共查询到19条相似文献,搜索用时 203 毫秒
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This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances c1 and c2 of two edge dislocations are non-zero, and the condition k2w08+32c1c2(w02-2c1c2)z2>0 is fulfilled (k-wave number, w0-waist width). A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples. 相似文献
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利用定量相场模型, 以Mg-0.5 wt.%Al合金为例模拟了基面((0001)面)内镁基合金的等温自由枝晶生长过程. 通过研究该合金体系数值模拟的收敛性, 获得了最优化值耦合参数λ = 5.5及网格宽度Δx/W0 = 0.4, 并在该参数下系统研究了各向异性强度和过饱和度对枝晶尖端生长速度、尖端曲率半径、Péclet数及稳定性常数σ* 的影响. 结果表明, 由微观可解性理论得到的稳定性系数σ* 与ε6 拟合值σ*≅ ε6 1.81905, 更接近理想值σ * (ε6) ≅ε6 1.75. 此外, 当过饱和度Ω < 0.6时, 稳定性系数σ * 不随ε6 的变化而变化, 而当Ω > 0.6时, 稳定性系数σ * 随着ε6 的增加而减小. 这反映了枝晶的生长由扩散控制向动力学控制的转变. 随着过饱和度的增加, 枝晶形貌由雪花状枝晶向圆状枝晶转变. 相似文献
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本文构造了解色散方程u1=auxxx的若干三层恒稳的半显式差分格式。第Ⅰ、Ⅱ类格式的局部截断误差的阶为O(τ2+h2+(τ2)/(h3));而第Ⅲ、Ⅳ类格式的局部截断误差的阶为O(τ2+h4+((τ)/(h))2+τh)。用判别稳定性的Von Neumann准则可证明:第Ⅰ、Ⅱ类格式及当参数α≤1时的第Ⅲ、Ⅳ类格式都是无条件稳定的,并且当必须的边界条件给定时它们可以显式地进行计算。 相似文献
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研究了裂变系统在宽脉冲外中子源注入驱动下裂变链统计涨落问题.提出了概率分布Wn方程的分解-合成数值模拟计算方法,使裂变系统注入中子源数值模拟计算扩展到一般广义条件(具有任意时间分布、注入时间零点t0概率分布函数P(t0)和数概率分布S(n)等).同时讨论了应用物理模型的等效条件.将基本前提等效条件从单介质区模型扩展到多介质区模型.为解概率分布Wn方程必备参数提供了计算平均公式. 相似文献
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考虑一类演化方程ut=au∂2k+1(其中a是常数,u∂2k+1=∂2k+1u/∂x2k+1,k=1,2……)的有限差分解法。构造了两类具有高稳定性的显式差分格式。并用引入耗散项的方法建立了两类半显式差分格式,它们是无条件稳定的且可显式地进行计算。 相似文献
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本文考虑到d8电子组态中所有自旋三重态和自旋单态对基态的影响,用高阶微扰法导出了d8电子组态在三角对称晶场下光谱和基态EPR普遍公式。发现在三角对称晶场下,d8电子组态离子的g⊥ > g‖或g⊥ < g‖和D > 0或D < 0是以立方对称晶场为界,晶体中顺磁离子的配体沿C3轴伸长或压缩所致。利用所得公式计算了NiCl2和NiSiF6·6H2O晶体的EPR参量,其结果与实验吻合较好。 相似文献
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为了进一步研究纳米导线阵列的排列形状以及阵列数目对其场发射行为的影响,利用镜像悬浮球模型对正方形以及六边形排列的纳米导线阵列的场发射行为进行计算与模拟,近似的得到纳米导线阵列的场发射增强因子满足如下的变化趋势:β=h/ρ(1/1+W)+1/2(1/1+W)2+3,其中h为纳米导线的高度,ρ为纳米导线的半径,W是以R为自变量的函数,R为纳米导线阵列的间距.结果显示纳米导线阵列的排列形状对其场发射性能的影响较小,而阵列间距则是影响场发射性能的关键因素:当R<R0时,场发射增强因子随着阵列间距的减小而急剧减小;当R>R0时,场发射增强因子基本不变,其中R0为导线阵列场发射的最佳间距.进一步研究表明改变纳米导线阵列的数目基本不会改变阵列的场发射性能随间距的变化趋势,但是随着阵列数目的增加,R0会有一定程度的减小,场发射增强因子也会降低.
关键词:
纳米导线
场发射
增强因子
阵列数目 相似文献
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研究多种正幂势函数与逆幂势函数紧密耦合条件下薛定谔径向方程解析解的求解方法.对势函数为V(r)=α1r8+α2r3+α3r2+β3r-1+β2r-3+β1r-4的径向薛定谔方程存在解析解的条件以及精确的解析解进行了研究. 根据量子系统波函数必须满足单值、有界和连续的标准条件,首先求出径向坐标r→∞以及r→0时的渐近解,然后采用非正则奇点邻域附近的波函数级数解法与求得的渐近解相结合,通过幂级数系数比较法得到径向薛定谔方程在势函数系数紧密耦合条件下的一系列定态波函数解析解以及相应的能级结构,并作适当讨论与结论.
关键词:
级数解法
幂势函数
径向波函数
渐近解 相似文献
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The existence of wall or boundary free energies is discussed generally and analyzed explicitly for general lattice systems with scalar (real-valued) spin variables. For systems with ferromagnetic (positive) spin interaction potentials,K, in the bulk andW, for the walls, correlation inequalities and appropriate stability and tempering conditions are used to establish the existence and uniqueness of the limiting free energy per unit area,f
x(K,W), of an infinite planar wall. 相似文献
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A. Heintz 《Journal of statistical physics》1998,90(3-4):663-695
The paper is concerned with the Enskog equation with a constant high density factor for large initial data in L
1(R
n). The initial boundary value problem is investigated for bounded domains with irregular boundaries. The proof of an H-theorem for the case of general domains and boundary conditions is given. The main result guarantees the existence of global solutions of boundary value problems for large initial data with all v-moments initially finite and domains having boundary with finite Hausdorff measure and satisfying a cone condition. Existence and uniqueness are first proved for the case of bounded velocities. The solution has finite norm
where q = (t
0, x) is taken on all possible n-dimensional planes Q(v) in R
n+l intersecting a fixed point and orthogonal to vectors (1, v), v R
n. 相似文献
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We give here a rigorous deduction of the “hydrodynamic” equation which holds in the hydrodynamic limit, for a model system of one-dimensional identical hard rods interacting through elastic collisions. The equation should be considered as the analog of the Euler equation of real hydrodynamics. Owing to the degeneracy of the model, it is written in terms of a functiong(q, v, t) expressing the density of particles with velocityv at the pointq at timet. For this equation we prove an existence and uniqueness theorem in some natural class of functions. Our main result is the proof that if {∈, ∈ >0} is a class of initial states which are homogeneous on a scale much less than ε?1, and if the corresponding particle densities tend, asε→0, in the proper scale, to the initial hydrodynamic densityg o (q,v), then, under some general assumptions on the states ∈? and ong 0, the particle densities of the evolved states at timeε ?1 t, tend asε→0 to the unique solution of the hydrodynamic equation with initial conditiong 0. The proof is completed by exhibiting a large class of initial families {∈, ∈ >0} which possess the required properties. 相似文献
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This paper studies initial-boundary value problems for a class
of nonlinear thermoelastic plate equations. Under some certain
initial data and boundary conditions, it obtains an existence and
uniqueness theorem of global weak solutions of the nonlinear
thermoelstic plate equations, by means of the Galerkin method.
Moreover, it also proves the existence of strong and
classical solutions. 相似文献
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在高维情况下,首先研究了无单元Galerkin方法的形函数构造方法——移动最小二乘法在Sobolev空间Wk,p(Ω)中的误差估计.然后,在势问题的无单元Galerkin方法的基础上,研究了势问题的通过罚函数法施加本质边界条件的无单元Galerkin方法在Sobolev空间中的误差估计.当节点和形函数满足一定条件时,证明了该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响半径密切相关.最后,通过算例验证了结论的正确性.
关键词:
无网格方法
无单元Galerkin方法
势问题
误差估计 相似文献
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This work is devoted to investigating exact solutions of generalized nonlinear fractional diffusion equations with external force and absorption. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we obtain the corresponding exact solution, its diffusive behavior, and the sufficient and necessary conditions for solutions satisfying the boundary condition W(±∞,t)=0 and the sharp initial condition W(x,0)=δ(x). 相似文献
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C. Cercignani 《Journal of statistical physics》1996,84(3-4):875-888
Recently R. Illner and the author proved that, under a physically realistic truncation on the collision kernel, the Boltzmann equation in the one-dimensional slab [0, 1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. Here it is proved that when the Maxwellians associated with the boundary conditions atx=0 andx=1 are the same MaxwellianM
w
, then the solution is uniformly bounded and tends toM
w
fort. 相似文献
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We prove the uniqueness of Riemann solutions in the class of entropy solutions in with arbitrarily large oscillation for the 3 × 3 system of Euler equations in gas dynamics. The proof for solutions with
large oscillation is based on a detailed analysis of the global behavior of shock curves in the phase space and the singularity
of centered rarefaction waves near the center in the physical plane. The uniqueness of Riemann solutions yields their inviscid
large-time stability under arbitrarily large
perturbation of the Riemann initial data, as long as the corresponding solutions are in L
∞ and have local bounded total variation satisfying a natural condition on its growth with time. No specific reference to any
particular method for constructing the entropy solutions is needed.
The uniqueness result for Riemann solutions can easily be extended to entropy solutions U(x,t), piecewise Lipschitz in x, for any t > 0, with arbitrarily large oscillation.
Received: 23 April 2001 / Accepted: 20 September 2001 相似文献
19.
A.S. Fokas 《Communications in Mathematical Physics》2002,230(1):1-39
A rigorous methodology for the analysis of initial-boundary value problems on the half-line, is applied to the nonlinear §(NLS), to the sine-Gordon (sG) in laboratory coordinates, and to the Korteweg-deVries (KdV)
with dominant surface tension. Decaying initial conditions as well as a smooth subset of the boundary values are given, where n=2 for the NLS and the sG and n=3 for the KdV. For the NLS and the KdV equations, the initial condition q(x,0) = q
0
(x) as well as one and two boundary conditions are given respectively; for the sG equation the initial conditions q(x,0) = q
0
(x), q
t
(x,0) = q
1
(x), as well as one boundary condition are given. The construction of the solution q(x,t) of any of these problems involves two separate steps: (a) Given decaying initial conditions define the spectral (scattering)
functions {a(k),b(k)}. Associated with the smooth functions , define the spectral functions {A(k),B(k)}. Define the function q(x,t) in terms of the solution of a matrix Riemann-Hilbert problem formulated in the complex k-plane and uniquely defined in terms of the spectral functions {a(k),b(k),A(k),B(k)}. Under the assumption that there exist functions such that the spectral functions satisfy a certain global algebraic relation, prove that the function q(x,t) is defined for all , it satisfies the given nonlinear PDE, and furthermore that . (b) Given a subset of the functions as boundary conditions, prove that the above algebraic relation characterizes the unknown part of this set. In general this
involves the solution of a nonlinear Volterra integral equation which is shown to have a global solution. For a particular class of boundary conditions, called
linearizable, this nonlinear equation can be bypassed and {A(k),B(k)} can be constructed using only the algebraic manipulation of the global relation. For the NLS, the sG, and the KdV, the following
particular linearizable cases are solved: , respectively, where χ is a real constant.
Received: 22 October 2001 / Accepted: 22 March 2002 Published online: 22 August 2002 相似文献