Time-like geodesic structure of a spherically symmetric black hole in the brane-world

Recently Malihe Heydari-Fard obtained a spherically symmetric exterior black hole solution in the brane-world scenario, which can be used to explain the galaxy rotation curves without postulating dark matter. By analysing the particle effective potential, we have investigated the time-like geodesic structure of the spherically symmetric black hole in the brane-world. We mainly take account of how the cosmological constant α and the stellar pressure β affect the time-like geodesic structure of the black hole. We find that the radial particle falls to the singularity from a finite distance or plunges into the singularity, depending on its initial conditions. But the non-radial time-like geodesic structure is more complex than the radial case. We find that the particle moves on the bound orbit or stable (unstable) circle orbit or plunges into the singularity, or reflects to infinity, depending on its energy and initial conditions. By comparing the particle effective potential curves for different values of the stellar pressure β and the cosmological constant α, we find that the stellar pressure parameter β does not affect the time-like geodesic structure of the black hole, but the cosmological constant α has an impact on its time-like geodesic structure.     

对均匀的数学描述及其与混沌的关系

基于独占球的概念定义的瞬时混沌度和k步混沌强度是混沌轨道的稳定特征,应用独占球的概念定义了均匀度,它对均匀性的描述与人对均匀的理解非常符合.被含均匀度是一个过渡概念,它与均匀度非常相似,但有更好的数学性质,对于随机轨道,被含均匀度统计收敛于1/V_n（1）（V_n（1）是n维欧氏空间的单位球体积）,而当轨道上的点充分多时,均匀度与被含均匀度近似相等.只要适当选择包含动力系统吸引盆的多 关键词： 独占球 均匀度 混沌 瞬时混沌强度     

Orbit determination for Chang’E-2 lunar probe and evaluation of lunar gravity models

The Unified S-Band (USB) ranging/Doppler system and the Very Long Baseline Interferometry (VLBI) system as the ground tracking system jointly supported the lunar orbit capture of both Chang’E-2 (CE-2) and Chang’E-1 (CE-1) missions. The tracking system is also responsible for providing precise orbits for scientific data processing. New VLBI equipment and data processing strategies have been proposed based on CE-1 experiences and implemented for CE-2. In this work the role VLBI tracking data played was reassessed through precision orbit determination (POD) experiments for CE-2. Significant improvement in terms of both VLBI delay and delay rate data accuracy was achieved with the noise level of X-band band-width synthesis delay data reaching 0.2–0.3 ns. Short-arc orbit determination experiments showed that the combination of only 15 min’s range and VLBI data was able to improve the accuracy of 3 h’s orbit using range data only by a 1–1.5 order of magnitude, confirming a similar conclusion for CE-1. Moreover, because of the accuracy improvement, VLBI data was able to contribute to CE-2’s long-arc POD especially in the along-track and orbital normal directions. Orbital accuracy was assessed through the orbital overlapping analysis (2 h arc overlapping for 18 h POD arc). Compared with about 100 m position error of CE-1’s 200 km×200 km lunar orbit, for CE-2’s 100 km×100 km lunar orbit, the position errors were better than 31 and 6 m in the radial direction, and for CE-2’s 15 km×100 km orbit, the position errors were better than 45 and 12 m in the radial direction. In addition, in trying to analyze the Delta Differential One-Way Ranging (ΔDOR) experiments data we concluded that the accuracy of ΔDOR delay was dramatically improved with the noise level better than 0.1 ns and systematic errors better calibrated, and the Short-arc POD tests with ΔDOR data showed excellent results. Although unable to support the development of an independent lunar gravity model, the tracking data of CE-2 provided evaluations of different lunar gravity models through POD. It is found that for the 100 km×100 km lunar orbit, with a degree and order expansion up to 165, JPL’s gravity model LP165P did not show noticeable improvement over Japan’s SGM series models (100×100), but for the 15 km×100 km lunar orbit, a higher degree-order model can significantly improve the orbit accuracy.

     

Statistical characteristics of meso-scale vortex effects on the track of a tropical cyclone

This paper examines initial meso-scale vortex effects on the motion of a tropical cyclone (TC) in a system where coexisting two components of TC and meso-scale vortices with a barotropic vorticity equation model. The initial meso-scale vortices are generated stochastically by employing Reinaud’s method. The 62 simulations are performed and analysed in order to understand the statistical characteristics of the effects. Results show that the deflection of the TC track at t=24 h induced by the initial meso-scale vortices ranges from 2km to 37 km with the mean value of 13.4 km. A more significant deflection of the TC track can be reduced when several initial meso-scale vortices simultaneously appear in a smaller TC circulation area. It ranges from 22 km to 37 km with the mean value of 28 km,this fact implies that the initial meso-scale vortices-induced deflection may not be neglected sometimes.     

Type-D vacuum solutions with cosmological constant

All type-D vacuum (nonnull orbit and null orbit) solutions with are exhibited in canonical coordinates. The nonnull orbit metrics with contain four families of solutions: the static Levi-Cività metrics, the nondivergingD's, the divergingD's, and the diverging and twisting solutions. The null orbit metrics subdivide into two subclasses of solutions: the divergenceless null orbitD's, and the diverging and twisting null orbit solution.     

Quantum Thermodynamics with Missing Reference Frames: Decompositions of Free Energy Into Non-Increasing Components

If an absolute reference frame with respect to time, position, or orientation is missing one can only implement quantum operations which are covariant with respect to the corresponding unitary symmetry group G. Extending observations of Vaccaro et al., I argue that the free energy of a quantum system with G-invariant Hamiltonian then splits up into the Holevo information of the orbit of the state under the action of G and the free energy of its orbit average. These two kinds of free energy cannot be converted into each other. The first component is subadditive and the second superadditive; in the limit of infinitely many copies only the usual free energy matters.Refined splittings of free energy into more than two independent (non-increasing) terms can be defined by averaging over probability measures on G that differ from the Haar measure.Even in the presence of a reference frame, these results provide lower bounds on the amount of free energy that is lost after applying a passive covariant channel. If the channel properly decreases one of these quantities, it decreases the free energy necessarily at least by the same amount, since it is unable to convert the different forms of free energies into each other. For instance, if an electrical, optical, or acoustical signal loses some time accuracy after it has passed a passive time-invariant device, the results provide lower bounds on the free energy lost in the latter.     

Classification of Gauge Orbit Types for SU(n)-Gauge Theories

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed.     

Observation of magnetic breakdown in double quantum wells

We report on our studies of magnetic breakdown (MB) in coupled GaAs/Al_0.3Ga_0.7As double quantum wells (DQWs) subject to crossed magnetic fields. MB is a failure of semiclassical theory that occurs when a magnetic field causes electrons to tunnel across a gap ink-space from one Fermi surface (FS) branch to another. We study MB in a two-branch FS created by subjecting a DQW to an in-plane magnetic field (B_∥). The principal effect ofB_∥is a distortion in the dispersion curve of the system, yielding a FS consisting of two components, a lens-shaped inner orbit and an hour-glass-shaped outer orbit. The perpendicular field (B_⊥) causes Landau level formation and Shubnikov–de Haas (SdH) oscillations for each branch of the FS. At higher perpendicular fields MB occurs and electrons tunnel throughk-space from one FS orbit to the other. MB is observed by noting which peaks are present in the Fourier power spectrum of the magnetoresistance versus 1/B_⊥at constantB_∥. We observe MB in two DQW samples over a range ofB_∥.     

Vergleich von klassischen und BORN-Wirkungsquerschnitten bei Elektronenstößen am H-Atom

Comparison of Classical and BORN Cross Sections for Electron-H-Collisions In Part I first BORN approximation cross-sections σ(n → n + Δn) for collision-induced transitions n = 10, 20, 30; Δn = 1 are calculated by Monte-Carlo methods. It is shown that the simplier circular orbit approximation (i.e. taking into account the highest momenta (? n ?1) only) approximates the exact results by BORN quite well. Circular orbit approximation cross-sections are tabulated up to n = 150 and Δn = 1. In Part II cross-sections are calculated classically in the adiabatic approximation [1, 2]. This method yields quite accurate cross-sections for small projectile energies where usual momentum approximations (binary encounter approximations) work not so well. In the paper is also presented a selection rule according to which for high n and l dipole-transitions in the H-atom are possible only for Δn = 1.     

Spin–orbit coupling in biradicals. 5. Zero-field splitting in triplet dimethylnitrenium,dimethylphosphenium and dimethylarsenium cations

The spin dipole–spin dipole and spin–orbit coupling contributions to the zero-field splitting parameters D and E of [CH₃–N–CH₃]⁺, [CH₃–P–CH₃]⁺, and [CH₃–As–CH₃]⁺ have been calculated from CASSCF(14,14)/cc-pVTZ wave functions and the Breit–Pauli Hamiltonian at T₁ B3LYP/cc-pVTZ optimized geometries. The spin–orbit coupling contributions represent a minor correction for the dimethylnitrenium cation, which has a triplet ground state. They dominate the spin–spin terms by an order of magnitude in the dimethylphosphenium cation and by more than two orders of magnitude in the dimethylarsenium cation, both of which have a singlet ground state. The properties of all these biradicaloids follow expectations based on the simple algebraic 2-in-2 model of biradical structure.     

The emission positions of kHz QPOs and Kerr spacetime influence

Based the Alfven wave oscillation model (AWOM) and relativistic precession model (RPM) for twin kHz QPOs, we estimate the emission positions of most detected kHz QPOs to be at r=18+/−3 km (R/15 km), except Cir X-1 at r∼30+/−5 km (R/15 km). For the proposed Keplerian frequency as an upper limit to kHz QPO, the spin effects in Kerr Spacetime are discussed, which have about a 5% (2%) modification for that of the Schwarzchild case for the spin frequency of 1000 (400) Hz. The application to the four typical QPO sources, Cir X-1, Sco X-1, SAX J1808.4-3658 and XTE 1807-294, is mentioned.

     

Multiple Melting Behavior of High-Speed Melt Spun Polylactide Fibers

High-speed melt spinning of polylactide (PLA) was conducted and the structure and multiple melting behavior of the as-spun fibers were investigated. In the analysis of temperature modulated differential scanning calorimetry (TMDSC) thermograms for the as-spun PLA fibers taken-up at 1 and 6 km/min, the peaks around the melting temperature region in the reversing heat flow (RHF) and nonreversing heat flow (NRHF) curves were mainly separated into (1) a pair of an endothermic peak (Peak L) in RHF and an exothermic peak (Peak R) in NRHF in a low temperature region, (2) an endothermic peak (Peak M) both in RHF and NRHF (only in RHF for PLA fiber spun at the low-speed) in an intermediate temperature region, and (3) an endothermic peak (Peak H) both in RHF and NRHF in a higher temperature region. Wide-angle X-ray diffraction (WAXD) measurements were conducted during the heating process of the as-spun fibers cut into powders. In the case of fibers obtained at 1 km/min, disordered crystals, i.e. α′-form crystals, were formed through cold crystallization followed by a disorder-to-order phase transition, i.e. α′ to α crystalline modification, with partial melting of the α′ crystals around 148.5°C in the temperature range of Peaks R and L. Finally, the α form crystals melted above 169.4°C, in the temperature range of Peak H. On the other hand, the PLA crystals generated by the orientation-induced crystallization during the spinning process at a spinning velocity of 6 km/min did not show a WAXD profile of perfect α form crystals but showed an intermediate structure having lattice spacings between the α′ and α forms. Such intermediate crystals did not transformed into α form crystals during the heating process.     

Atmospheric ultraviolet and red-infrared flashes from Universitetsky-Tatiana-2 satellite data

Millisecond ultraviolet (240–400 nm) and red-infrared (610–800 nm) flashes were detected in the nighttime atmosphere with the scientific payload installed onboard the Universitetsky-Tatiana-2 micro-satellite. Flashes with various numbers of photons, from 10²⁰ to 10²⁶, were detected within the atmospheric area 300 km in diameter observed by the detector. The flashes differ in duration and temporal profile: from single short flashes ～1 ms in duration to flashes with a complex profile more than 100 ms in duration. Different global geographic distributions are observed for flashes with different numbers of photons. Flashes with fewer than 10²² photons are distributed uniformly over the Earth’s map. Flashes with more than 10²² photons are concentrated near the equator and above the continents. Series of flashes were observed in one turn of the satellite when flying not only over thunderstorm regions but also over cloudless ones. The flash number distribution has been derived from the ratio of the numbers of red-infrared and ultraviolet photons. As applied to discharges in the upper atmosphere, whose glow is dominated by the emission in the first and second positive systems of molecular nitrogen bands (1PN₂ and 2PN₂), this distribution is equivalent to the flash altitude distribution in the atmosphere. The observed ratio of the numbers of photons in red-infrared and ultraviolet flashes agrees with the calculated one for electric discharges at altitudes higher than 50 km. In-orbit measurements of the charged particle flux (with a threshold energy for electrons of 1 MeV) provide no evidence for a synchronous occurrence of an ultraviolet flash and a burst in the particle flux in the orbit.     

Numerical Range for Orbits Under a Central Force

We present an explicit form for the central force that describes the orbit of some roulette curve, and interpret the orbit of the roulette curve as an algebraic curve F(1, x, y) = 0 associated to the homogeneous polynomial F(t, x, y) of a matrix A. The hodograph of the orbit is obtained as the boundary generating curve of the numerical range of A.     

Observations of Trapped Electrons and Positrons with E > 50 MeV in the Inner Radiation Belt by the PAMELA Magnetic Spectrometer

Geomagnetically trapped electrons and positrons with energy above 50 MeV were observed in PAMELA experiment on board Resurs DK satellite. The instrument consists of magnetic spectrometer, imaging electromagnetic calorimeter, time-of-flight system, anticoincidence and neutron detectors that provide unique particle identification and background rejection. PAMELA was collecting data since June 2006 till January 2016. The satellite orbit with initial altitude 350–600 km and inclination 70° crosses the inner radiation belt in South Atlantic Anomaly at L-shell ∼1.2. The trapped electrons and positrons were selected on the basis of a trajectory simulation in the Earth magnetic field. Features of the energy spectra of electrons and positrons at low energies are analyzed.

     

Local Critical Perturbations of Unimodal Maps

We introduce a new complete metric in the space of unimodal C ²-maps of the interval, with two maps close if they are close in the C ²-metric and differ only on a small interval containing their critical points. We identify all structurally stable maps in the sense of this metric. They are maps for which either (1) the trajectory of the critical point is attracted to a topologically attracting (at least from one side) periodic orbit, but never falls into this orbit, or (2) the critical point is mapped by some iterate to the interior of an interval consisting entirely of periodic points of the same (minimal) period. We verify the generalized Fatou conjecture for and show that structurally stable maps form an open dense subset of . Partially supported by NSF grant DMS 0456748. Partially supported by NSF grant DMS 0456526.     

Spin-orbit interactions from self consistent field wavefunctions

Effects of the spin-orbit Hamiltonian H_LS , including both the spin-same orbit and spin-other orbit terms, are studied at the self consistent field (SCF) level of theory. Separate calculations are carried out for each state considered, and biorthogonal orbitals are constructed for the evaluation of matrix elements. Doublet-doublet and singlet-triplet interactions are discussed. The evaluation of the Gaussian basis function integrals is described in a Cartesian component representation, these integrals being directly related to one and two electron second derivative integrals. This new SCF spin-orbit code is used to (i) determine the spatial dependence of the spin-orbit parameters for the Renner-Teller ²B₁, ²A₁ states of H₂O⁺, (ii) determine the spin-orbit splitting of the ²Π states of OH as a function of bond-length and (iii) calculate the radiative lifetime of the a ³Σ⁺ state of NO⁺. In each case these calculations are compared with more sophisticated configuration interaction studies, but it is found that the evaluation of these effects near equilibrium geometries at the SCF level is sufficiently accurate, provided that a large basis set is used.     

On some electromagnetic phenomena in the tether magnetoplasma cloud

Summary The tethered satellite system (TSS) will be accompanied by a variety of electromagnetic phenomena. An independent interconnected formation, a ?tethered magnetoplasma cloud? (TMC), moving in space along the orbit of TSS, at an altitude of about 300 km, will be created. This time-dependent cloud will be a very complicated inhomogeneous formation including electromagnetic oscillations and waves of different type. Some of these waves will be observed on the Earth's surface. Rarefiel regions of the magnetoplasma behind, and dense regions in front of the shuttle orbiter (SO) and the subsatellite (SS) will arise. The neutral nitrogen beam ejected by the thruster becomes an ion beam on the day-light part of the orbit. Its energy is much greater than the local thermal energy. Instabilities of different kind as well as diffusion and recombination effects are expected to accompany the interaction of these beams with the surrounding plasma. The electron beams will produce other types of instabilities. By the electrons precessing along the magnetic-field lines, a current (5·10³V, 0.5 A) should be induced in the 20th km length conducting tether. It will be closed at the bottom of the ionosphere. This huge magnetic loop, so-called ?phantom loop? (PL), should accompany the tether system along its orbit. The length of this ?tether electromagnetic tail? (TEMT) is about 200 km, its magnetic moment will be about 10¹³ A·cm². Alfvén waves and nonlinear effects of heating type may be produced by this loop along the magnetic-field lines. ?Strings? of hot plasma may accompany the tether system.     

Back to Balls in Billiards

We consider a billiard in the plane with periodic configuration of convex scatterers. This system is recurrent, in the sense that almost every orbit comes back arbitrarily close to the initial point. In this paper we study the time needed to get back in an ε-ball about the initial point, in the phase space and also for the position, in the limit when ε → 0. We establish the existence of an almost sure convergence rate, and prove a convergence in distribution for the rescaled return times.