A new version of Bishop frame and an application to spherical images

In this work, we introduce a new version of Bishop frame using a common vector field as binormal vector field of a regular curve and call this frame as “Type-2 Bishop Frame”. Thereafter, by translating type-2 Bishop frame vectors to the center of unit sphere of three-dimensional Euclidean space, we introduce new spherical images and call them as type-2 Bishop spherical images. Frenet-Serret apparatus of these new spherical images are obtained in terms of base curve's type-2 Bishop invariants. Additionally, we express some interesting relations and illustrate two examples of our main results.     

Cosine expansion‐based differential quadrature algorithm for numerical solution of the RLW equation

The differential quadrature method based on cosine expansion is applied to obtain numerical solutions of the RLW equation. The propagation of single solitary wave is studied to validate the efficiency of the algorithm. Then, test problems including interaction of two and three solitary waves, undulation, and evolution of solitary waves are implemented. Solutions are compared with earlier results. Discrete conservation quantities are computed for test experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

入射平面电磁波两类球面波函数展开式的等价性证明

入射平面电磁波的球面波函数展开是求解不同圆球结构的平面波散射问题的重要工具,相关文献分别利用场的坐标分解和矢量势法得到了入射平面波的球面波函数的两种不同形式的展开式.利用偏微分方程边值问题解的存在唯一性定理,给出了这两种展开式的等价性的一个简洁的解析证明,并进行了数值验证.     

非协调有限元与本征值下界

与协调有限元相比,非协调有限元常常给出本征值下界.这种现象已经由很多数值例子观察到.但是理论上的证明最近才做的更多.以Morley非协调元作为更简单的范例,来说明这种理论为何成功.     

形式Laurent级数域上交错Oppenheim展开的研究

该文介绍了形式Laurent级数域上交错Oppenheim展开的算法,得到了该展开中数字的强(弱)大数定理、中心极限定理和重对数率,并且研究了这些级数部分和的逼近的度.     

实现金属环动态拉伸的电磁加载技术研究

描述了实现金属环动态拉伸的电磁膨胀环实验方法,改进了快速放电和短路开关两个实现自由膨胀的关键问题,为研究材料本构关系、动态断裂和破碎提供了一条简单而实用的加载途径。主回路电流由Rogowski线圈测量获得,金属环的膨胀速度由狭缝扫描相机测量得到,并由电动力学方程可计算出金属环中的流动应力、应变、应变率以及温升等动态力学参数。     

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R² ∼L and by free-energy fluctuations of order ΔF(L) ∼O(1). The low-temperature phase is characterized by an anomalous wandering exponent R²/L ∼L^ω and by free-energy fluctuations of order ΔF(L) ∼L^ω where ω∼0.18. In this paper, we first study the scaling behavior of various properties to localize the critical temperature T_c. Our results concerning R²/L and ΔF(L) point towards 0.76 < T_c ≤T₂=0.79, so our conclusion is that T_c is equal or very close to the upper bound T₂ derived by Derrida and coworkers (T₂ corresponds to the temperature above which the ratio remains finite as L ↦ ∞). We then present histograms for the free-energy, energy and entropy over disorder samples. For T ≫T_c, the free-energy distribution is found to be Gaussian. For T ≪T_c, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order ΔS ∼L^1/2 and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term ΔF ∼L^ω is a near cancellation of energy and entropy contributions of order L^1/2.     

无穷级数sum from n=1 to ∞(1/(2n-1)~(2k))的一种计算方法

根据无穷多项式理论,将余弦函数的幂级数展开式构造成无穷乘积的形式.并且利用ln(1+x)幂级数展开,得到sum from n=1 to ∞(1/(2n-1)～(2k))(k为正整数)的一种计算方法.     

Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations

The ‘tanh-coth expansion method’ for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the 1990s. It usually delivers three types of solution, namely a tanh-function expansion, a coth-function expansion, and a tanh-coth expansion. It is known that, for every tanh-function expansion solution, there is a corresponding coth-function expansion solution. It is shown that there is a tanh-coth expansion solution that is merely a disguised version of the coth solution. In many papers, such tanh-coth solutions are erroneously claimed to be ‘new’. However, other tanh-coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh-function method. Similar remarks apply to tan, cot and tan-cot expansion solutions.     

On ANOVA expansions and strategies for choosing the anchor point

The classic Lebesgue ANOVA expansion offers an elegant way to represent functions that depend on a high-dimensional set of parameters and it often enables a substantial reduction in the evaluation cost of such functions once the ANOVA representation is constructed. Unfortunately, the construction of the expansion itself is expensive due to the need to evaluate high-dimensional integrals. A way around this is to consider an alternative formulation, known as the anchored ANOVA expansion. This formulation requires no integrals but has an accuracy that depends sensitively on the choice of a special parameter, known as the anchor point.We present a comparative study of several strategies for the choice of this anchor point and argue that the optimal choice of this anchor point is the center point of a sparse grid quadrature. This choice induces no additional cost and, as we shall show, results in a natural truncation of the ANOVA expansion. The efficiency and accuracy is illustrated through several standard benchmarks and this choice is shown to outperform the alternatives over a range of applications.