A Model for Periodic Nonlinear Electric Field Structures in Space Plasmas

In this study, we present a physical model to explain the generation mechanism of nonlinear periodic waves with a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field. The ＂Sagdeev potential＂ from the MHD equations is derived and the nonlinear electric field waveforms are obtained when the Mach number, direction of propagation, and the initial electric field satisfy certain plasma conditions. For the parallel propagation, the amplitude of the electric field waves with ion-acoustic mode increases with the increase of initial electric field and Mach number but its frequency decreases with the increase of Mach number. The amplitude and frequency of the electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky, and its amplitude increases with the increase of initial electric field. For the oblique propagation, only periodic electric field wave with an ion-cyclotron mode obtained, its amplitude and frequency increase with the increase of Mach number and become spiky. From our model the electric field structures show periodic, spiky, and saw-tooth behaviours corresponding to different plasma conditions.     

A Model for Periodic Nonlinear Electric Field Structures in Space Plasmas

In this study, we present a physical model to explain the generation mechanism of nonlinear periodic waves with a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field. The ``Sagdeev potential' fromthe MHD equations is derived and the nonlinear electric field waveforms are obtained when the Mach number, direction of propagation, and the initial electric field satisfy certain plasma conditions. For the parallel propagation, the amplitude of theelectric field waves with ion-acoustic mode increases with the increase of initial electric field and Mach number but its frequency decreases with the increase of Mach number. The amplitude and frequency of the electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky, andits amplitude increases with the increase of initial electric field. For the oblique propagation, only periodic electric field wave with an ion-cyclotron mode obtained, its amplitude and frequency increase with the increase of Mach number and become spiky. From our model the electric field structures show periodic, spiky, and saw-tooth behaviours corresponding to different plasma conditions.     

A Laplace Decomposition Method for Nonlinear Partial Diferential Equations with Nonlinear Term of Any Order

A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial diferential equations with nonlinear term of any order,utt+auxx+bu+cup+du2p 1=0,which contains some important equations of mathematical physics.Three distinct initial conditions are constructed and generalized numerical solutions are thereby obtained,including numerical hyperbolic function solutions and doubly periodic ones.Illustrative figures and comparisons between the numerical and exact solutions with diferent values of p are used to test the efciency of the proposed method,which shows good results are achieved.     

A Laplace Decomposition Method for Nonlinear Partial Differential Equations with Nonlinear Term of Any Order

A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial differential equations with nonlinear term of any order, utt ＋ auxx ＋ bu ＋ cup ＋ du^2p-1 = 0, which contains some important equations of mathematical physics. Three distinct initial conditions are constructed and generalized numerical solutions are thereby obtained, including numerical hyperbolic function solutions and doubly periodic ones. Illustrative figures and comparisons between the numerical and exact solutions with different values of p are used to test the efficiency of the proposed method, which shows good results are azhieved.     

Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully developed turbulence increases as Re ⁴, and not as Re ³ expected from Kolmogorov’s theory, where Re is a large-scale Reynolds number. Various relations for the moments of acceleration and velocity derivatives are derived. An infinite set of exact constraints on dynamically consistent subgrid models for Large Eddy Simulations (LES) is derived from the Navier–Stokes equations, and some problems of principle associated with existing LES models are highlighted     

On the Fully Implicit Solution of a Phase-Field Model for Binary Alloy Solidification in Three Dimensions

A fully implicit numerical method, based upon a combination of adaptively refined hierarchical meshes and geometric multigrid, is presented for the simulation of binary alloy solidification in three space dimensions. The computational techniques are presented for a particular mathematical model, based upon the phase-field approach, however, their applicability is of greater generality than for the specific phase-field model used here. In particular, an implicit second order time discretization is combined with the use of second order spatial differences to yield a large nonlinear system of algebraic equations as each time step. It is demonstrated that these equations may be solved reliably and efficiently through the use of a nonlinear multigrid scheme for locally refined grids. In effect, this paper presents an extension of earlier research in two space dimensions (J. Comput. Phys., 225 (2007), pp. 1271-1287) to fully three-dimensional problems. This extension is validated against earlier two-dimensional results and against some of the limited results available in three dimensions, obtained using an explicit scheme. The efficiency of the implicit approach and the multigrid solver are then demonstrated and some sample computational results for the simulation of the growth of dendrite structures are presented.     

A Quick Numerical Method for Analyzing Nonlinear Effects of Excited State Absorption

A semi-analytical difference method for analyzing nonlinear effects of excited state optical absorption is presented. In comparison with Hughes' method and traditional difference method, the advantages of the semi-analytical difference method are speed-up in computation time, high accuracy and good stabilization.     

A Quick Numerical Method for Analyzing Nonlinear Effects of Excited State Absorption

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An Extension of Mapping Deformation Method and New Exact Solution for Three Coupled Nonlinear Partial Differential Equations

In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.     

Weak Power-Counting Theorem for the Renormalization of the Nonlinear Sigma Model in Four Dimensions

The formulation of the non linear σ-model in terms of flat connection allows the construction of a perturbative solution of a local functional equation by means of cohomological techniques which are implemented in gauge theories. In this paper we discuss some properties of the solution at the one-loop level in D = 4. We prove the validity of a weak power-counting theorem in the following form: although the number of divergent amplitudes is infinite only a finite number of counterterms parameters have to be introduced in the effective action in order to make the theory finite at one loop, while respecting the functional equation (fully symmetric subtraction in the cohomological sense). The proof uses the linearized functional equation of which we provide the general solution in terms of local functionals. The counterterms are expressed in terms of linear combinations of these invariants and the coefficients are fixed by a finite number of divergent amplitudes. These latter amplitudes contain only insertions of the composite operators φ₀ (the constraint of the non linear σ-model) and F _μ (the flat connection). The structure of the functional equation suggests a hierarchy of the Green functions. In particular once the amplitudes for the composite operators φ₀ and F _μ are given all the others can be derived by functional derivatives. In this paper we show that at one loop the renormalization of the theory is achieved by the subtraction of divergences of the amplitudes at the top of the hierarchy. As an example we derive the counterterms for the four-point amplitudes. PACS numbers: 11.10.Gh, 11.30.Rd     

Statistical analysis of cellular detonation dynamics from numerical simulations: one-step chemistry

In this paper, two methods are developed for statistically analysing the nonlinear cellular dynamics from numerical simulations of gaseous detonations, one use of which is the systematic determination of detonation cell sizes from such simulations. Both these methods rely on signed vorticity records in which the individual families of transverse waves are captured independently. The first method involves an automated extraction of the main triple-point tracks from the vorticity records, allowing statistical analysis of the spacings between neighbouring tracks. The second method uses the autocorrelation function to spectrally analyse the vorticity records. These methods are then employed for a preliminary analysis of the cellular dynamics of the standard, idealized one-step chemistry model. Evidence is found for ‘cell size doubling’ bifurcations in the one-step model as the cellular dynamics become more irregular (e.g. as the activation is increased). It is also shown that the statistical models converge slowly due to systematic ‘shot-to-shot’ variation in the cellular dynamics for fixed parameters with different initial perturbations. Instead, it appears that a range of equally probable cell sizes can be obtained for given parameters.     

Electric Black Holes in a Model of Nonlinear Electrodynamics

The electric counterpart of the magnetic black hole solution found in nonlinear electrodynamics (NED) is presented. The electric field emerges regular and confined whereas the spacetime which satisfies all the energy conditions is singular. Our result is in conformation with a theorem proved before about the existence of regular electric black holes. The thermal properties of the black hole including the first law, Smarr's formula, and the thermal stability are investigated. This provides a chance to compare the electric and magnetic types of black holes in a particular model of NED.     

一种多元非线性模型在激光诱导击穿光谱定量分析中的应用

现有的激光诱导击穿光谱定量分析模型大多是基于激光诱导等离子体处于局部热平衡这一假设,而实际上等离子体只是在有限的时间、空间内近似处于热平衡状态。非热平衡状态下各个能级上的粒子布居数不服从玻尔兹曼分布,故用某一能级的单一谱线做定量分析会带来一定误差。考虑到等离子体的非热平衡状态,提出了一种多元非线性定量分析模型,该模型充分利用了待分析粒子的不同上能级对应的多条跃迁谱线信息,能够有效减小信号不稳定对定量分析结果的影响。利用此模型和建立在等离子体局部热平衡假设上的单谱线内标模型分别对30块钢铁样品中Mn元素的含量进行定量分析对比,对比结果表明,多元非线性模型的测量准确性和重复性均优于单谱线内标模型。     

Similarity Reduction and Integrability for the Nonlinear Wave Equations from EPM Model

Four types of similarity reductions are obtained for the nonlinear wave equation arising in the elasto-plastic-microstructure model by using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou.As a result,the nonlinear wave equation is not integrable.     

扩展互作用振荡器非线性理论与模拟

为了对扩展互作用振荡器(EIO)进行更为高效研究与设计,提出了一种非线性理论与数值模拟相结合的方法对其进行分析,编制了基于一维电子圆盘模型的数值计算程序,并结合MAGIC模拟结果对其准确性进行了讨论。非线性模拟中,35 GHz EIO输出功率为125 W,频率为35.01 GHz,对应的MAGIC模拟结果分别为100 W,35.11 GHz;110 GHz EIO输出功率为220 W,频率为107.9 GHz,对应的MAGIC模拟结果分别为190 W,107.93 GHz。非线性方法使得模拟速度有了很大的提高,单次计算时间小于5 min,并且所得数据与传统软件模拟得到的特性曲线相比变化趋势一致、数值上也较为接近。     

扩展互作用振荡器非线性理论与模拟

为了对扩展互作用振荡器(EIO)进行更为高效研究与设计,提出了一种非线性理论与数值模拟相结合的方法对其进行分析,编制了基于一维电子圆盘模型的数值计算程序,并结合MAGIC模拟结果对其准确性进行了讨论。非线性模拟中,35GHz EIO输出功率为125W,频率为35.01GHz,对应的MAGIC模拟结果分别为100W,35.11GHz;110GHz EIO输出功率为220W,频率为107.9GHz,对应的MAGIC模拟结果分别为190W,107.93GHz。非线性方法使得模拟速度有了很大的提高,单次计算时间小于5min,并且所得数据与传统软件模拟得到的特性曲线相比变化趋势一致、数值上也较为接近。     

封闭圆内开缝圆自然对流的非线性特性研究

本文通过数值计算对封闭圆内开缝圆自然对流的非线性特性进行了研究。数值计算以整个流场为计算区域,采用非稳态数学模型和具有QUICK差分格式的SIMPLE算法。计算结果表明,在不同参数下流动和换热存在稳态定常解、周期性振荡解、拟周期性振荡解和非周期性振荡解。稳态定常解的相图是一个点;周期性振荡解的相图是一个极限环,对应功率谱含一个基频及其谐波;拟周期性振荡解的相图为环面,对应功率谱含两个不相关的频率及它们的线性组合频率;非周期性振荡解的功率谱为无规则的宽带连续谱。     

Numerical Solutions of a Class of Nonlinear Evolution Equations with Nonlinear Term of Any Order

In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions： numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.     

底部加热长方体腔内自然对流的非线性特性

采用SIMPLE算法,QUICK差分格式,对底部加热三维长方体腔内空气的自然对流进行了数值模拟。根据模拟结果,探讨了方腔内流体流动与换热的静态分岔与振荡等非线性现象。数值结果显示,在固定的几何尺寸和不同Ra的情况下,当初始场不同时,会出现若干不同的解,即存在解的静态分岔;在固定的几何尺寸和相同的初始场情况下,低Ra时流动和换热处于稳态,当Ra超过某一临界值时,流动和换热就会随时间振荡,并通过倍周期分岔过渡到混沌;当方腔的几何尺寸不同时,分岔点的特征值Ra也发生变化。