Based on the Ehresmann connection theory and symplectic geometry, the canonical formulation of nonholonomic constrained mechanical systems is described. Following the Lagrangian formulation of the constrained system, the Hamiltonian formulation is given by Legendre transformation. The Poisson bracket defined by an anti-symmetric tensor does not satisfy the Jacobi identity for the nonintegrability of nonholonomic constraints. The constraint manifold can admit symplectic submanifold for some cases, in which the Lie algebraic structure exists.

This paper studies the response cumulants for a kind of special nonholonomic systems under non-Gaussian, delta-correlated excitations. We present a new methodology for formulating the equations governing the evolution of the response cumulants of the stochastic dynamic systems. The response cumulant differential equations (CDEs) derived can be used to calculate the response cumulants for both linear and nonlinear systems. One example is given to illustrate how to use the CDEs for calculating response cumulants.

After a Birkhoff system is restricted by constraints, the determining equations, the Lie symmetries, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some Lie symmetries will disappear and under certain conditions some Lie symmetries will still remain present. The condition under which Lie symmetries and conserved quantities of the system will remain is given.

A method that allows one to control chaotic and hyperchaotic systems by a random proportional pulse feedback of system variables is proposed. This method is illustrated with the Rossler chaotic and the complex Lorenz-Harken hyperchaotic systems, and a better control result is obtained. The advantage of this method is that just one perturbed system variable is enough to obtain a stabilized periodic orbit.

The interaction mean free path of He projectile fragments, produced by the collisions of ^{16O at 60 A GeV in a nuclear emulsion, has been investigated. In the present analysis, 1555 He projectile fragments, giving rise to 320 secondary interactions, have been used. At a level of 3% a very weak signal of anomalons is observed, which comes mainly from the 3×He channel.}

The experimentally observed special line-shape induced by the interaction between two counter-propagating equal-frequency fields and an Y-type four-level system with two mixed upper levels has been analyzed theoretically. Serious line-shape variations of the two-photon transitions due to the quantum interference are discussed and predicted.

L-shell ionization cross sections of Nb by electron impact in the energy range from 3 to 40 keV have been determined with a Si(Li) X-ray detector. Influence of reflected electrons from backing on the measurement was corrected using an electron transport model. The experimental results are compared with theoretical calculations of Gryzinski and McGuire.

The Rayleigh identity, based on a multipole expansion theory, is extended to analyse the forces between particles in an electrorheological system. The shear modulus for chains of particles arrayed on a square lattice is calculated. It is found that the modulus increases linearly with the ratio of dielectric constants of the dispersed particles to that of the continuous phase; as the ratio becomes larger, contrary to the expectations from a simple dipole approximation, the modulus would saturate. In the case of conducting particles, the modulus varies with the frequency of the applied field. In a limiting case of perfectly conducting particles, the conductivity is also considered. It is found that the particle-particle forces are extremely sensitive to their separations from each other.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Harmonic emission was studied from a plasma produced by ultrashort laser pulses. Unlike the harmonics from plasmas created by long (ns) laser pulses, the 3/2 harmonic emission was not observed in the interaction between plasmas and ultrashort laser pulses. A simple model is proposed to explain this phenomenon.

A relativistic quasi-static model for the motion of the electrons in relativistic laser fields is proposed. Using the model, the recent experimental results about the generation of the hot electrons in relativistic laser fields can be fit quite well and the important role of the rescattering can be shown clearly.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The multiple cluster growth of ultra-thin films on a hexagonal substrate with fractal, dendritic and compact morphology has been studied by computer simulation. The influence of the different diffusion processes along island edges on the island shape has been investigated. The results show that the anisotropic corner diffusion induces the dendritic growth, and the anisotropic step diffusion can promote the anisotropic growth and cause the ramified islands growing in three directions. In the case of compact growth, the island shape is mainly determined by the anisotropic corner crossing process. The nonuniform distribution of the multiple cluster formation can be described quantitatively by multifractal. With patterns changing from fractal to compact islands, the width and height of the bell-like or hook-like multifractal spectra increase, while the top f(α) decreases.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Single crystal Bi_{0.19}MoO_{3} has been grown by fused salt electrolytic technique. X-ray powder diffraction shows that the unit cell parameters are: a=1.9985nm, b=0.4085nm and c=1.4437nm. The temperature dependence of resistivity demonstrates a semiconductor characteristic. X-ray photoemission spectroscopy studies provide that the valence band of Bi_{0.19}MoO_{3} are made up of oxygen p_{π} and the π^{*, π and σ bonding bands formed by orbital combination. The shoulder at 0.4 eV near the top of valence band may be formed from the non-bonding dxy orbitals of some Mo atoms. The O1s core-electron spectrum reveals the presence of two inequivalent bonds of oxygen ions in Bi0.19MoO3. Bi4f core-level spectrum shows two bonding characters of Bi atoms in bismuth molybdenum oxide single crystals. Mo3d core-level spectrum could be decomposed into two kinds of valence states of molybdenum(Mo+5 and Mo+6).}

A complete set of spectroscopic parameters, including Judd-Ofelt parameters, radiative transition probabilities, radiative lifetime, branching ratios and integrated absorption cross section, have been calculated for Tm^{3+- doped fluoroaluminate (AYF) glass, based on the measured absorption spectra. The mechanism of Tm3+→Tm3+ and Yb3+\Leftrightarrow Tm3+ energy transfers and fluorescence properties have been investigated in both Tm3+ single-doped and Yb3+/Tm3+ double-doped AYF glasses. The cross-relaxation process, 3F4+3H6→23H4, is proved, which makes the optimum Tm3+ concentration of 1.77μm fluorescence (3H4→3H6) much higher than 1.45μm fluorescence (3F4→33H4) in Tm3+:AYF glasses. In Yb3+/Tm3+:AYF glasses, a stronger concentration quenching is found for the 476nm emission than that for the 797nm emission, and is discussed under the 970nm-excitation.}

A new high-T_c (HT_c) rf SQUID working at around 1.3GHz has been developed to avoid electromagnetic interference such as growing mobile communication jamming. This new system works in a frequency range from 1.23 to 1.42GHz (centred at 1.3GHz), which is not occupied by commercial communication. The sensor used in the 1.3GHz rf SQUID is made of a HT_c coplanar superconducting resonator and a large-area HT_c superconducting film concentrator. We have achieved in the 1.3GHz HT_c rf SQUID system a minimal flux noise of 2.5×10^{-5}Φ_0/\sqrt{Hz} and a magnetic field sensitivity of 38fT/\sqrt{Hz} in white noise range, respectively. The effective area of the concentrator fabricated on a 15×15mm^2 substrate is 1.35mm^2. It is shown that the 1.3GHz rf SQUID system has a high field sensitivity. Design and implementation of 1.3GHz HT_c rf SQUID offers a promising direction of rf SQUID development for higher working frequency ranges.

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