We investigate the thermodynamics of the slowly rotating Kerr-Newman (K-N) black hole in the grand canonical ensemble with York's formalism. Some thermodynamical properties, such as the thermodynamical action, entropy, thermodynamical energy and heat capacity are studied, and solutions of the slowly rotating K-N black hole with different boundary conditions are analysed. We find stable solutions and instantons under certain boundary conditions.

We investigate the electronic energy levels in the field of the micro-Kerr black hole under the approximation condition a<2, and obtain some interesting results.

We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.

By using the charge and current in a quantization resistance-inductance-capacitance (RLC) electric circuit, we construct a pair of canonical variables. Using this pair of variables and the thermal field dynamics, we obtain the fluctuations of charge and current in the RLC electric circuit at finite temperatures. It is shown that the fluctuations increase with increasing temperature and decrease with prolonging of time.

We study the quantum effects of a damped LC parallel circuit considering its different performance from an RLC series circuit in classical physics. The damped LC parallel circuit with a source is quantized and the quantum fluctuations of magnetic flux and electric charge in the circuit in displaced squeezed Fock state are investigated. It is shown that, as in the RLC series circuit, the fluctuations only depend on the squeezing parameter and the parameters of the circuit components in the damped LC parallel circuit, but the effects of the circuit components on the fluctuations are different in the two circuits.

A novel adaptive control and identification on-line method is proposed for a class of chaotic system with uncertain parameters. We prove that, using the presented method, a controller and identifier is developed which can remove chaos in nonlinear systems and make the system asymptotically stabilizing to an arbitrarily desired smooth orbit. And at the same time, estimates to uncertain parameters converge to their true values. The advantage of our method over the existing result is that the controller and identifier is directly constructed by analytic formula without knowing unknown bounds about uncertain parameters in advance. A computer simulation example is given to validate the proposed approach.

A set of similarity equations is derived to describe the hydrodynamics of transient X-ray lasers from slab plasmas generated by combined irradiation of nanosecond and picosecond laser pulses. By separating nanosecond and picosecond laser heating processes into different periods, analytical solutions are obtained for the similarity equations. The calculated results are in agreement with numerical simulations and experimental data.

The theoretical study of PuO^{n+}(n=1,2,3) using a density functional method shows that PuO^{+} (X^{6}Σ^{-}) and PuO^{2+} (X^{5}Σ^{-}, ^{7}Σ^{-}, ^{9}Σ^{-}) ions are stable, and the PuO^{3+} (^{4}Σ^{+}, ^{6}Σ^{+}) ion is unstable. The analytic potential energy functions of X^{6}Σ^{-} for PuO^{+} and X^{5}Σ^{-}, ^{7}Σ^{-}, ^{9}Σ^{-} for PuO^{2+} have been derived, and their force constants and spectroscopic data have been calculated.

We have calculated the forbidden transition energies and magnetic dipole transition probabilities of 2s^{2}2p^{4}(^{3}P_{1}－^{3}P_{2}) and 2s^{2}2p^{4} (^{3}P_{0}－^{3}P_{1}) of oxygen-like isoelectronic sequences (Z=10－32) by a method of polarization potential correction. The transition energies show good agreement with experiment and are much better than the calculations in the literature. These results also illustrate that it is feasible to use the dipole expansion of the polarization potential to deal with some dynamic and non-dynamic effects in the central field approach. The relation of polarizability and cut-off radius with atomic number is discussed. We also give the fitted formula between the polarizability α_{1} and atomic number Z as α_{1}=0.73429-9.56644×10^{-4}Z+7.43016×10^{-5}Z^{2-2.53298×10-6Z3+2.08306×10-8Z4.}

Hyperfine structure spectra of singly ionized europium have been measured by collinear fast-ion-beam laser spectroscopy. All the spectral lines were resolved and the magnetic dipole and electric quadrupole coupling constants of the metastable and excited levels were determined.

The kaon meson electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson and Bethe-Salpeter formulation in simplified impulse approximation (dressed vertex) with modified flat-bottom potential, which is a combination of the flat-bottom potential taking into consideration the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. All the numerical results give a good fit to experimental values.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Parametric simultaneous solitary wave (simulton) excitations are shown to be possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example, we consider the nonlinear coupling between the upper cut-off mode of acoustic branch (as a fundamental wave) and the upper cut-off mode of optical branch (as a second harmonic wave). Based on a quasi-discreteness approach the Karamzin－Sukhorukov equations for two slowly varying amplitudes of the fundamental and the second harmonic waves in the lattice are derived when the condition of second harmonic generation is satisfied. The lattice simulton solutions are given explicitly and the results show that these lattice simultons can be nonpropagating when the wave vectors of the fundamental wave and the second harmonic waves are exactly at π/a (where a is the lattice constant) and zero, respectively.

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

The features of energetics and electronic properties of carbon nanotubes, containing a pentagon-heptagon pair (5/7) topological defect in the hexagonal network of the zigzag configuration, are investigated using the extended Su-Schriffer-Heeger model based on the tight binding approximation in real space. Our calculations show that this pentagon-heptagon pair defect in the nanotube structures is not only responsible for a change in nanotube diameter, but also governs the electronic behaviour around Fermi level. Furthermore, we have calculated the densities of states of the (9,0)-(8,0) and (8,0)-(7,0) systems. For the (9,0)-(8,0) system, a narrow gap exists in the vicinity of the Fermi energy. In contrast, for the (8,0)-(7,0) system, a little peak of the density of states occurs at the Fermi energy. These can be attributed to the addition of a pair of pentagon-heptagon defects in the interface between two isolated carbon nanotubes.

The eigenstates and eigenspectrum of a charged particle in a one-dimensional semiconductor superlattice with an impurity under the action of a dc electric field are investigated employing the single-band tight-binding model. We find that the system undergoes a series of avoided crossings, at which resonant oscillations between the impurity and its nearest neighbour occur if appropriate conditions are met, suggesting an effective two-level approximation. This phenomenon shows that introducing an impurity in a perfect lattice provides a promising structure for the observation of terahertz radiation.

The thermodynamics of the vortex lattice of high-temperature superconductors has been studied by solving the generalized Ginzburg-Landau equations derived microscopically. Our numerical simulation indicates that the structure of the vortex lattice is oblique at the temperature far away from the transition temperature T_{c}, where the mixed s-d_{x}^{2}-y^{2} state is expected to have the lowest energy. Whereas, very close to T_{c}, the d_{x}^{2}-y^{2} wave is slightly lower energetically, and a triangular vortex lattice recovers. The coexistence and the coupling between the s and d waves would account for the unusual dynamic behaviours such as the upward curvature of the upper critical field curve H_{C2}(T), as observed in dc magnetization measurements on single-crystal YBa_{2}Cu_{3}O_{7} samples.

We study the C_{2} Ruijsenaars-Schneider model with interaction potential of trigonometric type. The Lax pairs for the model with and without spectral parameters are constructed. Also given are the involutive Hamiltonians for the system. Taking a non-relativistic limit, we obtain the Lax pair of C_{2} Calogero-Moser model.

The demagnetization curve as a function of intensity of the inter-grain exchange interaction was calculated for single-phase nanocrystalline Nd-Fe-B magnets by use of the finite-element technique of micromagnetics. Also, the strength of the exchange interaction was estimated as a function of the Nd content x for the nanocrystalline Nd_{x}Fe_{94-x}B_{6} magnets by comparing the above result with the experimental relation between _{i}H_{c} and x for the magnets. We found that the inter-grain exchange interaction decreases with the increase of x, are ≈70% and ≈60% of the inter-grain exchange interaction for x=15.5(μ_{0}_{i}H_{c}≈2.0T) and x=19(μ_{0}_{i}H_{c}≈2.3T), respectively.

A one-dimensional NMR method is presented for measuring the transverse relaxation time, T_{2,n}, of intermolecular multiple quantum coherences (IMQCs) of coherence order n in highly polarized spin systems. The pulse sequence proposed in this paper effectively suppresses the effects of radiation damping, molecular diffusion, inhomogeneity of magnetic field, and variations of dipolar correlation distance, all of which may affect quantitation of T_{2,n}. This pulse sequence can be used to measure not only IMQC transverse relaxation time T_{2,n}(n>1) quickly and directly, but also the conventional transverse relaxation time. Experimental results demonstrate that the quantitative relationship between T_{2,n}(n≥1) and T_{2} is T_{2,n}≈T_{2}/n. These results will be helpful for understanding the fundamental properties and mechanisms of IMQCs.

Investigates the up-conversion luminescence of Yb-doped oxyfluoride glass excited by a 960nm-diode laser. A new up-conversion cooperative radiation luminescence is found, which is rather strong and positioned at 476.1 nm. It comes from the coupled states of two-Yb^{3+-ions cluster. It is significant because it is an effective and convenient method of producing blue light.}

We present a strong correlation of the gamma-ray (above 100 MeV) mean spectral indices α_{γ} and X-ray (1 keV) mean spectral indices α_{X} for 34 gamma-ray-loud blazars (16 BL Lac objects and 18 flat spectrum radio quasars). A strong correlation is also found between the gamma-ray flux densities F_{γ} and X-ray flux densities F_{X} in the low state for 47 blazars (17 BL Lac and 30 flat spectrum radio quasars). Possible correlation on the gamma-ray emission mechanism is discussed. We suggest that the main gamma-ray radiation mechanism is probably the synchrotron process. The gamma-ray emission may be somewhat different from that of BL Lac objects and flat spectrum radio quasars.