Self-organized Criticality Model for Ocean Internal Waves

In this paper, we present a simple spring-block model for ocean internal waves based on the self-organized criticality （SOC）. The oscillations of the water blocks in the model display power-law behavior with an exponent of -2 in the frequency domain, which is similar to the current and sea water temperature spectra in the actual ocean and the universal Garrett and Munk deep ocean internal wave model [Geophysical Fluid Dynamics 2 （1972） 225; J. Geophys. Res. 80 （1975） 291]. The influence of the ratio of the driving force to the spring coefficient to SOC behaviors in the model is also discussed.     

Benford＇s Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford＇s law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford＇s logarithmic distribution of β-deeay half-lives can be explained in terms of Neweomb＇s justification of Benford＇s law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford＇s law. This indicates that Benford＇s law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.     

Integrating Factors and Conservation Laws of Generalized Birkhoff System Dynamics in Event Space

In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.     

Competition Between Self-birth and Catalyzed Death in Aggregation Growth with Catalysis Injection

We propose two irreversible aggregation growth models of aggregates of two distinct species (A and B) to study the interactions between virus aggregates and medicine efficacy aggregates in the virus-medicine cooperative evolution system. The A-species aggregates evolve driven by self monomer birth andB-species aggregate-catalyzed monomer death in model I and by self birth, catalyzed death, and self monomer exchange reactions in model II, while the catalyst B-species aggregates are assumed to be injected into the system sustainedly or at a periodic time-dependent rate. The kinetic behaviors of the A-species aggregates are investigated by the rate equation approach based on the mean-field theory with the self birth rate kernel I_A(K)=Ik, catalyzed death rate kernel J_AB(k)=Jk and self exchange rate kernel K_A(k,l)=Kkl. The kinetic behaviors of the A-species aggregates are mainly dominated by the competition between the two effects of the self birth (with the effective rate I) and the catalyzed death (with the effective rate JB₀), while the effects of the self exchanges of the A-species aggregates which appear in an effectiverate KA₀ play important roles in the cases of I>JB₀ and I=JB₀. The evolution behaviors of the total mass M^A(t)₁ and the total aggregate number M^A(t)₀ are obtained, and the aggregate size distribution a_k(t) of species A is found toapproach a generalized scaling form in the case of I ≧ JB₀ and a special modified scaling form in the case of I0. The periodical evolution of the B-monomers concentration plays an exponential form of the periodic modulation.     

围压状态下的混凝土本构模型

利用已有不同围压下的混凝土三向压缩试验, 分析研究不同围压条件对混凝土强度和应力-应变关系的影响。试验表明, 把混凝土简单视为脆性材料的观点并不符合实际情况, 塑性特征也是混凝土材料主要力学特征。由热力学定律出发, 本文提出了多次方形式的屈服函数和与围压状态相关联的损伤标准化函数, 提出了考虑围压状态的混凝土本构模型。试验结果与数值计算比较表明, 该本构关系可以很好地描述混凝土在不同围压状态下的力学损伤发展和脆-塑性转换力学特征, 也可以描述拉伸作用下的应力-应变关系, 具有一定的普遍意义。     

一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

Radiation energy flux of Dirac field of static spherically symmetric black holes

By the statistical entropy of the Dirac field of the static spherically symmetric black hole, the result is obtained that the radiation energy flux of the black hole is proportional to the quartic of the temperature of its event horizon. That is, the thermal radiation of the black hole always satisfies the generalised Stenfan--Boltzmann law. The derived generalised Stenfan--Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient related to the space--time metric near the event horizon and the average radial effusion velocity of the radiation particles from the thin film. Finally, the radiation energy fluxes and the radiation powers of the Schwarzschild black hole and the Reissner--Nordstrõm black hole are derived, separately.     

Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model

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.     

湍流能量耗散率标度律实验研究

应用粒子图像测速(PIV)系统对平板湍流边界层内流向和法向的瞬时速度进行了测量。湍流的能量耗散率由轴对称假设得到,同时在研究湍流动能耗散率标度律的过程中采用传统的统计学方法。实验结果显示,对于不同尺度上和不同法向位置湍流耗散率标度律来说,湍流耗散主要发生在小尺度上,也就是说湍动能耗散率标度律在小尺度上具有普适性。另外,根据层次结构理论假设,通过PIV实验数据对最高激发态的标度指数进行了研究,结果发现,最高激发态存在绝对标度指数,并且绝对标度律是由信号中最强耗散涨落的局部结构产生的。     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001