Giant Pulses with Nanosecond Time Resolution detected from the Crab Pulsar at 8.5 and 15.1 GHz

We present a study of shape, spectra and polarization properties of giant pulses (GPs) from the Crab pulsar at the very high frequencies of 8.5 and 15.1 GHz. Studies at 15.1 GHz were performed for the first time. Observations were conducted with the 100-m radio telescope in Effelsberg in Oct-Nov 2007 at the frequencies of 8.5 and 15.1 GHz as part of an extensive campaign of multi-station multi-frequency observations of the Crab pulsar. A selection of the strongest pulses was recorded with a new data acquisition system, based on a fast digital oscilloscope, providing nanosecond time resolution in two polarizations in a bandwidth of about 500 MHz. We analyzed the pulse shapes, polarisation and dynamic spectra of GPs as well as the cross-correlations between their LHC and RHC signals. No events were detected outside main pulse and interpulse windows. GP properties were found to be very different for GPs emitted at longitudes of the main pulse and the interpulse. Cross-correlations of the LHC and RHC signals show regular patterns in the frequency domain for the main pulse, but these are missing for the interpulse GPs. We consider consequences of application of the rotating vector model to explain the apparent smooth variation in the position angle of linear polarization for main pulse GPs. We also introduce a new scenario of GP generation as a direct consequence of the polar cap discharge. We find further evidence for strong nano-shot discharges in the magnetosphere of the Crab pulsar. The repetitive frequency spectrum seen in GPs at the main pulse phase is interpreted as a diffraction pattern of regular structures in the emission region. The interpulse GPs however have a spectrum that resembles that of amplitude modulated noise. Propagation effects may be the cause of the differences.Comment: Astronomy & Astrophysics (accepted

How to Spread a Rumor: Call Your Neighbors or Take a Walk?

We study the problem of randomized information dissemination in networks. We compare the now standard PUSH-PULL protocol, with agent-based alternatives where information is disseminated by a collection of agents performing independent random walks. In the VISIT-EXCHANGE protocol, both nodes and agents store information, and each time an agent visits a node, the two exchange all the information they have. In the MEET-EXCHANGE protocol, only the agents store information, and exchange their information with each agent they meet. We consider the broadcast time of a single piece of information in an $n$-node graph for the above three protocols, assuming a linear number of agents that start from the stationary distribution. We observe that there are graphs on which the agent-based protocols are significantly faster than PUSH-PULL, and graphs where the converse is true. We attribute the good performance of agent-based algorithms to their inherently fair bandwidth utilization, and conclude that, in certain settings, agent-based information dissemination, separately or in combination with PUSH-PULL, can significantly improve the broadcast time. The graphs considered above are highly non-regular. Our main technical result is that on any regular graph of at least logarithmic degree, PUSH-PULL and VISIT-EXCHANGE have the same asymptotic broadcast time. The proof uses a novel coupling argument which relates the random choices of vertices in PUSH-PULL with the random walks in VISIT-EXCHANGE. Further, we show that the broadcast time of MEET-EXCHANGE is asymptotically at least as large as the other two's on all regular graphs, and strictly larger on some regular graphs. As far as we know, this is the first systematic and thorough comparison of the running times of these very natural information dissemination protocols.The authors would like to thank Thomas Sauerwald and Nicol\'{a}s Rivera for helpful discussions. This research was undertaken, in part, thanks to funding from the ANR Project PAMELA (ANR-16-CE23-0016-01), the NSF Award Numbers CCF-1461559, CCF-0939370 and CCF-18107, the Gates Cambridge Scholarship programme, and the ERC grant DYNAMIC MARCH

Origin of magnetoelectric behavior in BiFeO3_3

The magnetoelectric behavior of BiFeO$_3$ has been explored on the basis of accurate density functional calculations. The structural, electronic, magnetic, and ferroelectric properties of BiFeO$_3$ are predicted correctly without including strong correlation effect in the calculation. Moreover, the experimentally-observed elongation of cubic perovskite-like lattice along the [111] direction is correctly reproduced. At high pressure we predicted a pressure-induced structural transition and the total energy calculations at expanded lattice show two lower energy ferroelectric phases, closer in energy to the ground state phase. Band-structure calculations show that BiFeO$_3$ will be an insulator in A- and G-type antiferromagnetic phases and a metal in other magnetic configurations. Chemical bonding in BiFeO$_3$ has been analyzed using various tools and electron localization function analysis shows that stereochemically active lone-pair electrons at the Bi sites are responsible for displacements of the Bi atoms from the centro-symmetric to the noncentrosymmetric structure and hence the ferroelectricity. A large ferroelectric polarization (88.7 $\mu$C/cm$^{2}$) is predicted in accordance with recent experimental findings. The net polarization is found to mainly ($>$ 98%) originate from Bi atoms. Moreover the large scatter in experimentally reported polarization values is due to the large anisotropy in the spontaneous polarization.Comment: 19 pages, 12 figures, 4 table

Моделирование процесса комбинированного воздействия засухи и остаточных гербицидов на зерновые культуры

Using two-factor experimental design the combined action of osmotic pressure (simulated drought) and residual herbicide Frontier through a radical zone of maize and wheat seedlings was studied. The regressions between the module of superoxide dismutase activity shift and factors varied at three levels were obtained. The indices of plant tolerance to exogenous factors correlate with enzymatic activity. На прикладі комбінованого впливу двох факторів – осмотичного тиску (імітованої посухи) та залишкового гербіциду фронтьєр через прикореневу зону на паростки кукурудзи та пшениці в межах повного двофакторного лабораторного експерименту отримані регресійні залежності модуля зсуву активності супероксиддисмутази від варіювання на трьох рівнях факторів. Отримані корельовані з ферментативною активністю оцінки індексу стійкості досліджуваних рослин до екзогенного впливу факторів. На прикладі комбінованого впливу двох факторів – осмотичного тиску (імітованої посухи) та залишкового гербіциду фронтьєр через прикореневу зону на паростки кукурудзи та пшениці в межах повного двофакторного лабораторного експерименту отримані регресійні залежності модуля зсуву активності супероксиддисмутази від варіювання на трьох рівнях факторів. Отримані корельовані з ферментативною активністю оцінки індексу стійкості досліджуваних рослин до екзогенного впливу факторів.

The Kinematic Algebra From the Self-Dual Sector

We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.Comment: 29 pages, 5 figures. v2: references added, published versio

Extension of Bogoliubov theory to quasi-condensates

We present an extension of the well-known Bogoliubov theory to treat low dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretisation in cells of size $l$. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two and three dimensions with no ultraviolet or infrared divergence. Furthermore this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, the first order and second order correlations functions of the field. Explicit calculations are done for homogeneous systems.Comment: 32 pages, 2 figures; typos corrected in revised versio

Fragmentation of Bose-Einstein Condensates

We present the theory of bosonic systems with multiple condensates, unifying disparate models which are found in the literature, and discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the types of fragmentation, eventually leading to strongly correlated states with no trace of condensation.Comment: 16 pages, 1 figure, revtex

Spherical model of the Stark effect in external scalar and vector fields

The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of quasistationary level are generalized by taking into account the relativistic effects, spin and Lorentz structure of interaction potentials. The relativistic quasi-classical theory of ionization of the Coulomb system (V_{Coul}=-\xi/r) by radial-constant long-range scalar (S_{l.r.}=(1-\lambda)(\sigma r+V_0)) and vector (V_{l.r.}=\lambda(\sigma r+V_0)) fields is constructed. In the limiting cases the approximated analytical expressions for the position E_r and width \Gamma of below-barrier resonances are obtained. The strong dependence of the width \Gamma of below-barrier resonances on both the bound level energy and the mixing constant \lambda is detected. The simple analytical formulae for asymptotic coefficients of the Dirac radial wave functions at zero and infinity are also obtained.Comment: 25 pages, 4 figures. Submitted to Int. J. Mod. Phys.

Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries

We extend the Mason-Newman Lax pair for the elliptic complex Monge-Amp\`ere equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. We identify the real and imaginary parts of the potential, which we call partner symmetries, with the translational and dilatational symmetry characteristics respectively. Then we choose the dilatational symmetry characteristic as the new unknown replacing the K\"ahler potential which directly leads to a Legendre transformation and to a set of linear equations satisfied by a single real potential. This enables us to construct non-invariant solutions of the Legendre transform of the complex Monge-Amp\`ere equation and obtain hyper-K\"ahler metrics with anti-self-dual Riemann curvature 2-form that admit no Killing vectors.Comment: submitted to J. Phys.

Effective-action approach to a trapped Bose gas

The effective-action formalism is applied to a gas of bosons. The equations describing the condensate and the excitations are obtained using the loop expansion for the effective action. For a homogeneous gas the Beliaev expansion in terms of the diluteness parameter is identified in terms of the loop expansion. The loop expansion and the limits of validity of the well-known Bogoliubov and Popov equations are examined analytically for a homogeneous dilute Bose gas and numerically for a gas trapped in a harmonic-oscillator potential. The expansion to one-loop order, and hence the Bogoliubov equation, is shown to be valid for the zero-temperature trapped gas as long as the characteristic length of the trapping potential exceeds the s-wave scattering length.Comment: 17 pages, 10 figures, accepted for publication in Phys. Rev.