation. We use the group character table to uncouple the equations by diagonalizing the group algebra. Using the full octahedral point symmetry group for G, our uncoupled Weyl equations have the symmetry of the Standard Model fermions plus a dark matter particle. We describe the symmetry properties of dark matter.

NONCONFORMING FINITE ELEMENT PENALTY METHOD FOR STOKES EQUATION

a special penalty method is presented to improve the accuracy of the standard penalty method for solving Stokes equation with nonconforming finite element.It is shown that this method with a larger penalty parameter can achieve the same accuracy as the standard method with a smaller penalty parameter. The convergence rate of the standard method is just half order of this penalty method when using the same penalty parameter, while the extrapolation method proposed by Faik et al can not yield so high accuracy of convergence.At last, we also get the super convergence estimates for total flux. Received October 14, 1996 1991 MR Subject Classification: 65N30.

Standard Model Masses Explained

The Standard Model of particle physics requires nine lepton and quark masses as inputs, but does not incorporate neutrino masses required by neutrino oscillation observations. This analysis addresses these problems, explaining Standard Model particle masses by describing fundamental particles as solutions of Einstein’s equations, with radii 1/4 their Compton wavelength and half of any charge on rotating particles located on the surface at each end of the axis of rotation. The analysis relates quark and lepton masses to electron charge and mass, and identifies neutrino masses consistent with neutrino oscillation observations.

一种光波大气折射率剖面模型构建方法

根据经典光波折射率计算公式和ITU-R建议书中水汽密度经验公式,给出了一种新的光波大气折射率计算公式;借鉴Hopfield折射率静力项剖面模型和ITU-R建议书中水汽密度剖面模型,给出了一种基于历史气象探空数据构建光波大气折射率剖面模型的方法。以青岛地区为例,通过对1986—1995年历史气象探空数据的处理并结合参考标准大气,建立了适合当地的光波大气折射率剖面模型;统计剖面模型预测折射率剖面与实测折射率剖面的均方根误差,结果表明:构建的剖面模型具有较好的预测精度,这对光学外测设备的折光修正数据处理具有很好的参考价值。

具有非标准Lagrange函数的分数阶动力学系统的正则变换

分数阶模型由于所具有的系统开放性、时间依赖性和空间全域性,为复杂物理、力学和工程问题的建模提供了有力的数学工具。作为分析力学的重要内容之一,变换在方程简化与求解过程中发挥重要作用,通过正则变换可使原本难以求解的方程得到简化且变换后仍保持原方程的形式。因此,研究分数阶动力学系统的正则变换具有重要意义。文章研究具有非标准Lagrange函数(包括指数Lagrange函数、幂律Lagrange函数和对数Lagrange函数)的分数阶动力学系统的正则变换。首先,定义分数阶广义动量和非标准Hamilton函数,导出三类非标准分数阶动力学系统的Hamilton正则方程;其次,建立非标准分数阶动力学系统的正则变换的判据方程,依据母函数的不同选择给出四种基本形式的正则变换;最后,通过若干算例介绍结果的应用。

基于湍流模型的飞行器温度场数值仿真研究

飞行器红外成像仿真需要不同飞行条件下的温度场分布。本文利用标准(Standard)k-ε模型、剪切应力传输(SST)k-ε模型和Spalart-Allmaras(S-A)模型分别进行数值模拟仿真计算,研究不同飞行速度和飞行高度下的飞行器温度场分布,并对不同模型的结果进行对比分析。首先,利用MultiGen Creator软件对飞行器进行三维建模;其次采用Hypemesh软件和Fluent meshing软件中进行面网格划分和体网格划分,最后采用Fluent 2022R1软件仿真飞行器静态温度场分布,通过改变湍流模型与边界条件设置,对不同飞行速度和不同高度下飞行器温度场进行数值模拟仿真,并与理论结果进行了对比分析。实验结果显示,3种湍流模型均能较好的模拟飞行器蒙皮与尾喷管内壁壁面温度值。飞行器蒙皮温度随着飞行马赫数的增加不断升高;随着飞行高度的升高而不断地降低,与理论结果变化规律一致。在尾喷管内壁面温度仿真中,3种湍流模型仿真的内壁面温度最高相差21 K,相对误差在1.8%左右,在红外仿真中近似忽略不计,故3种湍流模型均适合尾喷管内壁面温度场仿真。在蒙皮温度场仿真中,3种湍流模型仿真计算的蒙皮平均温度值与理论温度值的相对误差均在5%以内,均可满足红外成像仿真的温度差值要求,其中k-ε模型在蒙皮温度场模拟中与理论温度值最为接近,因此k-ε模型精度更高,更适合于飞行器的流场仿真,能更好地仿真出空气动力加热对飞行器温度场的影响。

空间分数阶偏微分方程非标准有限差分方法的稳定性和收敛性

本文研究空间分数阶偏微分方程非标准有限差分方法数值解的相关问题.采用Grünwald-Letnikov公式和平移Grünwald-Letnikov公式分别对两个空间分数阶导数进行离散.再运用带有时间和空间步长的分母函数构造非标准有限差分方法.进而利用von Neumann分析方法对差分格式的稳定性和收敛性进行研究,获得了一些新的结果.数值例子验证了非标准有限差分方法用于求解空间分数阶偏微分方程的有效性.