流体力学的一个定理及在气象学上的应用(大气温度直降率的变化及对流顶同质点造成的条件)

一.基本关系的导出 设某量值s(k,y,z,t)在连续体中为x,y,z,t的函数,则其随质点运动的变化率可写成 ds/dt=s/t+u(s/x)+v(s/t)+w(s/z) (1)以上u,v,w,代表该质点在x,y,z三方向的分速;代表s数值在空间的陡度;其余符号与通常相同,将上式对x微分,得 (2)以连续方程 (3)中的u/x数值代入(2)式,此处ρ为连续的密度,In代表自然对数,则得     

截面的几何形状决定三维函数的混沌特性

计算仿真发现,函数f(x,y,z)=sin(k(x2+y2+z2)),f(x,y,z)=k(1-(x2+y2+z2))e(-(x+y+z+u)2),f(x,y,z)=k((x2+y2+z2)/3)(1-(x2+y2+z2)/3)分别与另外两个随机产生的二次多项式函数均可组合成一个三维离散动力系统,当系数k,u在一定范围内取值时,系统出现混沌吸引子的概率可以大于90%.通过绘制分岔图、Lyapunov指数图等对上述系统的混沌特性进行了分析.分析发现,出现混沌概率高的原因是这3个函数的截面都是中间凸起或中间凹陷的曲面,在这样的截面条件下系统容易出现混沌.这普遍适用于三维函数,利用这些三维离散动力系统绘制出的大量吸引子图形具有使用价值和研究价值.     

非线性系统可逆的多轨线方法

乌克兰科学院A．M．kovalev教授于1993年首次提出了针对一般非线性系统{x=f(t,x,u)；y=h(t,x,u),x(t0)=x0的多轨线求逆方法。本文将该方法引入仿射非线性系统，使不可逆系统在一定条件下成为可逆。并给出了具体的求逆步骤，举例说明。     

非线性振子的矩阵元及其经典近似

对于势能为V(x)=1/2 mω2x2+λx4的非线性谐振子,不能用微扰论对经典方程进行求解.这里利用海森伯对应原理,由量子力学的矩阵元得到了非线性振子的经典解,从而对于非线性振子的性质有了进一步的理解.     

特殊洛仑兹变换的一种简单推导

本文介绍一种简便的推导特殊洛仑兹变换的方法以供初学者参考. 1.根据相对性原理和初始时刻(t=t‘=0)坐标系∑(x’、y’、z’)和∑(x,y,z原点(0’,0)重合可知,变换必须是线性齐次的. 2.如图示,因xoy面与x’o’y’面始终重合,故无论x、y.t、x’、y’、t’取何值,z=0,z’=0总是同时成立.、所以z’=αz其中α为常数.考虑到z与z之间相互交换是对等的.应有z=αz’则有α=±1,因z’轴与z轴指向相同,应取α=1,即得z=z’(1) 同理,考察zOx面与z’O’x’而始终重合,可得 y=y’(2) 3.因yoz面与y’o’z’面始终平行,在某一时刻t,∑’系的原点o’对∑系…     

含外力项的广义KdV方程的类孤子解

本文利用广义KP方程的B?cklund变换,获得了含外力项的广义KdV方程u_t+6uu_x+u_xxx+6f(t)u=g(t)+x(f′+12f²) (1)的类孤子解。 关键词：     

关于牛顿第二定律表达式的商榷

河北矿冶学院的林声衡、孔非吾同志在《大学物理》1986年第6 期上发表了“f=ma和f=哪个适合火箭运动?”的文章(下称林文),本文提出几点与林文商榷.这里(1)一(6)式沿用林文中的公式号码.一、本文的推导方法 在t时刻,火箭本体质量为M(t)(林文中的m),绝对速度为u(t).在t+t时刻,从本体分离出m,它的绝对速度为u(t+t),分离后本体质量变为M(t+t),绝对速度变为v(t+t). 我们选一个包括本体的(瞬时)不变质量系统为研究对象,在t时刻不变质量系统是M(t),在t+t时刻是M(t+t) +m,即有 M(t)=M(t+t)+m=M(t)+M+m(8) 我们对不变质量系统应用质点系的动量定…     

对2010年高考全国卷Ⅰ第21题答案的质疑

题目:(2010年高考全国卷Ⅰ第21题)一简谐振子沿x轴振动,平衡位置在坐标原点.t=0时刻振子的位移x=-0.1m;t=4/3s时刻x=0.1m;t=4s时刻x=0.1m.该振子的振幅和周期可能为     

求解(H^)=5/3(a^)+(a^)+2/3((a^)2+(a^)+2)量子系统能谱新方法

通过对形如(H^)=5/3(a^)+(a^)+2/3((a^)2+(a^)+2)哈密顿量的分析、还原和改造,给出求解该量子系统量子化能谱的两种新方法.     

关于光圈颜色的计算分析

一、色度计算简介人眼除了能辨别亮度差别外,还具有分辨彩色的能力。彩色光在人眼中由三种彩色灵敏度不同的接收器官来衡量。三个相对彩色灵敏度的最大值位于光谱的红色、绿色、蓝色区域。这三种基色以不同强度比例组合起来,就产生了彩色视觉。为了研究问题的方便,便于计算,1931年国际上采用了一种新的系统,称为标准基色量系统。一个彩色量可表示为:F=X(x)+Y(y)+Z(z)式中,(x)、(y)、(z)称为标准基色量。X、Y、Z称为标准三色系数。(x)(y)(z)实际上已不代表真正的颜色,只是三种作为计算单位的假想颜色。     

Compactification of patterns by a singular convection or stress

A wide variety of propagating disturbances in physical systems are described by equations whose solutions lack a sharp propagating front. We demonstrate that presence of particular nonlinearities may induce such fronts. To exemplify this idea, we study both dissipative u_{t}+ partial differential_{x}f(u)=u_{xx} and dispersive u_{t}+ partial differential_{x}f(u)+u_{xxx}=0 patterns, and show that a weakly singular convection f(u)=-u;{alpha}+u;{m}, 0相似文献   

Line soliton interactions of the Kadomtsev-Petviashvili equation

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u(t)+6uu(x)+3u(xxx))(x)+u(yy)=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y-->infinity coincide with those of the N asymptotic line solitons as y-->-infinity. We also show that the (2N-1)!! types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.     

Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps

Ensemble averages of the sensitivity to initial conditions xi(t) and the entropy production per unit of time of a new family of one-dimensional dissipative maps, x(t+1)=1-ae(-1/|x(t)|(z))(z>0), and of the known logisticlike maps, x(t+1)=1-a|x(t)|(z)(z>1), are numerically studied, both for strong (Lyapunov exponent lambda(1)>0) and weak (chaos threshold, i.e., lambda(1)=0) chaotic cases. In all cases we verify the following: (i) both [ln((q)x triple bond (x(1-q)-1)/(1-q); ln((1)x=ln(x] and [S(q) triple bond (1- sigma p(q)(i))/(q-1); S(1)=- sigma p(i)ln(p(i)] linearly increase with time for (and only for) a special value of q, q(av)(sen), and (ii) the slope of and that of coincide, thus interestingly extending the well known Pesin theorem. For strong chaos, q(av)(sen)=1, whereas at the edge of chaos q(av)(sen)(z)<1.     

Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

In this paper, we introduce a new invariant set ˜E₀={u:u_x=f^ˊ(x)F(u)+ε [g^ˊ(x) -f^ˊ(x)g(x)]F(u)exp(-∫^u(1/F(z))dz), where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact solutions to nonlinear diffusion equation u_t=(D(u)u_x)_x+Q(x,u)u_x+P(x,u), are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set ˜E₀.     

FROM THREE-TORUS TO FRACTAL AND THEN TO CHAOS

We use numerical methods to study the model x(n+l)=λx(n) (x(n)-1)+ef(θ(n),φ(n)),θ(n+1)=θ(n)+A, φ(n+1)=φ(n)+B. As e is small, we get doubled three-tori. Increasing e the tori become fractal three-tori, the dimension is not integer, while the trajectory does not diverge exponentially. Finally it changes into chaos. The critical parameter values.for chaos are approximately calculated. So one of the roads from three-tori to chaos is three-tqri→fractal three-tori (not chaos)→chaos.     

Painleve' analysis of a variable coefficient Sine-Gordon equation

In this paper we study a variable coefficient Sine-Gordon (vSG) equation given by theta(tt)-theta(xx)+F(x,t)sin theta=0 where F(x,t) is a real function. To establish if it may be integrable we have performed the standard test of Weiss, Tabor, and Carnevale (WTC). We have got that the (vSG) equation has the Painleve' property (Pp) if the function F(x,t) satisfies a well-defined nonlinear partial differential equation. We have found the general solution of this last equation and, consequently, the functions F(x,t) such that the (vSG) equation possesses the (Pp), are given by F(x,t)=F(1)(x+t)F(2)(x-t) where F(1)(x+t) and F(2)(x-t) are arbitrary functions. Using this last result we have obtained some particular solutions of the vSG equation. (c) 1995 American Institute of Physics.     

Reaction and concentration dependent diffusion model

We study the formation of patterns in the genuinely nonlinear reaction diffusion model equation u(t)+2a(u(2))(x) = (u(2))(xx)+F(x,u), where u may be viewed as an amplitude of a thermal wave in plasma or density of a biological species and F = u(1-u) or F = q(x)u(l), l = 0,2. We provide a transformation which maps the model into a purely diffusive process free of its interacting part and its intrinsic temporal and spatial scales. The well known attractors of the diffusive process enable us to completely characterize the emerging patterns which, depending on F and initialization, may be a semicompact, or a compact, traveling wave or a nontrivial equilibrium.     

钠分子B^1∏u与2^1∑g^＋间的碰撞激发转移

The B 1pi(u) electronic state of Na2 was excited by the 441.6 nm He-Cd laser line. The Na atomic transitions and the A 1sigma(u)+ --> X 1sigma(g)+ band of Na2 were recorded. From the intensities and spectra of the Na and Na2 fluorescence several collisional processes in the excited sodium atom-dimer system were identified. The Na atomic lines are the result of collisional energy transfer from Na2 (B 1pi(u)) to Na(3P). Predissociation process may also contribute to atomic fluorescence. The A 1sigma(u)+ --> X 1sigma(g)+ band is interpreted through a populating mechanism involving collisional transfer from B 1pi(u) to 2 1sigma(g)+ followed by a radiative transfer to the A 1sigma(u)+ state. From the decay constants and fluorescence intensities, the rate coefficient at 360 degrees C for collisional energy transfer from Na2 (B 1pi(u)) to Na2 (2 1sigma(g)+) was found to be 5.7 x 10(-10) cm3 x s(-1). The predissociation rate of the B 1pi(u) is 2.7 x 10(6) s(-1).     

对非线性量子场论与激光理论中的微扰谐振梯度算子方法的改进

当微优按Hermite多项式H_k的收敛级数作如下展开时,V(X)=b²X²+Σ_k C_kH_k(b^1/2X), 则可将其微扰梯度算子方法应用于微扰谐振子波动方程的求解中.发现若将Hermite多项式基与二项式系数函数依量子数一起使用,则可大大简化微扰梯度与因子分解函数.因此,在不增加其复杂性的情况下,便可求得任意级微扰的本征值与本征函数的分析表示式.通过计算,本文给出了X的偶性微扰势函数V(X),为了说明如何应用改进后的微扰梯度算子方法,本文重新研究了其势函数为V(x)=x²+λX²/(1+gX²),且g>0时的Schr?dinger方程的求解过程. 关键词：     

图象复原的新后验方法

本文就某系统的动态图象的复原,阐述了复原的主要技术过程。提出了一种新的后验模型,即退化信息不是从退化图象本身中提取,而是从给定样本的一系列退化象中提取,从而可以用线性空不变系统的求解模型来处理非线性空变系统的图象复原问题。本文给出了用此方法所获得的处理结果。