魏高原
1、拉胀基元和拉胀聚合物的设计、合成、结构与拉胀性；2、聚合物及拉胀复合材料的制备、结构与拉胀性；3、拉胀材料的计算机模拟；4、无规形体、受限结晶和拉胀性理论
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 姓名：魏高原
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博士生导师
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学科领域：
勘查地质学
 研究兴趣：1、拉胀基元和拉胀聚合物的设计、合成、结构与拉胀性；2、聚合物及拉胀复合材料的制备、结构与拉胀性；3、拉胀材料的计算机模拟；4、无规形体、受限结晶和拉胀性理论
魏高原，教授，1961年6月生，湖南辰溪人。1982年1月获华南理工大学高分子化工工学士，1985年8月获康奈尔大学化学工程理学硕士，1990年6月获西雅图华盛顿大学化学博士学位。1982~83年，华南理工大学材料科学研究所教育部出国代培研究生。1990年6~7月，华盛顿大学化学系博士后；1990~92年，剑桥大学卡文迪什实验是凝聚态理论组博士后。1997~98年，剑桥大学物理及聚合物和胶体组英国皇家学会王宽诚基金访问学者。1992年7月入北京大学化学系高分子组任教，历任讲师、副教授，并于1999年晋升为化学学院高分子系教授。编写教材《化学专业基础英语（I、II）》和《高分子物理》。回国后发表拉胀性和高分子形体理论方面论文近30篇。获得1994年度“北京大学优秀学术骨干”称号及1996年度“国家教委优秀青年教师基金”奖励。由魏高原教授牵头的北京大学拉胀研究室主要从事以下研究：1、拉胀基元和拉胀聚合物的设计、合成、结构与拉胀性；2、聚合物及拉胀复合材料的制备、结构与拉胀性；3、拉胀材料的计算机模拟；4、无规形体、受限结晶和拉胀性理论

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【期刊论文】Shapes and Sizes of Linear and Circular Multiplering Macromolecules
魏高原， Gaoyuan Wei
Polymers for Advanced Technologies Volume 8, pp. 265269，0001，（）：
1年11月30日
The shapes and sizes of linear and circular multiplering macromolecules in the framework of the Gaussian model have been numerically investigated in terms of shape factors, asphericity and prolateness factors and parameters, and shrinking factors. Simple analytic expressions for the eigenpolynomials of the Kirchhoff or architecture atrices for both linear and circular multirings in the limit of an infinitely large individual ring have been obtained via a new recursion method. It is found that for both types of multiple rings, shape asymmetry increases while size decreases as the number of rings increases, and that asphericity and prolateness parameters for a circular 99ring macromolecule or a doubly stranded closed random walk have stronger dependence on dimensionality of the space in which the molecule is embedded than those of its linear counterpart.
polymer configuration， size and shape， Guassian model， mutiplering macromolecules， twisted random walks

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魏高原， Gaoyuan Wei a， *， Xuexian Zhu b
Physica A 237 (1997) 423440，0001，（）：
1年11月30日
For arbitrary random walks in any ddimensional space, expansions in powers of l/d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed, which, at O(1/d3), yield very good approximations to exact values of the parameters for chains, rings, dumbbells and 3 and 5arm regular stars. The 1/dexpansions have also been used to obtain an estimate of these shape asymmetry parameters for 3D Edwards chains, rings, dumbbells and 3arm stars and to give a mathematical proof that infinitely large random nets such as Bethe lattice or starburst and Mckay's net exhibit spherical symmetry. For arbitrary random walks at d=∞, it is proved that these parameters coincide with their corresponding factors, while for an endlooped selfavoiding walk, it is found that its shape asymmetry is even larger than that of an open SAW. An I/ƒexpansion of the parameters for farm regular stars has also been obtained, and a comparison of the dimensionality dependence of the parameters with that of the corresponding factors has been made for the four types of random walks.
Random walks， Shapes and sizes， Polymer configuration statistics， Asphericity and prolateness parameters， Macromolecules

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【期刊论文】Polymer Networks with Negative Poisson's Ratios
魏高原， Gaoyuan Wei* and S.F. Edwards
Computational Polymer Science, 1992, 2, 4454，0001，（）：
1年11月30日
Effective Poisson's ratios of two model polymer networks with special types of microstructures which are randomly oriented have been numerically evaluated. The results, having been graphically represented, show the micromechanical condition under which these networks exhibil negative Poisson's ratios. thus being of great importance in aiding experimental synthesis of such liquidcrystallike polymer networks in which stretchable and bendable rodlike molecular segments (arms and backbones) meet at rigid molecular crosslinks (junctions),
negative Poisson'， s ratio， liquidcrystallike polymer networks， model molecular network design， auxetics

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【期刊论文】Poisson ratio in composites of auxetics
魏高原， Gaoyuan Wei， ， * and S.F. Edwards
，0001，（）：
1年11月30日
Meanfield theory of elastic moduli of a twophase disordered composite with ellipsoidal inclusions is reviewed together with an indication as to how interactions among inclusions may be taken into account. In the meanfield approximation, the effective Poisson ratio σe in composites with auxetic inclusions of various shapes such as discs, spheres, blades, needles, and disks is studied analytically and numerically. It is shown that phase properties such as inclusion volume or area fraction and matrix and inclusion Poisson ratios (sm and s) and Young's moduli (Em and E) have a marked effect on σe. The earlier theoretical findings of the existence of auxeticity windows and the widening effect of inclusioninclusion interactions on the window for 〥=E/Em are reconfirmed for composites of auxetic spheres in both two and three dimensions, with new auxeticity windows discovered for the other inclusion shapes. For a composite with σ=0.8, σm=0.25, and ф=0.4, it is found that the sphere is the most σelowering or negativeσeproducing inclusion shape for around 1/2, while disklike inclusions yield a most negative σe for d greater than 1. [S1063651X(98)039117]

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【期刊论文】On shape asymmetry of Gaussian molecules
魏高原， Gaoyuan Wei and B.E. Eichinger
J. Chem. Phys. 93 (2), 14301435 15 July 1990，0001，（）：
1年11月30日
A method of calculating average moments, to an arbitrary order m, of the principal components of the gyration tensor of a Gaussian molecule imbedded in any kdimensional space is presented. These average moments are then used in generalized shape parameters Am of degree m≤k, which measure the asymmetry of the shapes of Gaussian molecules. Simple formulas for A2, A3, and the average moments up to third order are given. Explicit expressions for A2 and A3 for linear and circular chains, regular stars with infinitely long arms, double rings of a large number of beads, and combs with many side chains are obtained, and the shape characteristics of these molecules are discussed. It is found that Gaussian molecules are, on the average, prolate rather than oblate even in an infinite dimensional space, with the exception of regular stars with densely radiated long arms which exhibit perfect symmetry. The problem of analytic characterizations of shape asymmetry of Gaussian molecules or nonselfavoiding random walks of any kind is thus solved in complete generality.

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【期刊论文】On a Fourier integral over SO(3)
魏高原， Gaoyuan Wei and B.E. Eichinoer
J. Math. Phys. Vol. 31, No.11, November 1990，0001，（）：
1年11月30日
A twomatrix function of general interest in the areas of collfiguration statistics of macromolecules, number theory, harmonic analysis, and multivariate statistics is studied. The function is defined as a Fourier integral over SO (3), the Lie group of orthogonal 3

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【期刊论文】New approaches to shapes of arbitrary random walks
魏高原， Gaoyuan Wei
Physica A 222 (1995) 155160，0001，（）：
1年11月30日
The problem of the shape of a random object such as a flexible polymer chain was first tackled by Kuhn nearly thirty years after the answer to the probability distribution of its size was publicly sought for by Pearson in 1905. Since then, significant progress in the field has been made, but the important task of evaluating both analytically and accurately averaged individual principal components of the shape or inertia tensor for a walk of a certain architectural type remains unfinished. We have recently developed a new and general formalism for both exact and approximate calculations of these and other averages such as asphericity and prolateness parameters, which is illustrated here for an endlooped random walk and a selfavoiding or Edwards chain. We find that this combined open and closed random walk has surprisingly larger shape asymmetry than a simply open walk despite its smaller size.

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【期刊论文】Negative and conventional Poisson's ratios of polymeric networks with special microstructures
魏高原， Gaoyuan Wei
J. Chem. Phys., Vol. 96, No.4, 15 February 1992，0001，（）：
1年11月30日
A theoretical model for evaluating effective Poisson's ratios of polymeric networks with special microstructures has been developed, which takes into account both stretching and bending deformation mechanisms. It is a complete generalization of the formalism first presented by Warren and Kraynik [Mech. Mater. 6,27 (1987) and J. Appl. Mech. 55,341 (1988)] for analytically calculating effective elastic properties of certain types of polymeric foams. Structural anisotropy in two special microstructures considered is found to have very significant effects on both magnitude and sign of the effective Poisson's ratios of the macroscopically isotropic network materials containing them. As two limiting cases, the effective Poisson's ratios of random assemblies of 2D and 3D bars or rods are shown to be l/3 and l/4, respectively, the latter of which recovers the wellknown Poisson's result.

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【期刊论文】Exact shapes of random walks in two dimensions.
魏高原， Gaoyuan Wei
Physica A 222 (1995) 152154，0001，（）：
1年11月30日
Since the random walk problem was first presented by Pearson in 1905, the shape of a walk which is either completely random or selfavoiding has attracted the attention of generations of researchers working in such diverse fields as chemistry, physics, biology and statistics. Among many advances in the field made in the past decade is the formulation of the threedimensional shape distribution function of a random walk as a triple Fourier integral plus its numerical evaluation and graphical illustration. However, exact calculations of the averaged individual principal components of the shape tensor for a walk of a certain architectural type including an open walk have remained a challenge. Here we provide an exact analytical approach to the shapes of arbitrary random walks in two dimensions. Especially, we find that an endlooped random walk surprisingly has an even larger shape asymmetry than an open walk.

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【期刊论文】Evaluations of distribution functions for flexible macromolecules by the saddlepoint method.
魏高原， Gaoyuan Wei and B.E. Eichinger.
J. Math. Phys. 31 (5), May 1990，0001，（）：
1年11月30日
The method of steepest descents has been applied to the evaluation of distribution functions for flexible macromolecules of arbitrary complexity with the effective potential of the mean force being a quadratic form. Approximate evaluations of the distribution functions of the radius of gyration and the twodimensional shape distribution functions over the entire variable domains are shown to be both feasible and effective. The asymptotics of the distribution functions are also studied, and a simple asymptotic formula is obtained that is valid for flexible macromolecules confined to a plane and of any structure such that the smallest eigenvalue of the Kirchhoff matrix has odd degeneracy.

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