复射影空间CP~((n+p)/2)中具有2-调和的一般子流形

本文研究了复射影空间中具有2-调和的一般子流形问题.利用活动标架法,获得了这类子流形成为极小子流形的Pinching定理和Simons型积分不等式,此外还得到关于2-调和伪脐一般子流形的一个刚性定理,推广了复射影空间中具有2-调和全实子流形的一些相应结果.     

D-admissible hybrid control of a class of singular systems

This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.     

Addendum to “Switching effect and the metal–insulator transition in electric field” by A.L. Pergament et al. [J. Phys. Chem. Solids 71 (2010) 874]

In the paper mentioned above we reported on the switching mechanism in vanadium dioxide which was shown to be based on the electronically-induced Mott insulator-to-metal transition occurring in conditions of the non-equilibrium carrier density excess in the applied electric field, and the proposed model involved the dependence of the carrier density n on electric field (the Poole–Frenkel effect), as well as the dependence of the critical electric field on n. The data on the n(T) dependence were obtained on the assumption of a temperature-independent carrier mobility μ, and the problem of n reduction at lower temperatures was not fully understood. In this Letter we revisit this problem in the light of some recent data on the μ(T) dependence for VO₂. It is shown that the adjusted values of n, taking into account this μ(T), correspond to the Mott critical density within an order of magnitude.     

Investigation of the performance of bipolar transverse plate ESP in the sintering flue control

In order to improve the particle collection efficiency of the electrostatic precipitator (ESP), a transverse plate ESP with bipolar discharge electrodes is proposed. The simulations of the velocity distribution have shown that when the inlet velocity is 1 m/s, within the range of 40 mm from electrode plate, the average velocities of windward side and leeward side are less than 0.7 m/s and 0.3 m/s respectively. It is clear that the velocity near the collection electrode plate of this bipolar ESP is much lower than that of the ordinary ESP at the same inlet velocity. This low velocity can lead to higher efficiency for fine dust collection due to the less dust re-entrainment in ESP. It is also found that the average velocities are getting lower when the distance between plates electrodes are greater than 150 mm in accordance with the simulations. The voltage current characteristics of the bipolar ESP are superior to the ordinary ESP. The pressure drop of the bipolar ESP is about 30% higher than that of the ordinary one. The dust penetration of the bipolar ESP is about 54% less than that of the ordinary ESP when the sintering dust with 25.405 μm mass median diameter is used as the test particulate under the condition of the electric field from 2.1 kV/cm to 3.2 kV/cm and the velocity from 1.0 m/s to 1.5 m/s.     

On Non-Symmetric Deformations of Neo-Hookean Solids

Deformations possible (i.e., those satisfying the governing three-dimensional equations of equilibrium and the incompressibility constraint) within a class of non-symmetric deformations for a neo-Hookean nonlinearly elastic body were determined in [1], where it was found that only three special cases of the class of deformation fields considered could be solutions. One of these is the trivial solution, one the solution describing radially symmetric deformation, and the other a (non-symmetric, non-homogeneous) deformation contained within a family of universal deformations. In this paper, the results reported in [1] are shown to hold for a substantially broadened deformation field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Self-Contact for Rods on Cylinders

We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a second-order functional of a single scalar variable, and the self-contact constraint is written as an integral inequality. Using techniques from ordinary differential equation theory (comparison principles) and variational calculus (cut-and-paste arguments) we fully characterize the structure of constrained minimizers. An important auxiliary result states that the set of self-contact points is continuous, a result that contrasts with known examples from contact problems in free rods.     

Electroelastic analysis for a piezoelectric layer with surface electrodes

An electroelastic analysis of a transverse isotropic piezoelectric layer with surface electrodes is made. The piezoelectric layer is infinite long along the poling direction, and the top surface is perfectly bonded to a rigid electrode. The problem is solved via the conformal mapping technique for two cases of elastic boundary conditions on the bottom surface with two spaced electrodes, and the distribution of the electrostatic field in the entire piezoelectric layer is determined in an explicit analytic form, respectively. It is found that for the bottom surface electrodes with vanishing stiffness, the induced strain is singular, but no stress. Instead, for the bottom electrodes with stiffness as infinity, the induced stress is singular, but no strain.