优化MGM(1,n)模型及其应用研究

从最小二乘估计的适用条件出发,在建立MGM(1,n)模型前,先采用BoxCox变换对原始数据进行变换,以解决或缓解误差项的正态性偏离问题.首先,以模型拟合平均误差最小化为目标,建立非线性优化模型,在参数的置信区间内,应用PSO(Particle Swarm Optimization)算法求最优解.然后,应用求解得到的参数,建立优化MGM(1,n)模型.在实例分析中,将优化MGM(1,n)模型应用于深基坑围护结构变形预测,实验结果表明通过对原始数据做合适的Box-Cox变换,能够有效提高模型的拟合及预测精度,拓广多变量灰色预测模型的适用范围.     

Load’s temporal characteristics for annulling forced vibrations of linear elastic plates

We consider trapezoidal load-time pulses with linearly increasing and affinely decreasing durations equal to integer multiples of the time period of the first bending mode of vibration of a linearly elastic structure. For arbitrary spatial distributions of loads applied to monolithic and laminated orthotropic plates, it is shown through numerical solutions that plates’ vibrations become miniscule after the load is removed. This phenomenon is independent of the dwell time (i.e., the time duration between the rising and the falling portions) during which the load is kept constant. The primary reason for this response is that for such time-dependent loads, nearly all of plate’s strain energy is concentrated in deformations corresponding to the fundamental bending mode of vibration. Thus plate’s deformations can be studied by taking the mode shape of the 1st bending mode as the basis function and reducing the problem to that of solving a single second-order ordinary differential equation. We have verified this postulate by comparing strain energies computed from the 3-dimensional deformations of different plate geometries and boundary conditions with those determined by using the single degree of freedom (DoF) model. Thus for trapezoidal time-dependent loads applied on plates, the 1 DoF model provides reasonably accurate results and saves considerable computational effort.     

Identification of functionally key residues in maltose transporter with an elastic network model-based thermodynamic method

Periplasmic binding protein-dependent maltose transport system (MBP-MalFGK₂) of Escherichia coli, an important member of the Adenosine triphosphate-binding cassette transporter superfamily, is in charge of the transportation of maltoses across cellular membrane. Studies have shown that this transport processes are activated by the binding of maltose and are accompanied by large-scale cooperative movements between different domains which are mediated by a network of important residues related to signal transduction and allosteric regulation. In this paper, the functionally crucial residues and long-range allosteric pathway of the regulation of the system by substrate were identified by utilising a coarse-grained thermodynamic method proposed by our group. The residues whose perturbations markedly change the binding free energy between maltoses and MBP-MalFGK₂ were considered to be key residues. In result, the key residues in 62 clusters distributed in different subdomains were identified successfully, and the results from our calculation are highly consistent with experimental and theoretical observations. Furthermore, we explored the long-range cooperation within the transporter. These studies will help us better understand the physical mechanism of the effects of the maltose on MBP-MalFGK₂ by long-range allosteric modulation.     

Young＇s modulus surface and Poisson＇s ratio curve for tetragonal crystals

This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.     

Structure properties and Noether symmetries for super-long elastic slender rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.     

First-principles calculations for elastic properties of rutile TiO2 under pressure

This paper studies the equilibrium structure parameters and the dependences of the elastic properties on pressure for rutile TiO2 by using the Cambridge Serial Total Energy Package （CASTEP） program in the frame of density functional theory. The obtained equilibrium structure parameters, bulk modulus B0 and its pressure derivative B′0 are in good agreement with experiments and the theoretical results. The six independent elastic constants of rutile TiO2 under pressure are theoretically investigated for the first time. It is found that, as pressure increases, the elastic constants C11, C33, C66, C12 and C13 increase, The variation of elastic constant C44 is not obvious and the anisotropy will weaken.     

铝的动态屈服强度测量及再加载弹性前驱波的形成机理分析

利用激光干涉测速技术(VISAR)测量LY12铝合金在20—34 GPa冲击压力下经历加载-卸载和加载-再加载过程的样品/窗口界面粒子速度剖面，采用AC方法确定了具有较高精度的动态屈服强度值.实验结果和文献发表的数据具有较好的一致性.通过以平面焊接方式制作组合飞片，克服了组合飞片在气炮发射过程中可能发生分离的技术困难，使铝的动态屈服强度测量压力范围从22 GPa扩展到了34 GPa.同时，根据对不同实验条件下的加载-再加载过程的比较，对再加载弹性前驱波的形成机理进行了讨论，认为位错是形成该现象的主要原因.     

Soliton solution and interaction property for a coupled modified Korteweg-de Vries （mKdV） system

Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.     

The effect of a surface energy term on the distribution of phases in an elastic medium with a two‐well elastic potential

We consider the problem of minimizing among functions u:?^d?Ω→?^d, u_∣?Ω=0, and measurable subsets E of Ω. Here f_h⁺, f^? denote quadratic potentials defined on Ω¯×{symmetric d×d matrices}, h is the minimum energy of f_h⁺ and ε(u) is the symmetric gradient of the displacement field u. An equilibrium state û, Ê of J(u,E) is called one‐phase if E=?? or E=Ω, two‐phase otherwise. For two‐phase states, σ∣?E∩Ω∣ measures the effect of the separating surface, and we investigate the way in which the distribution of phases is affected by the choice of the parameters h??, σ>0. Additional results concern the smoothness of two‐phase equilibrium states and the behaviour of inf J(u,E) in the limit σ↓0. Moreover, we discuss the case of additional volume force potentials, and extend the previous results to non‐zero boundary values. Copyright © 2002 John Wiley & Sons, Ltd.     

The effect of a penalty term involving higher order derivatives on the distribution of phases in an elastic medium with a two‐well elastic potential

We consider the problem of minimizing 0<p<1, h∈?, σ>0, among functions u:?^d?Ω→?^d, u_∣?Ω=0, and measurable characteristic functions χ:Ω→?. Here ?⁺_h, ?^?, denote quadratic potentials defined on the space of all symmetric d×d matrices, h is the minimum energy of ?⁺_h and ε(u) denotes the symmetric gradient of the displacement field. An equilibrium state û, χ?, of I [·,·,h, σ] is termed one‐phase if χ?≡0 or χ?≡1, two‐phase otherwise. We investigate the way in which the distribution of phases is affected by the choice of the parameters h and σ. Copyright 2002 John Wiley & Sons, Ltd.