1.

An Explicit Fractal Interpolation Algorithm for Reconstruction of Seismic Data





李信富 李小凡《中国物理快报》,2008年第25卷第3期


Based on our previous investigation and the pioneering work of other researchers, a novel explicit fractal interpolation method based on affine transform is proposed, in which we approximate the vertical scaling factors by the locally explicit expression. Numerical experiments indicate that the explicit fractal interpolation method shows great accuracy of reconstruction of the seismic profile and yields significant improvement over waveequation based trace interpolation methods （unified approach）.

2.

PARAMETER IDENTIFICATION PROBLEM OF THE FRACTAL INTERPOLATION FUNCTIONS 被引次数：4





阮火军 沙震 苏维宜《高等学校计算数学学报(英文版)》,2003年第12卷第2期


Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function. In this paper, we first present an example to explain a relationship between iteration procedure and fractal function. Then we discuss conditions that vertical scaling factors must obey in

3.

Fractal interpolation: a sequential approach





《高校应用数学学报(英文版)》,2021年第3期


Fractal interpolation is a modern technique to fit and analyze scientific data. We develop a new class of fractal interpolation functions which converge to a data generating(original) function for any choice of the scaling factors. Consequently, our method offers an alternative to the existing fractal interpolation functions(FIFs). We construct a sequence of αFIFs using a suitable sequence of iterated function systems(IFSs). Without imposing any condition on the scaling vector, we establish constrained interpolation by using fractal functions. In particular,the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data. The existence of CrαFIFs is investigated. We identify suitable conditions on the associated scaling factors so that αFIFs preserve rconvexity in addition to the C~rsmoothness of original function.

4.

On cubic Hermite coalescence hidden variable fractal interpolation functions





Puthan Veedu Viswanathan Arya Kumar Bedabrata Chand《高校应用数学学报(英文版)》,2015年第30卷第1期


Hermite interpolation is a very important tool in approximation theory and numerical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set,and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the shortcoming that the functions that can be well approximated are highly restricted to the class of selfaffine functions. The primary objective of this paper is to suggest a C1cubic Hermite interpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a selfaffine and nonselfaffine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global C2continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an alternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15(1)(2007), pp. 4153].

5.

A Fractal Model for Effective Thermal Conductivity of Isotropic Porous Silica Lowk Materials 被引次数：1





董锡杰 胡一帆 吴玉莹 赵军 万珍珠《中国物理快报》,2010年第27卷第4期


We establish a new model based on fractal theory and cubic spline interpolation to study the effective thermal conductivity of isotropic porous silica lowk materials. A 3D fractal model is introduced to describe the structure of the silica xerogel and silica hybrid materials （such as methylsilsesquioxane, MSQ）. Combined with fractal structure, a more suitable medium approximation is developed to study the isotropic porous silica xerogel and MSQ materials. Cubic spline interpolation for fitting discrete predictions from the fractal model is used to obtain the continuous function of the effective thermal conductivity versus porosity. Compared with other common models, the effective thermal conductivity predicted by our model presents better agreement with the experimental data for all porosity. These results indicate that the proposed model is valid.

6.

Energy and Laplacian of fractal interpolation functions





Xiaohui Li Huojun Ruan《高校应用数学学报(英文版)》,2017年第32卷第2期


In this paper, we first characterize the finiteness of fractal interpolation functions(FIFs) on post critical finite selfsimilar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket(SG). As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5: Δu = 0 on SG\{q_1, q_2, q_3}, and u(q_i) = a_i, i = 1, 2, 3, where q_i, i = 1, 2, 3, are boundary points of SG.

7.

EQ 1 rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations





Yanmin Zhao Fenling Wang Dongyang Shi《应用数学学报(英文版)》,2013年第29卷第1期


EQ rot 1 nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semidiscrete and fullydiscrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2 ) one order higher than its interpolation error O(h), the superclose results of order O(h2 ) in broken H1 norm are obtained. At the same time, the global superconvergence in broken H1 norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4 ) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ rot 1 element. Finally, optimal error estimate is gained for a proposed fullydiscrete scheme by different approaches from the previous literature.

8.

Noncommutative Differential Calculus and Its Application on Discrete Spaces





LIU Zhen BAI YongQiang WU Ke GUO HanYing《理论物理通讯》,2008年第49卷第1期


We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a twodimensional integral models with infinite sequence of conserved currents. Then an EulerLagrange cohomology with symplectic structurepreserving is given in the discrete classical mechanics.

9.

Image encryption using random sequence generated from generalized information domain





《中国物理 B》,2016年第5期


A novel image encryption method based on the random sequence generated from the generalized information domain and permutation–diffusion architecture is proposed. The random sequence is generated by reconstruction from the generalized information file and discrete trajectory extraction from the data stream. The trajectory address sequence is used to generate a Pbox to shuffle the plain image while random sequences are treated as keystreams. A new factor called drift factor is employed to accelerate and enhance the performance of the random sequence generator. An initial value is introduced to make the encryption method an approximately onetime pad. Experimental results show that the random sequences pass the NIST statistical test with a high ratio and extensive analysis demonstrates that the new encryption scheme has superior security.

10.

Surface structures of equilibrium restricted curvature model on two fractal substrates





宋丽建 唐刚 张永伟 韩奎 寻之朋 夏辉 郝大鹏 李炎《中国物理 B》,2014年第23卷第1期


With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature(ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension df, but possess different dynamic exponents of random walk zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk zrw. The ERC model growing on the two substrates follows the wellknown Family–Vicsek scaling law and satisfies the scaling relations 2α + df≈ z ≈ 2zrw. In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins–Herring equation.

11.

A NEW INVERSION METHOD OF TIMELAPSE SEISMIC





陈勇 韩波《高等学校计算数学学报(英文版)》,2005年第14卷第3期


TimeLapse Seismic improves oil recovery ratio by dynamic reservoir monitoring. Because of the large number of seismic explorations in the process of timelapse seismic inversion, traditional methods need plenty of inversion calculations which cost high computational works. The method is therefore inefficient. In this paper, in order to reduce the repeating computations in traditional, a new timelapse seismic inversion method is put forward. Firstly a homotopyregularization method is proposed for the first time inversion. Secondly, with the first time inversion results as the initial value of following model, a model of the second time inversion is rebuilt by analyzing the characters of timelapse seismic and localized inversion method is designed by using the model. Finally, through simulation, the comparison between traditional method and the new scheme is given. Our simulation results show that the new scheme could save the algorithm computations greatly.

12.

BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS 被引次数：1





Xiaoyuan Qian 《计算数学(英文版)》,2002年第4期


AbstractNontensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced. The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.

13.

Tone model integration based on discriminative weight training for Putonghua speech recognition





HUANG Hao ZHU Jie《Chinese Journal of Acoustics》,2008年第27卷第3期


A discriminative framework of tone model integration in continuous speech recognition was proposed. The method uses model dependent weights to scale probabilities of the hidden Markov models based on spectral features and tone models based on tonal features. The weights are discriminatively trained by minimum phone error criterion. Update equation of the model weights based on extended BaumWelch algorithm is derived. Various schemes of model weight combination are evaluated and a smoothing technique is introduced to make training robust to over fitting. The proposed method is ewluated on tonal syllable output and character output speech recognition tasks. The experimental results show the proposed method has obtained 9.5% and 4.7% relative error reduction than global weight on the two tasks due to a better interpolation of the given models. This proves the effectiveness of discriminative trained model weights for tone model integration.

14.

Biometric feature extraction using local fractal autocorrelation





陈熙 张家树《中国物理 B》,2014年第9期


Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal autocorrelation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme:(i) using twodimensional Gabor filter to extract the texture features of biometric images;(ⅱ) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal autocorrelation algorithm; and(ⅲ) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach.

15.

Mechanical properties of irradiated multiphase polycrystalline BCC materials





Dingkun Song Xiazi Xiao Jianming Xue Haijian Chu Huiling Duan《Acta Mechanica Sinica》,2015年第31卷第2期


Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility,resulting from irradiationinduced defects such as vacancies,interstitials and dislocation loops,etc.In this paper,we develop an elasticviscoplastic model for irradiated multiphase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both explored.At the microscopic grain scale,we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop,which facilitates the analysis of the defect loop evolutions and dislocationdefect interactions.At the macroscopic polycrystal scale,the selfconsistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal properties.Based on the proposed model,we found that the workhardening coefficient decreases with the increase of irradiationinduced defect loops,and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid factors.At the polycrystalline scale,numerical results for pure Fe match well with the irradiation experiment data.The model is further extended to predict the hardening effect of dispersoids in oxidedispersed strengthened steels by the considering the Orowan bowing.The influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials.

16.

WAVELET TRANSFORM IN FRACTAL IMAGE ENCODING





纪辉 王嘉松《高等学校计算数学学报(英文版)》,1997年第2期


This paper presents some results of the relation between wavelet transform and fractal transform. The wavelet transform of the attractor of fractal transform posseses translational and scale invariance. So we speed the fractal image encoding by testing the invariance of the wavelet transform appropriate for image encoding. The classfication scheme of range blocks by wavelet transform is given in this paper.

17.

MULTISCALE NUMERICAL MODEL FOR SIMULATING CONCRETE MATERIAL BASED ON FRACTAL THEORY





Qiang Xu Jianyun Chen Jing Li Mingming Wang《Acta Mechanica Solida Sinica》,2013年第26卷第4期


A new multiscale numerical model is presented using the fractal theory and adopting FEM to simulate the failure of concrete.The relation between the fractal box dimension in large scale and the damage to concrete in small scale is deduced.And the evolutionary process of elastic modulus and strength in small scale is given.Consequently,the multiscale numerical model is proposed to describe the constitutive relation of concrete between small scale and large scale.A twodimensional static analysis of a concrete block is performed by using this model and the calculation result is discussed.The propagation of cracks of the concrete block is also studied.

18.

Unified proof to oscillation property of discrete beam





郑子君 陈璞 王大钧《应用数学和力学(英文版)》,2014年第35卷第5期


The oscillation property （OP） is a fundamental and important qualitative property for the vibrations of single span onedimensional continuums such as strings, bars, torsion bars, and Euler beams. Any properly discretized continuum model should keep the OP. In literatures, the OP of discrete beam models is discussed essentially by means of matrix factorization. The discussion is modelspecific and boundarycondition specific. Besides, matrix factorization is difficult in handling finite element （FE） models of beams. In this paper, according to a sufficient condition for the OP, a new approach to discuss the property is proposed. The local criteria on discrete displacements rather than global matrix factorizations are given to verify the OP. Based on the proposed approach, known results such as the OP for the 2node FE beams via the Heilinger Reissener principle （HRFE beams） as well as the 5point finite difference （FD） beams are verified. New results on the OP for the 2node PEFE beams and the FE Timoshenko beams with small slenderness are given. Through a simple manipulation, the qualitative property of discrete multibearing beams can also be discussed by the proposed approach.

19.

Fractal Character for Tortuous Streamtubes in Porous Media 被引次数：4





郁伯铭《中国物理快报》,2005年第22卷第1期


An analytical model for fractal dimension of tortuous streamtubes in porous media is derived. The proposed fractal dimension for tortuous streamtubes in porous media is expressed as a function of porosity and scale, and there is no empirical constant in the proposed expression. The model predictions for the fractal dimension of tortuous streamtubes in porous media are in good agreement with those by the boxcounting method and with the observations of other researchers.

20.

Implicit Shape Reconstruction of Unorganized Points Using PDEBased Deformable 3D Manifolds





Elena《高等学校计算数学学报(英文版)》,2010年第3卷第4期


In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)based diffusion model derived by a minimal volumelike variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite covolume schemes and semiimplicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of userinteraction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.
