Jet Magnetically Accelerated from Advection Dominated Accretion Flow

A jet model for the jet power arising from a steady, optically thin, advection dominated accretion flow （ADAF） around a Kerr black hole （BH） is proposed. We investigate the typical numerical solutions of ADAF, and calculate the jet power from an ADAF using a general relativistic version of electronic circuit theory. It is shown that the jet power concentrates in the inner region of the accretion flow, and the higher the degree to which the flow advection-dominated is, the lower the jet power from the ADAF is.     

An Electromagnetic Model for Jet Power from an Advection Dominated Accretion Flow around a Rotating Black Hole

We discuss jet production from an advection dominated accretion flow (ADAF) around a rotating black hole (BH) in an electromagnetic regime. An analytical expression for the jet power is derived by using an equivalent circuit in the BH magnetosphere. It turns out that a large fraction of jet powers is contributed from the inner region of the ADAF, and the jet power depends sensitively on the degree to which the flow is advection-dominated. In addition, we use our model to fit the strong jet powers of several BL Lac objects, which cannot be explained by virtue of the BZ process.     

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M-dimensional loop algebra \tilde{X} is produced. By taking advantage of \tilde{X}, a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra \tilde{F}_M of the loop algebra \tilde{X} is presented. Based on the \tilde{F}_M, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.     

Two Kinds of Magnetic Connection in Black-Hole Accretion Disc

We discuss two kinds of magnetic connection （MC） in the black hole （BH） accretion disc： the magnetic connection between the BH and the disc （MCHD） and that between the plunging region and the disc （MCPD）. The magnetic field configuration is produced by an electric current flowing at the inner edge of the disc. It turns out that the transfer direction of energy and angular momentum depends on the BH spin and a parameter λ for adjusting the angular velocities of the plunging matter, which corresponds to at most five regions in the disc. The effect of MCPD results in a much steeper emissivity than a standard accretion disc in the inner disc, however it fails to reach the observation range 4.3-5.5 in several objects, such as Seyfert 1 galaxy MCG-6-30-15, microquasars XTE J1650-500 and GX 399-4.     

A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation

Based on the displacement-squeezing related squeezed coherent state representation ≤ft\vert z\right\rangle _{g} and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens--Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz-rz^{\ast } in the % ≤ft\vert z\right\rangle _{g} representation, while ≤ft\vert z\right\rangle _{g} in phase space is graphically denoted by an ellipse.     

Characterization of doped hydrogenated nanocrystalline silicon films prepared by plasma enhanced chemical vapour deposition

The B- and P-doped hydrogenated nanocrystalline silicon films (nc-Si\jz{0.2ex}{:}H) are prepared by plasma-enhanced chemical vapour deposition (PECVD). The microstructures of doped nc-Si\jz{0.2ex}{:}H films are carefully and systematically characterized by using high resolution electron microscopy (HREM), Raman scattering, x-ray diffraction (XRD), Auger electron spectroscopy (AES), and resonant nucleus reaction (RNR). The results show that as the doping concentration of PH₃ increases, the average grain size (d) tends to decrease and the crystalline volume percentage (X_c) increases simultaneously. For the B-doped samples, as the doping concentration of B₂H\xj{6} increases, no obvious change in the value of d is observed, but the value of X_c is found to decrease. This is especially apparent in the case of heavy B₂H₂ doped samples, where the films change from nanocrystalline to amorphous.     

A hybrid quantum encoding algorithm of vector quantization for image compression

Many classical encoding algorithms of vector quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45\sqrt{N} times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than \sqrt{N} for most images, and it is more efficient than the pure quantum algorithm.     

Valence orbital method of calculating harmonic emission from diatomic molecule

We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N₂ and O₂ molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N₂ and O₂ molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of \sigma and \pi orbitals, the bonding orbital (\sigma _{2pz} )^2 of N₂ determines the maximum of harmonic emission when the molecular axis of N₂ is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O₂ molecule the antibonding orbitals (\pi _{2py}^\ast )^1 and (\pi _{2pz}^\ast )^1 contribute to the maximum of harmonic yield when O₂ is aligned at 45^{\circ} and bonding orbitals (\pi _{2py} )^2 and (\pi _{2pz} )^2 slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45^{\circ}.     

Effects of Magnetic Coupling on Profile of Emission Lines and Images of an Accretion Disc Around a Black Hole

The profiles of emission lines and images of an accretion disc around a black hole (13tt) are simulated by considering the effects of the magnetic coupling (MC) of a central BH with the disc. The MC effects are discussed for both slow- and fast-spinning BHs, and the following results are obtained. Firstly, the width of the emission lines and the brightness of the disc are reduced and augmented for slow- and fast-spinning BHs, respectively. Secondly,the image of the disc becomes dimmer and brighter near the inner edge of the disc for slow- and fast-spinning BHs, respectively. It turns out that all these results arise from the MC effects on the position of the dominant emission region of the accretion disc.     

$\Lambda$ resonances studied in $K^-p\rightarrow \Sigma^0\pi^0$ in a chiral quark model

A chiral quark-model approach is extended to the study of the $\bar{K}N$ scattering at low energies. The process of $K^-p\rightarrow \Sigma^0\pi^0$ at $P_K\lesssim 800$ MeV/c (i.e. the center mass energy $W\lesssim 1.7$ GeV) is investigated. The $\Lambda(1405)S_{01}$ dominates the reactions over the energy region considered here. Around $P_K\simeq 400$ MeV/c, the $\Lambda(1520)D_{03}$ is responsible for a strong resonant peak in the cross section. Our analysis suggests that there exist configuration mixings within the $\Lambda(1405)S_{01}$ and $\Lambda(1670)S_{01}$ as admixtures of the $[\textbf{70},^2\textbf{1},1/2]$ and $[\textbf{70},^2\textbf{8},1/2]$ configurations. The $\Lambda(1405)S_{01}$ is dominated by $[\textbf{70},^2\textbf{1},1/2]$, and $\Lambda(1670)S_{01}$ by $[\textbf{70},^2\textbf{8},1/2]$. The non-resonant background contributions, i.e. $u$-channel and $t$-channel, also play important roles in the explanation of the angular distributions due to amplitude interferences.     

Maximal possible accretion rates for slim disks

It was proved in the previous work that there must be a maximal possible accretion rate $ \dot M_{max} $ \dot M_{max} for a slim disk. Here we discuss how the value of $ \dot M_{max} $ \dot M_{max} depends on the two fundamental parameters of the disk, namely the mass of the central black hole M and the viscosity parameter α. It is shown that $ \dot M_{max} $ \dot M_{max} increases with decreasing α, but is almost independent of M if $ \dot M_{max} $ \dot M_{max} is measured by the Eddington accretion rate $ \dot M_{Edd} $ \dot M_{Edd} , which is in turn proportional to M.     

Coevolution of competing systems: local cooperation and global inhibition

Using a set of heterogeneous competing systems with intra-system cooperation and inter-system aggression, we show how the coevolution of the system parameters (degree of organization and conditions for aggression) depends on the rate of supply of resources [(S)\dot]\dot{S}. The model consists of a number of units grouped into systems that compete for the resource S; within each system several units can be aggregated into cooperative arrangements whose size is a measure of the degree of organization in the system. Aggression takes place when the systems release inhibitors that impair the performance of other systems. Using a mean field approximation we show that i) even in the case of identical systems there are stable inhomogeneous solutions; ii) a system steadily producing inhibitors needs large perturbations to leave this regime; and iii) aggression may give comparative advantages. A discrete model is used in order to examine how the particular configuration of the units within a system determines its performance in the presence of aggression. We find that full-scale, one sided aggression is only profitable for less-organized systems, and that systems with a mixture of degrees of organization exhibit robustness against aggression. By using a genetic algorithm we find that, in terms of the full-occupation resource supply rate [(S)\dot]_F\dot{S}_{F}, the coevolution of the set of systems displays the following behavior: i) for [(S)\dot] < [(S)\dot]_F/10\dot{S}< \dot{S}_{F}/10 aggressions are irrelevant and most systems exhibit a high degree of organization; ii) For [(S)\dot]_F/10 < [(S)\dot] < [(S)\dot]_F/3\dot{S}_{F}/10 < \dot{S} < \dot{S}_{F}/3 aggressions are frequent, making systems with a low degree of organization competitive; iii) for [(S)\dot]_F/3 < [(S)\dot] < [(S)\dot]_F/2\dot{S}_{F}/3 < \dot{S} < \dot{S}_{F}/2 the systems display global evolutive transitions between periods of calm (few aggressions and high degree of organization) and periods of belligerence (frequent aggressions and low degree of organization); iv) for $ \dot{S} > \dot{S}_{F}/2$ \dot{S} > \dot{S}_{F}/2 the periods of aggression becomes progressively rarer and shorter. Finally, when [(S)\dot]\dot{S} approaches [(S)\dot]_F\dot{S}_{F} the selection pressure on the cooperativity and the aggression between systems disappears. This kind of model can be useful to analyse the interplay of the cooperation/competition processes that can be found in some social, economic, ecological and biochemical systems; as an illustration we refer to the competition between drug-selling gangs.     

A Complete Set of Riemann Invariants

There are at most 14 independent real algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space. In the general case, these invariants can be written in terms of four different types of quantities: R , the real curvature scalar, two complex invariants I and J formed from the Weyl spinor, three real invariants I₆, I₇ and I₈ formed from the trace-free Ricci spinor and three complex mixed invariants K, L and M. Carminati and McLenaghan [5] give some geometrical interpretations of the role played by the mixed invariants in Einstein-Maxwell and perfect fluid cases. They show that 16 invariants are needed to cover certain degenerate cases such as Einstein-Maxwell and perfect fluid and show that previously known sets fail to be complete in the perfect fluid case. In the general case, the invariants I and J essentially determine the components of the Weyl spinor in a canonical tetrad frame; likewise the invariants I₆, I₇ and I₈ essentially determine the components of the trace-free Ricci spinor in a (in general different) canonical tetrad frame. These mixed invariants then give the orientation between the frames of these two spinors. The six real pieces of information in K, L and M are precisely the information needed to do this. A table is given of invariants which give a complete set for each Petrov type of the Weyl spinor and for each Segre type of the trace-free Ricci spinor This table involves 17 real invariants, including one real invariant and one complex invariant involving , and in some degenerate cases.     

Exponential lower bounds to solutions of the Schrödinger equation: Lower bounds for the spherical average

For a large class of generalizedN-body-Schrödinger operators,H, we show that ifE<Σ=infσ_ess(H) and ψ is an eigenfunction ofH with eigenvalueE, then $$\begin{array}{*{20}c} {\lim } \\ {R \to \infty } \\ \end{array} R^{ - 1} \ln \left( {\int\limits_{S^{n - 1} } {|\psi (R\omega )|} ^2 d\omega } \right)^{1/2} = - \alpha _0 ,$$ with α ₀ ² +E a threshold. Similar results are given forE≧Σ.     

Unfolding the singularities in superspace

A method is described for unfolding the singularities in superspace, \(\mathcal{G} = \mathfrak{M}/\mathfrak{D}\) , the space of Riemannian geometries of a manifoldM. This unfolded superspace is described by the projection $$\mathcal{G}_{F\left( M \right)} = \frac{{\mathfrak{M} \times F\left( M \right)}}{\mathfrak{D}} \to \frac{\mathfrak{M}}{\mathfrak{D}} = \mathcal{G}$$ whereF(M) is the frame bundle ofM. The unfolded space \(\mathcal{G}_{F\left( M \right)}\) is infinite-dimensional manifold without singularities. Moreover, as expected, the unfolding of \(\mathcal{G}_{F\left( M \right)}\) at each geometry [g _o] ∈ \(\mathcal{G}\) is parameterized by the isometry groupIg _o (M) of g₀. Our construction is natural, is generally covariant with respect to all coordinate transformations, and gives the necessary information at each geometry to make \(\mathcal{G}\) a manifold. This construction is a canonical and geometric model of a nonrelativistic construction that unfolds superspace by restricting to those coordinate transformations that fix a frame at a point. These particular unfoldings are tied together by an infinite-dimensional fiber bundleE overM, associated with the frame bundleF(M), with standard fiber \(\mathcal{G}_{F\left( M \right)}\) , and with fiber at a point inM being the particular noncanonical unfolding of \(\mathcal{G}\) based at that point. ThusE is the totality of all the particular unfoldings, and so is a grand unfolding of \(\mathcal{G}\) .     

Solar System planetary tests of $${\dot c/c}$$

Analytical and numerical calculations show that a putative temporal variation of the speed of light c, with the meaning of space-time structure constant c _ST, assumed to be linear over timescales of about one century, would induce a secular precession of the longitude of the pericenter v{\varpi} of a test particle orbiting a spherically symmetric body. By comparing such a predicted effect to the corrections D[(v)\dot]{\Delta\dot\varpi} to the usual Newtonian/Einsteinian perihelion precessions of the inner planets of the Solar System, recently estimated by E.V. Pitjeva by fitting about one century of modern astronomical observations with the standard classical/relativistic dynamical force models of the EPM epehemerides, we obtained [(c)\dot]/c = (0.5±2)×10^-7 yr^-1{\dot c/c =(0.5\pm 2)\times 10^{-7} {\rm yr}^{-1}} . Moreover, the possibility that [(c)\dot]/c 1 0{\dot c/c\neq 0} over the last century is ruled out at 3−12σ level by taking the ratios of the perihelia for different pairs of planets. Our results are independent of any measurement of the variations of other fundamental constants which may be explained by a variation of c itself (with the meaning of electromagnetic constant c _EM). It will be important to repeat such tests if and when other teams of astronomers will estimate their own corrections to the standard Newtonian/Einsteinian planetary perihelion precessions with different ephemerides.     

On a Pre-Lie Algebra Defined by Insertion of Rooted Trees

Let K be a field of characteristic zero. For \({n \in \mathbb{N}^{*}}\) , let \({\mathcal{T}^{\,\prime}_{n}}\) be the vector space of non-planar rooted trees with n vertices (Foissy in Bull Sci Math 126, no. 3, 193–239; no. 4, 249–288, 2002). Let \({\vartriangleright}\) be the left pre-Lie product of insertion of a tree inside another defined on infinitesimal characters of the graded Hopf algebra \({\mathcal{H}}\) introduced by Calaque, Ebrahimi-Fard and Manchon. Let \({\mathcal{T}^{\,\prime}=\oplus_{n\geq 2}\mathcal{T}^{\,\prime}_{n}}\) . In this work, we first prove that \({(\mathcal{T}^{\,\prime}, \vartriangleright)}\) a pre-Lie algebra generated by the two ladders E ₁ and E ₂ where E ₁ is the ladder with one edge and E ₂ is the ladder with two edges. Second, we prove that \({(\mathcal{T}^{\,\prime}, \vartriangleright)}\) is not a free pre-Lie algebra, and we exhibit a family of relations.     

Kiselev黑洞的热力学性质和物质吸积特性

本文考虑带有黑洞视界和宇宙视界的Kiselev时空.研究以黑洞视界和宇宙视界为边界的系统的热力学性质.统一地给出了两个系统的热力学第一定律;在黑洞视界半径远小于宇宙视界半径的情况下,近似地计算了通过宇宙视界和黑洞视界的热能.然后,探讨Kiselev时空的物质吸积特性.在吸积能量密度正比于背景能量密度的条件下给出黑洞的吸积率,讨论了黑洞吸积率与暗能量态方程参数的关系.     

碱金属双原子分子部分电子态的完全振动能谱和离解能

对大多数双原子分子电子态的高阶振动能谱,现代实验方法和量子力学理论计算都难以得到较精确的振动能级.文中应用基于二阶微扰理论的代数方法(AM)以及计算双原子分子离解能的新表达式研究了碱金属双原子分子Li₂的3³Σ⁺_g,1³Δ_g和2³Π_g,Na₂的B¹Π_u以及K₂的4¹Σ⁺_g电子态的完全振动能谱{E_υ^AM}和离解能,理论计算结果不仅与已有的实验值相符,而且还给出了实验尚未得到的高阶振动能级.这些结果为碱金属双原子分子精确振动能谱和离解能的科学研究提供了重要数据. 关键词： 碱金属分子 高阶振动能级 离解能 代数方法     

KTiOPO4晶体理论习性

为了解决复杂结构离子晶体接触能E_att计算上的困难,本文给出了按PBC(periodic bond chain)理论导出的公式,并将其编成计算机程序。应用PBC理论,从KTiOPO₄晶体结构,对其界面进行分类表明,{100},{011}为F单形;{210},{101}和{010}为较重要的S单形;而{001}单形的晶面,属K面。根据以上公式及程序对各单形E_att进行了计算,得出了各晶面的相对重要性,其结果与观测结果符合得很好。文中提出的公式 关键词：