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1.
In order to describe the time delay in the surface roughing process the Kardar-Parisis-Zhang (KPZ) equation with memory effects is constructed and analysed using the dynamic renormalization group and the power counting mode coupling approach by Chattopadhyay [2009 Phys. Rev. E 80 011144]. In this paper, the scaling analysis and the classical self-consistent mode-coupling approximation are utilized to investigate the dynamic scaling behaviour of the KPZ equation with memory effects. The values of the scaling exponents depending on the memory parameter are calculated for the substrate dimensions being 1 and 2, respectively. The more detailed relationship between the scaling exponent and memory parameter reveals the significant influence of memory effects on the scaling properties of the KPZ equation. 相似文献
2.
Q.-M. Nie W. Zhou Q.-H. Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,65(4):485-489
The non-equilibrium phase transitions of the fullyfrustrated (f = 1/2) square lattice Coulomb gas (CG) modeldriven by external
electrical fields are studied in the frameworkof the short-time dynamic scaling approach. The criticaltemperature Tc, the static and dynamic critical exponents2β/ν, ν, and z are obtained for several smalldriving fields. The results show that
Tc decreases with theincrease of electric field, and 2β/ν and z arestrongly dependent on the external electric field. Interestingly,contrary
to the equilibrium case, in the presence of smallelectric field, the calculated exponent ν is close to that inpure 2D Ising
model, which provides numerical evidence thatexternal electric field may change the universality class of thef = 1/2 CG system. 相似文献
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W. Q. Duan 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(2):271-276
Identifying universal patterns in complex economic
systems can reveal the dynamics and organizing principles underlying the
process of system evolution. We investigate the scaling behaviours that have
emerged in the international trade system by describing them as a series of
evolving weighted trade networks. The maximum-flow spanning trees (constructed by maximizing the total
weight of the edges) of these networks exhibit two universal scaling
exponents: (1) topological scaling exponent η = 1.30 and (2) flow
scaling exponent ζ = 1.03. 相似文献
5.
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
6.
Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model
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In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model,the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method.In the simulation,noise reduction technique is used in order to eliminate the crossover effect.Our results show that due to the existence of the finite-size effect,the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L > 256.This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys.Rev.E 70 031607].In addition,our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour. 相似文献
7.
Recently, the scaling result z=d for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in order to determine the actual value of z. We study a model of quantum bosons at T=0 with disorder in 2D using highly effective worm Monte?Carlo simulations. Our data analysis is based on a finite-size scaling approach to determine the scaling of the quantum correlation time from simulation data for boson world lines. The resulting critical exponents are z=1.8±0.05, ν=1.15±0.03, and η=-0.3±0.1, hence suggesting that z=2 is not satisfied. 相似文献
8.
K. Uzelac Z. Glumac O. S. Barišić 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(1):101-108
We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying
interactions of the form 1/r1+σ. The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied.
The dynamical critical exponents θ' and z are derived in the cases q=2 and q=3 for several values of the parameter σ belonging
to the nontrivial critical regime. 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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The self-consistent mode-coupling approximation of Colaiori and Moore [Phys. Rev. Lett. 86 (2001) 3946] is generalized to the analysis of the Sun–Guo–Grant equation to investigate its dynamic scaling properties in the strong-coupling regime. The corresponding values of the dynamic exponents are calculated for the substrate dimension d=1 and 2, respectively, and are also compared with previous analytical and numerical results. It can be seen that our discussion and calculation made in present paper are reasonable and reliable. 相似文献
15.
We have investigated the proof of the H theorem within a
manifestly covariant approach by considering the relativistic
statistical theory developed in [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002); G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)]. As it
happens in the nonrelativistic limit, the molecular chaos hypothesis
is slightly extended within the Kaniadakis formalism. It is shown
that the collisional equilibrium states (null entropy source term)
are described by a κ power law generalization of the
exponential Juttner distribution, e.g.,
,
with θ=α(x)+βμpμ, where α(x) is a
scalar, βμ is a four-vector, and pμ is the
four-momentum. As a simple example, we calculate the relativistic
κ power law for a dilute charged gas under the action of an
electromagnetic field Fμν. All standard results are readly
recovered in the particular limit κ→0. 相似文献
16.
Z.-Q. Jiang L. Guo W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(3):347-355
A phenomenological investigation of the endogenous and
exogenous dynamics in the fluctuations of capital fluxes is carried
out on the Chinese stock market using mean-variance analysis,
fluctuation analysis, and their generalizations to higher orders.
Non-universal dynamics have been found not only in the scaling
exponent α, which is different from the universal values 1/2
and 1, but also in the distributions of the ratio η=
σexo / σendo of individual stocks. Both
the scaling exponent α of fluctuations and the Hurst exponent
Hi increase in logarithmic form with the time scale Δt
and the mean traded value per minute 〈fi 〉,
respectively. We find that the scaling exponent αendo
of the endogenous fluctuations is independent of the time scale.
Multiscaling and multifractal features are observed in the data as
well. However, the inhomogeneous impact model is not verified. 相似文献
17.
The form of the universal scaling law of the critical dynamic exponent, z = Dƒ + 2/υ, is found on a family of regular fractals by the exact TDRG method. Here, we generate a regular fractal by an anisotropic growing process. Identifying the growing probabilities as the interactions between Ising spins on the fractals, we map the growing probability clouds as a group of the anisotropic Ising Hamiltonians. Applying the RG transformations, we find that the systems of this group of Ising Hamiltonians can be described by two universal static correlation exponents υ0 = ∞ and υ = 1. So, the growing processes proposed by us capture the essential features in the directed DLA simulations. The studies about their critical dynamic behaviours reveal that unlike the one-dimensional chain the critical dynamics of the kinetic Ising model on the regular fractals is universal. The further discussions show that there is a universal scaling law form of the critical dynamic exponent of the kinetic Ising model, z = Dƒ + Rmax/2υ, on the site models of the regular fractals with Rmin = 2. Meanwhile, we discuss Daniel Kandal's correction to the formula of the,critical dynamic exponent in the TDRG method and show that our TDRG calculations are exact. 相似文献
18.
为探讨分形基底结构对生长表面标度行为的影响, 本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为. 研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学标度行为, 并且满足Family-Vicsek标度规律. 虽然谢尔宾斯基箭头和蟹状分形基底的分形维数相同, 但模拟得到的标度指数却不同, 并且粗糙度指数 α与动力学指数z也不满足在欧几里得基底上成立的标度关系α+z=2. 由此可以看出, 标度指数不仅与基底的分形维数有关, 而且和分形基底的具体结构有关. 相似文献
19.
M. Dubé M. Rost K.R. Elder M. Alava S. Majaniemi T. Ala-Nissila 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(4):701-714
The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous
imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered
medium appearing as a quenched random field . The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential,
which reproduces Washburn's equation for the slowing down motion of the average interface position H. The interface is found to be superrough, with global roughness exponent , indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively
reproduces the experimental results of Horv'ath and Stanley (Phys. Rev. E 52, 5166 (1995)) on the temporal scaling of the interface.
Received 24 November 1999 相似文献
20.
R. Schorr H. Rieger 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(3):347-354
We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random
potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the
strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed
as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d = 2 and 3. We show that the exponent relation 2ν - ω = 1 holds at least in d = 2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence
of strong disorder correlations.
Received 20 December 2002 / Received in final form 10 April 2003 Published online 20 June 2003
RID="a"
ID="a"e-mail: schorr@lusi.uni-sb.de 相似文献