In this paper, we study the Lie symmetries and the conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints. We give the conditions and the form of conserved quantities due to the Lie symmetries of the systems, and present the inverse problem of the above problem, i.e. finding the corresponding Lie symmetry transformation according to a given integral of the system. Finally, we give an example to illustrate the application of the results.

In this paper, we study the relation between the form invariance and Lie symmetry of non-holonomic systems. Firstly, we give the definitions and criteria of the form invariance and Lie symmetry in the systems. Next, their relation is deduced. We show that the structure equation and conserved quantity of the form invariance and Lie symmetry of non-holonomic systems have the same form. Finally, we give an example to illustrate the application of the result.

We propose a novel adaptive synchronization method for a class of nonlinear chaotic systems with uncertain parameters. Using the chaos control method, we derive a synchronizer, which can make the states of the driven system globally track the states of the drive system asymptotically. The advantage of our method is that our problem setting is more general than those that already exist, and the synchronizer is simply constructed by an analytic formula, without knowledge in advance of the unknown bounds of the uncertain parameters. A computer simulation example is given to validate the proposed approach.

In this paper we investigate the method for controlling the chaotic Chen system with unknown parameters using linear feedback functions based on parameter identification. The observer is applied to the identification of the unknown parameters of Chen system. Then an efficient feedback function is designed for controlling the Chen system. Numerical simulations are provided to show the effectiveness and feasibility of the developed controller.

The torus-doubling bifurcations of a quasi-periodically forced two-dimensional map are investigated numerically. The scaling law on the terminal points of the torus-doubling bifurcation sequences is obtained by a simple method, based on hyper-stable period point and phase sensitivity exponent analyses.

We have proven theoretically that there are sublinear, linear and superlinear relations between the response rates and total incident intensity for different cases of traps in photorefractive polymer materials. These relations were observed in inorganic photorefractive crystals many years ago. Also, the steady-state space-charge field is a function of the total incident intensity, which has also been found in inorganic photorefractive crystals. We have measured the relations of the steady-state diffraction efficiency and the response rate with respect to the total incident intensity in the photorefractive composite consisting of the polymer (N-vinylcarbazole) (PVK) doped with 4,4'-n-pentylcyanobiphenyl (5CB) and C_{60}. The results obtained show that the composite belongs to the case of low trap density.

We discuss the effects of the initial atomic coherent factors (including the phase and the distribution parameter) and the dipole-dipole interaction on the sum and two-atom dipole squeezing in the system. The results show that the maximum squeezing in both cases is determined by the phase and the distribution parameter, and the duration of squeezing becomes longer by strengthening the dipole-dipole interaction. In addition, the comparison of the two types of squeezing shows that one type of squeezing is obtained at the expense of increased fluctuations in the other squeezing function.

We propose a scheme of a bistable system with an electromagnetically induced grating and analyse the optical bistabilities in the system. The stationary equations describing the system have been derived. This bistable system shows typical hysteresis behaviour.

In this paper, we investigate the modulation instability for generating femtosecond pulses in fibres with slowly decreasing dispersion. Higher-order dispersion and higher-order nonlinear effects are taken into account when the continuous wave or quasi-continuous wave evolves into sub-picosecond and femtosecond pulses by modulation instability in the optical fibres. Our research results show that the gain spectrum of the dispersion-decreasing fibres is much wider than that in conventional fibres. The third-order dispersion effect has no contribution to gain spectrum, while the self-steepening effect reduces the maximum value and gain bandwidth, and the Raman self-scattering effect widens the extent to which the modulation instability occurs.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

By experimental observation we show that the plasma flow and heat transfer within a direct current (DC) non-transferred arc plasma torch always show appreciable three-dimensional (3D) peculiarity even when the geometrical construction of the torch and working gas admission and external electrical collection conditions are completely axisymmetrical. Previous two-dimensional (2D) modelling studies cannot predict the 3D peculiarity of the plasma torch. We have successfully performed 3D modelling, and in this paper we present the modelling results for the plasma flow and heat transfer characteristics in a laminar DC non-transferred arc argon plasma torch. The predicted arc-root location on the surface of the torch anode and arc voltage compare favourably with the corresponding experimental results.

We present experimental results of the stimulated Raman backscattering instability (BSRS) in an ultrashort intense (45fs, 5.7×10^{17}Wcm^{-2}) laser pulse interacting with an optically ionized helium gas. We have studied the stimulated Raman backscattering reflectivity and the phenomenon of the transition from strongly coupled BSRS to weakly coupled BSRS. We have obtained a good agreement between our experimental results and the theory of BSRS.

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

In this paper, we have obtained and investigated the magnetic behaviours of the ferromagnetic layer in the symmetric spin valves of Co/Cu/NiFe and NiFe/Cu/Co by measuring with a vibrating sample magnetometer and analysing in terms of the multi-domain Ising models. It has been found that some magnetic layer can have quite different magnetic behaviours in different structures of spin valves, depending on the properties of the under-layer. In our investigation, we have found that the magnetic behaviour of a Co layer depends mainly on the magnetization of the under-layer, whereas this is not the case for the NiFe layer.

We have carried out theoretical investigations on the electronic structure of GaAs(311)A and GaAs(311)B surfaces. The bulk electronic structure of GaAs has been described by the second-neighbour tight-binding formalism and the surface electronic structure was evaluated via an analytic Green function method. First, we present the surface band structure together with the projected bulk band of both Ga-terminated and As-terminated for GaAs(311)A and GaAs(311)B surfaces, respectively. In each case, the number of surface states is determined, and the localized surface features and orbital properties of these surface states along Γ-Y-S-X-Γ high symmetry lines of the surface Brillouin zone are discussed. For the Ga-terminated GaAs(311)A (1×1) surface, we have tested two possible structure models, i.e. "the bridge site" and "the hollow site" models. In comparison with the angle-resolved photoelectron spectroscopy studied recently, the results have shown that the surface electronic states of the hollow site model are in good agreement with the experiments, whereas those of the bridge site model are not. So we have concluded that the hollow site model is favourable for the Ga-terminated GaAs(311) (1×1) surface and the bridge site model should be excluded.

Using the ion-beam-sputtering technique, we have fabricated Fe/Al_{2}O_{3}/Fe magnetic tunnelling junctions (MTJs). We have observed double-peaked shapes of curves, which have a level summit and a symmetrical feature, showing the magnetoresistance of the junction as a function of applied field. We have measured the tunnel conductance of MTJs which have insulating layers of different thicknesses. We have studied the dependence of the magnetoresistance of MTJs on tunnel conductance. The microstructures of hard- and soft-magnetic layers and interfaces of ferromagnets and insulators were probed. Analysing the influence of MJT microstructures, including those having clusters or/and granules in magnetic and non-magnetic films, a magnetization reversal mechanism (MRM) is proposed, which suggests that the MRM of tunnelling junctions may be explained by using a group-by-group reversal model of magnetic moments of the mesoscopical particles. We discuss the influence of MTJ microstructures, including those with clusters or/and granules in the ferromagnetic and non-magnetic films, on the MRM.

In this paper, we systematically study the phase boundary T_{c}(\vec H) of a hexagonal-prism superconducting network in an external magnetic field \vec H of arbitrary magnitude and direction. The result indicates that the phase boundary of the hexagonal-prism superconducting circuit varies more sharply than that of the cubic circuit. The potential applications of the hexagonal-prism superconducting circuit are also discussed.

We have examined the effect of Nb addition on the thermal stability of the supercooled liquid before crystallization, the glass-forming ability and magnetic properties for the amorphous alloy series Fe_{73}Nb_{x}Al_{5-x}Ge_{2}P_{10}C_{6}B_{4} and Fe_{63}Co_{7}Nb_{x}Zr_{10-x}B_{20}. The supercooled liquid regions (ΔT_{x}=T_{x}-T_{g}) have maximum values of 66 and 79K, respectively, for Fe_{73}Nb_{1}Al_{4}Ge_{2}P_{10}C_{6}B_{4} and Fe_{63}Co_{7}Nb_{4}Zr_{6}B_{20} alloys. The saturation magnetization σ_{s} of the Fe_{73}Nb_{x}Al_{5-x}Ge_{2}P_{10}C_{6}B_{4} alloy system is much higher than that of the Fe_{63}Co_{7}Nb_{x}Zr_{10-x}B_{20} alloy system, and is almost unchanged with an increasing Nb content from 0 to 3 at%. But the σ_{s} of the Fe_{63}Co_{7}Nb_{x}Zr_{10-x}B_{20} alloys decreases linearly with increasing Nb content. The coercive force H_{c} of the two alloy series can have a minimum value of 31A/m for Fe_{73}Nb_{1}Al_{4}Ge_{2}P_{10}C_{6}B_{4} and 37A/m for Fe_{63}Co_{7}Nb_{4}Zr_{6}B_{20}. All these values are for the ribbons annealed at 773 and 873K for 15min in vacuum.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole is investigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of the Euler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin of the entropy of the black hole is related to the topology of its instanton.

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