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基于动力学重整化群理论研究表面界面生长动力学标度奇异性问题, 得到含时空关联噪声的表面生长方程标度奇异指数的一般结果,并将此方法应用于几种典型的局域生长方程——Kardar-Parisi-Zhang(KPZ)方程、线性生长方程、Lai-Das Sarma-Villain(LDV)方程.结果表明,在长波长极限下局域生长方程的动力学标度奇异性与最相关项、基底维数以及噪声有关,并且若出现标度奇异性,只会是超粗化(super rough)奇异标度行为,而不是内禀(intrinsically)奇异标度行为.
关键词:
标度奇异性
动力学重整化群理论
时空关联噪声 相似文献
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为探讨含关联噪声的空间分数阶随机生长方程的动力学标度行为,本文利用Riesz分数阶导数和Grümwald-Letnikov分数阶导数定义方法研究了关联噪声驱动下的空间分数阶Edwards-Wilkinson (SFEW)方程在1+1维情况下的数值解,得到了不同噪声关联因子和分数阶数时的生长指数、粗糙度指数、动力学指数等,所求出的临界指数均与标度分析方法的结果相符合.研究表明噪声关联因子和分数阶数均影响到SFEW方程的动力学标度行为,且表现为连续变化的普适类. 相似文献
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在(2+1)维情况下,利用数值模拟研究了Kuramoto-Sivashinsky (K-S)与Karda-Parisi-Z hang (KPZ)模型所决定的非平衡态界面生长演化过程.结果表明,KPZ与K-S模型都表现出明 显的时间和空间标度特性.相对于KPZ模型而言,K-S模型所对应的表面具有更明显的颗粒特 征,当生长时间较长时,生长界面呈现蜂窝状结构.通过数值相关分析得到了生长界面的粗 糙度指数、生长指数和动态标度指数等参数.从两种模型对应的表面形貌特征和表面参数来 看,在(2+1)维情况下,KPZ与K-S模型所决定的表面具有完全不同的动态标度行为,属于不 同的两类物理模型.
关键词:
Kuramoto-Sivashinsky (K-S)模型
Karda-Parisi-Zhang(KPZ)模型
分形
数值模拟 相似文献
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采用Kinetic Monte Carlo方法对1+1维抛射沉积(BD)模型内部结构的动力学行为进行了大量的数值模拟研究.分别分析了空洞密度和内部界面的动力学行为.研究表明,空洞密度呈高斯型分布,其平均值首先随生长时间快速增长,然后达到一个与基底尺寸无关的饱和值.除表面宽度,还引入了新的极值统计方法来分析该模型内部界面的动力学行为,分析结果显示,1+1维BD模型内部界面的演化满足标准的Family-Vicsek标度规律,并且属Kardar-Parisi-Zhang方程所描述的普适类.最后对表面宽度和极值统计两种理论方法的有限尺寸效应进行了比较. 相似文献
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利用Hirota方法及Riemann theta函数得到了(2+1)维Boussinesq方程的新的周期解.在极限情况下,该周期解退化为孤子解.
关键词:
Hirota方法
Riemann theta 函数
(2+1)维Boussinesq方程
周期解 相似文献
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将扩展的Riccati方程映射法推广到了(3+1)维非线性Burgers系统,得到了系统的分离变量解;由于在解中含有一个关于自变量(x,y,z,t)的任意函数,通过对这个任意函数的适当选取,并借助于数学软件Mathematica进行数值模拟,得到了系统的新而丰富的局域激发结构和分形结构.结果表明,扩展的Riccati方程映射法在求解高维非线性系统时,仍然是一种行之有效的方法,并且可以得到比(2+1)维非线性系统更为丰富的局域激发结构.
关键词:
扩展的Riccati方程映射法
(3+1)维非线性Burgers方程
局域激发结构
分形结构 相似文献
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L. Zhang G. Tang Z. Xun K. Han H. Chen B. Hu 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(2):227-234
The long-wavelength properties of the (d + 1)-dimensional
Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative
noises are investigated by use of the dynamic renormalization-group (DRG)
theory. The dynamic exponent z and roughness exponent α are
calculated for substrate dimensions d = 1 and d = 2, respectively. In the
case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5
, which are consistent with the results obtained by Ueno et al. in the
discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71,
046138 (2005)] and are believed to be identical with the dynamic scaling of
the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we
find a fixed point with the dynamic exponents z = 2.866 and α = -0.866
, which show that, as in the 1 + 1 dimensions situation, the existence of
the conservative noise in 2 + 1 or higher dimensional KS equation can also
lead to new fixed points with different dynamic scaling exponents. In
addition, since a higher order approximation is adopted, our calculations in
this paper have improved the results obtained previously by Cuerno and
Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS
equation, where the conservative noise is not taken into account. 相似文献
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It has recently been proposed that fluctuating "pulled" fronts propagating into an unstable state should not be in the standard Kardar-Parisi-Zhang (KPZ) universality class for rough interface growth. We introduce an effective field equation for this class of problems, and show on the basis of it that noisy pulled fronts in d+1 bulk dimensions should be in the universality class of the ((d+1)+1)D KPZ equation rather than of the (d+1)D KPZ equation. Our scenario ties together a number of heretofore unexplained observations in the literature, and is supported by previous numerical results. 相似文献
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Bahraminasab A. Tabei S. M. A. Masoudi A. A. Shahbazi F. Reza Rahimi Tabar M. 《Journal of statistical physics》2004,116(5-6):1521-1544
The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension d + 1-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height's PDF of zero tension KPZ equation shows lack of positivity after a finite time t c . The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale t c and the singularity time scale t c.v→0 of the KPZ equation with an infinitesimal surface tension is investigated. 相似文献
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We argue that while fluctuating fronts propagating into an unstable state should be in the standard Kardar-Parisi-Zhang (KPZ) universality class when they are pushed, they should not when they are pulled: The 1/t velocity relaxation of deterministic pulled fronts makes it unlikely that the KPZ equation is their proper effective long-wavelength low-frequency theory. Simulations in 2D confirm the proposed scenario, and yield exponents beta approximately 0.29+/-0.01, zeta approximately 0.40+/-0.02 for fluctuating pulled fronts, instead of the (1+1)D KPZ values beta = 1/3, zeta = 1/2. Our value of beta is consistent with an earlier result of Riordan et al., and with a recent conjecture that the exponents are the (2+1)D KPZ values. 相似文献
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S. V. Ghaisas 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(4):557-562
Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local
heights, measurable for any lattice model. Invariance in the
change of this distribution in time is used to determine the cross over
effects in various models. The analysis is applied to the discrete linear growth equation
and Kardar-Parisi-Zhang (KPZ) equation. A new model is devised that shows early convergence to the KPZ dynamics. Various known
conservative and non conservative models are tested on a one
dimensional substrate by comparing the growth results with the exact KPZ and linear growth equation results. The comparison
helps in establishing the condition that determines the presence of cross over effect for the given model. The new model is
used in (2+1) dimensions to predict close to the true value of roughness constant for KPZ equation. 相似文献
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We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable. Developing techniques for dealing with this initial condition in the replica analysis, we elucidate some exact nature of the height fluctuation for the KPZ equation. In particular, we obtain an explicit representation of the probability distribution of the height in terms of the Fredholm determinants. Furthermore from this expression, we also get the exact expression of the space-time two-point correlation function. 相似文献
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Based on the scaling idea of local slopes by López et al. [Phys. Rev. Lett. 94 (2005) 166103], we investigate anomalous dynamic scaling of (d+1)-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang (KPZ), Sun-Guo-Grant (SGG), and
Lai-Das Sarma-Villain (LDV) equations. The anomalous scaling exponents
in both the weak- and strong-coupling regions are obtained, respectively. 相似文献
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The continuum Kardar-Parisi-Zhang equation in one dimension is lattice discretized in such a way that the drift part is divergence free. This allows to determine explicitly the stationary measures. We map the lattice KPZ equation to a bosonic field theory which has a cubic anti-hermitian nonlinearity. Thereby it is established that the stationary two-point function spreads superdiffusively. 相似文献
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We study a noisy Kuramoto–Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar–Parisi–Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation. 相似文献