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1.
超疏水表面液滴的振动特性与接触线的移动、液滴体积、基底振幅等因素密切相关.本文在基底振幅较小且恒定的条件下,研究了超疏水表面液滴的共振振幅、模式区间、共振频率等振动特性及其与液滴体积(20—500μL)的关系.此外,将基于一般性疏水表面建立的Noblin共振频率计算模型应用于超疏水表面,并提出“虚驻点”的概念,借此对模型进行了误差分析和修正.研究表明:1)共振时,液滴高度变化率即比振幅随体积增大而增大,随阶数增大而减小;2)各模式区间的起止频率首尾相接,其范围随体积增大而减小;3)液滴体积越大,共振频率越小,随着阶数增大,共振频率f与体积V的关系趋于f-V–0.4,不同于一般性疏水表面上的f-V–0.5;4)直接应用Noblin模型计算共振频率会产生较大误差,主要原因在于液滴表面波波段数量统计存在较大偏差,而修正后的模型可以准确计算超疏水表面大体积液滴的共振频率. 相似文献
2.
给出了求解多自由度动力学系统响应的M atlab程序,这些程序基于振型叠加法可用于求解由质量矩阵M和刚度矩阵K以及常见阻尼矩阵描述的线性离散系统的时域和频域解.对于无阻尼系统,用户可以选择数值解或符号解析解(以时间或频率表示),并利用复模态叠加法计算了阻尼系统的数值解.总结了模态叠加方法下动力学响应的求解,并在简短的M atlab程序中实现.以三自由度系统和悬臂梁模型为例说明了程序的应用.这些程序也可用于工程应用中,通过对商用有限元软件包产生的质量和刚度进行后处理,产生感兴趣的时域和频域响应. 相似文献
3.
《Indagationes Mathematicae》2021,32(6):1229-1239
4.
We have performed numerical analysis of the one-dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple-scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves. 相似文献
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Biquadratic tensors play a central role in many areas of science.Examples include elastic tensor and Eshelby tensor in solid mechanics,and Riemannian curvature tensor in relativity theory.The singular values and spectral norm of a general third order tensor are the square roots of the M-eigenvalues and spectral norm of a biquadratic tensor,respectively.The tensor product operation is closed for biquadratic tensors.All of these motivate us to study biquadratic tensors,biquadratic decomposition,and norms of biquadratic tensors.We show that the spectral norm and nuclear norm for a biquadratic tensor may be computed by using its biquadratic structure.Then,either the number of variables is reduced,or the feasible region can be reduced.We show constructively that for a biquadratic tensor,a biquadratic rank-one decomposition always exists,and show that the biquadratic rank of a biquadratic tensor is preserved under an independent biquadratic Tucker decomposition.We present a lower bound and an upper bound of the nuclear norm of a biquadratic tensor.Finally,we define invertible biquadratic tensors,and present a lower bound for the product of the nuclear norms of an invertible biquadratic tensor and its inverse,and a lower bound for the product of the nuclear norm of an invertible biquadratic tensor,and the spectral norm of its inverse. 相似文献
7.
Riccardo Adami Ugo Boscain Valentina Franceschi Dario Prandi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(4):1095-1113
In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on is essentially self-adjoint in . A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on is never essentially self-adjoint in , if . We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass. 相似文献
8.
Youpei Zhang Limin Zhang Lixi Wen 《Journal of Mathematical Analysis and Applications》2021,493(2):124535
We are concerned with qualitative analysis of weak solutions for a class of magnetic Laplace equations with lack of compactness. By variational arguments, we establish related nonexistence, existence and multiplicity results. 相似文献
9.
Geometry of affine immersions is the study of hypersurfaces that are invariant under affine transformations. As with the hypersurface theory on the Euclidean space, an affine immersion can induce a torsion-free affine connection and a (pseudo)-Riemannian metric on the hypersurface. Moreover, an affine immersion can induce a statistical manifold, which plays a central role in information geometry. Recently, a statistical manifold with a complex structure is actively studied since it connects information geometry and Kähler geometry. However, a holomorphic complex affine immersion cannot induce such a statistical manifold with a Kähler structure. In this paper, we introduce complex affine distributions, which are non-integrable generalizations of complex affine immersions. We then present the fundamental theorem for a complex affine distribution, and show that a complex affine distribution can induce a statistical manifold with a Kähler structure. 相似文献
10.