Action of generalized symmetric groups on symmetric and exterior powers of their natural representations

We establish upper and lower bounds on the dimension of the space spanned by the symmetric powers of the natural character of generalized symmetric groups. We adapt the methods of Savitt and Stanley from [4 Savitt, D., Stanley, R. P. (2000). A note on the symmetric powers of the standard representation of S_n. Electron. J. Combin. 7:R6. [Google Scholar]] to obtain bounds both over the complex numbers and in prime characteristic.     

Central Schur rings over the projective special linear groups

In [1 Bannai, E. (1991). Subschemes of some association schemes. J. Algebra 14:167–188.[Crossref], [Web of Science ®] , [Google Scholar]], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these.     

Wave-like deformations for oscillating carbon nanotubes

Carbon nanostructures such as nanotubes and fullerenes, represent future materials because of their remarkable mechanical, electrical and thermal properties. Double-walled carbon nanotubes are widely studied as possible gigahertz oscillators, where the inner tube oscillates within the outer tube. These oscillators are believed to generate frequencies in the gigahertz range and typically of the order of 1–74 GHz. They are also known to generate wave-like formations on the outer surface. In this paper, we study such induced deformations on the surface of the outer tube, as generated by the moving inner tube. Following previous authors we assume that double-walled carbon nanotubes can be modelled as transversely isotropic linearly elastic materials. Using a previously derived approximate force distribution for the resultant van der Waals forces arising from the interatomic interactions, we solve a dynamic linearly elastic problem, and show that the resulting solution exhibits wave-like behaviour.     

Onset of Surface Damage in Modular Orthopedic Implants: Influence of Normal Contact Loading and Stress-assisted Dissolution

Surface damage at interfaces of modular implants results from repeated fretting contacts between metallic surfaces in a corrosive environment. As a first step in understanding this complex process, multi-asperity contact experiments were conducted to characterize roughness evolution due to action of contact loads and exposure to a reactive environment. Cobalt–chromium specimens with surface roughness similar to modular implant were first subjected to only contact loading and subsequently, to alternating contact loads and exposure to reactive environment. During repeated normal contact loading, amplitude of surface roughness reached a steady value after decreasing during the first few cycles. However during the second phase surface roughness amplitude continuously evolved—decreasing during contact loading and increasing on exposure to corrosive environment. The increase in roughness amplitude during surface reaction depended on the magnitude of applied contact loads. A damage mechanism that incorporates contact-induced residual stress development and stress-assisted dissolution is proposed to elucidate the measured surface roughness evolution.     

穿透短裂纹扩展趋偏现象的模型分析和实验研究

本文揭示了穿透短裂纹疲劳扩展中的一个特性－趋偏扩展特性。这一特性是穿透短裂纹预测和测试中产生偏问题的根本原因。通过对长、短裂纹扩展特性及主要影响因素的分析，提出了进行穿透短裂纹试验时必须注意的若干事项。     

Singular perturbation analysis of dynamic fields in a thermoelastic solid with a small surface-breaking crack

An asymptotic analysis is presented for a dynamic problem of a semi-infinite isotropic thermoelastic solid with a small surface breaking crack. The exterior surface of the solid is subjected to a series of short thermal pulses. The crack surface is traction free and an ideal thermal contact is assumed across the crack. The stress intensity factor is asymptotically evaluated as a function of the crack depth and time. The effect of a boundary layer associated with the diffusive term is identified. The theoretical model is supplied with numerical simulations.     

Transient Waves on the Free Surface of a Viscoelastic Anisotropic Half-Space

The Stroh formalism is employed to discuss the existence of transient surface waves on a viscoelastic anisotropic hall-space. The compatibility conditions, obtained using the integral formulation of Lothe and Barnett [13, 14], are examined on the basis of an asymptotic expansion of the viscoelastic kernel and a separation of space variables. Some previous results on elastic media are extended to viscoelasticity, exploiting the consequences of the second law of thermodynamics. It is found that all the allowed transient surface modes take the form of inhomogeneous plane waves whose amplitude exponentially decays along the propagation direction on the surface. Special solutions are derived explicitly for one-component surface waves where transient modes are admitted also in those cases in which stationary waves cannot occur. Mathematics Subject Classifications (2000) 74D05, 74J15.     

Twist Character of the Fourth Order Resonant Periodic Solution

In this paper, we will give, for the periodic solution of the scalar Newtonian equation, some twist criteria which can deal with the fourth order resonant case. These are established by developing some new estimates for the periodic solution of the Ermakov–Pinney equation, for which the associated Hill equation may across the fourth order resonances. As a concrete example, the least amplitude periodic solution of the forced pendulum is proved to be twist even when the frequency acroses the fourth order resonances. This improves the results in Lei et al. (2003). Twist character of the least amplitude periodic solution of the forced pendulm. SIAM J. Math. Anal. 35, 844–867.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model

Dislocation nucleation from a stressed crystal surface is analyzed based on the Peierls-Nabarro dislocation model. The variational boundary integral approach is used to obtain the profiles of the embryonic dislocations in various three-dimensional nucleation configurations. The stress-dependent activation energies required to activate dislocations from their stable to unstable saddle point configurations are determined. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the present analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, atomic information can be incorporated to reveal the dependence of the nucleation process on the profile of the atomic interlayer potential as compared to continuum elastic dislocation theory in which only elastic constants and Burgers vector are relevant. Finally, the presented methodology can also be readily used to study dislocation nucleation from the surface heterogeneities such as cracks, steps, and quantum structures of electronic devices.     

岩石结构面的表面形态特征研究

本文用理论分析和数值模拟方法对具有不同粗糙度和起伏度的岩石结构面的形态特征作了定量研究, 着重研究了结构面表面形态参数与基本形态特征参数的关系, 并研究了它们的采样效应。得到了一系列在建立表面形态参数与物理量相互关系时对合理选用表面形态参数有重要意义的结果, 并可为选取合理的采样间隔和最小采样长度提供依据。