Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I

We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete informations on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general 10-parameter family of discretizations of the nonlinear Schroedinger equation, consists of the following three steps: i) the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in epsilon, following the Degasperis - Manakov - Santini procedure; ii) the application, to such expansion, of the Degasperis - Procesi (DP) integrability test, to test the asymptotic integrability properties of the discrete system and its ``distance'' from its continuous limit; iii) the use of the main output of the DP test to construct infinitely many approximate symmetries and constants of motion of the discrete system, through novel and simple formulas.Comment: 34 pages, no figur

Non-linear electromagnetic response of graphene

It is shown that the massless energy spectrum of electrons and holes in graphene leads to the strongly non-linear electromagnetic response of this system. We predict that the graphene layer, irradiated by electromagnetic waves, emits radiation at higher frequency harmonics and can work as a frequency multiplier. The operating frequency of the graphene frequency multiplier can lie in a broad range from microwaves to the infrared.Comment: 5 pages, 3 figure

The GAMMA-400 space observatory: status and perspectives

The present design of the new space observatory GAMMA-400 is presented in this paper. The instrument has been designed for the optimal detection of gamma rays in a broad energy range (from ~100 MeV up to 3 TeV), with excellent angular and energy resolution. The observatory will also allow precise and high statistic studies of the electron component in the cosmic rays up to the multi TeV region, as well as protons and nuclei spectra up to the knee region. The GAMMA-400 observatory will allow to address a broad range of science topics, like search for signatures of dark matter, studies of Galactic and extragalactic gamma-ray sources, Galactic and extragalactic diffuse emission, gamma-ray bursts and charged cosmic rays acceleration and diffusion mechanism up to the knee

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

Search for anisotropies in cosmic-ray positrons detected by the PAMELA experiment

The PAMELA detector was launched on board of the Russian Resurs-DK1 satellite on June 15, 2006. Data collected during the first four years have been used to search for large-scale anisotropies in the arrival directions of cosmic-ray positrons. The PAMELA experiment allows for a full sky investigation, with sensitivity to global anisotropies in any angular window of the celestial sphere. Data samples of positrons in the rigidity range 10 GV $\leq$ R $\leq$ 200 GV were analyzed. This article discusses the method and the results of the search for possible local sources through analysis of anisotropy in positron data compared to the proton background. The resulting distributions of arrival directions are found to be isotropic. Starting from the angular power spectrum, a dipole anisotropy upper limit \delta = 0.166 at 95% C.L. is determined. Additional search is carried out around the Sun. No evidence of an excess correlated with that direction was found.Comment: The value of the dipole anisotropy upper limit has been changed. The method is correct but there was a miscalculation in the relative formul

PAMELA's measurements of geomagnetic cutoff variations during solar energetic particle events

Data from the PAMELA satellite experiment were used to measure the geomagnetic cutoff for high-energy ($\gtrsim$ 80 MeV) protons during the solar particle events on 2006 December 13 and 14. The variations of the cutoff latitude as a function of rigidity were studied on relatively short timescales, corresponding to single spacecraft orbits (about 94 minutes). Estimated cutoff values were cross-checked with those obtained by means of a trajectory tracing approach based on dynamical empirical modeling of the Earth's magnetosphere. We find significant variations in the cutoff latitude, with a maximum suppression of about 6 deg for $\sim$80 MeV protons during the main phase of the storm. The observed reduction in the geomagnetic shielding and its temporal evolution were compared with the changes in the magnetosphere configuration, investigating the role of IMF, solar wind and geomagnetic (Kp, Dst and Sym-H indexes) variables and their correlation with PAMELA cutoff results.Comment: Conference: The 34th International Cosmic Ray Conference (ICRC2015), 30 July - 6 August, 2015, The Hague, The Netherlands, Volume: PoS(ICRC2015)28

Solar energetic particle events: trajectory analysis and flux reconstruction with PAMELA

The PAMELA satellite experiment is providing first direct measurements of Solar Energetic Particles (SEPs) with energies from about 80 MeV to several GeV in near-Earth space, bridging the low energy data by other space-based instruments and the Ground Level Enhancement (GLE) data by the worldwide network of neutron monitors. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies. This work reports the analysis methods developed to estimate the SEP energy spectra as a function of the particle pitch-angle with respect to the Interplanetary Magnetic Field (IMF) direction. The crucial ingredient is provided by an accurate simulation of the asymptotic exposition of the PAMELA apparatus, based on a realistic reconstruction of particle trajectories in the Earth's magnetosphere. As case study, the results for the May 17, 2012 event are presented.Comment: Conference: The 34th International Cosmic Ray Conference (ICRC2015), 30 July - 6 August, 2015, The Hague, The Netherlands, Volume: PoS(ICRC2015)08

Mid-infrared plasmons in scaled graphene nanostructures

Plasmonics takes advantage of the collective response of electrons to electromagnetic waves, enabling dramatic scaling of optical devices beyond the diffraction limit. Here, we demonstrate the mid-infrared (4 to 15 microns) plasmons in deeply scaled graphene nanostructures down to 50 nm, more than 100 times smaller than the on-resonance light wavelength in free space. We reveal, for the first time, the crucial damping channels of graphene plasmons via its intrinsic optical phonons and scattering from the edges. A plasmon lifetime of 20 femto-seconds and smaller is observed, when damping through the emission of an optical phonon is allowed. Furthermore, the surface polar phonons in SiO2 substrate underneath the graphene nanostructures lead to a significantly modified plasmon dispersion and damping, in contrast to a non-polar diamond-like-carbon (DLC) substrate. Much reduced damping is realized when the plasmon resonance frequencies are close to the polar phonon frequencies. Our study paves the way for applications of graphene in plasmonic waveguides, modulators and detectors in an unprecedentedly broad wavelength range from sub-terahertz to mid-infrared.Comment: submitte

The Polarised Valence Quark Distribution from semi-inclusive DIS

The semi-inclusive difference asymmetry A^{h^{+}-h^{-}} for hadrons of opposite charge has been measured by the COMPASS experiment at CERN. The data were collected in the years 2002-2004 using a 160 GeV polarised muon beam scattered off a large polarised ^6LiD target and cover the range 0.006 < x < 0.7 and 1 < Q^2 < 100 (GeV/c)^2. In leading order QCD (LO) the asymmetry A_d^{h^{+}-h^{-}} measures the valence quark polarisation and provides an evaluation of the first moment of Delta u_v + Delta d_v which is found to be equal to 0.40 +- 0.07 (stat.) +- 0.05 (syst.) over the measured range of x at Q^2 = 10 (GeV/c)^2. When combined with the first moment of g_1^d previously measured on the same data, this result favours a non-symmetric polarisation of light quarks Delta u-bar = - Delta d-bar at a confidence level of two standard deviations, in contrast to the often assumed symmetric scenario Delta u-bar = Delta d-bar = Delta s-bar = Delta s.Comment: 7 pages, 3 figures, COMPASS, revised: details added, author list update

Multiplicities of charged pions and unidentified charged hadrons from deep-inelastic scattering of muons off an isoscalar target

Multiplicities of charged pions and unidentified hadrons produced in deep-inelastic scattering were measured in bins of the Bjorken scaling variable $x$, the relative virtual-photon energy $y$ and the relative hadron energy $z$. Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam and an isoscalar target ($^6$LiD). They cover the kinematic domain in the photon virtuality $Q^2$ > 1(GeV/c$)^2$, $0.004 < x < 0.4$, $0.2 < z < 0.85$ and $0.1 < y < 0.7$. In addition, a leading-order pQCD analysis was performed using the pion multiplicity results to extract quark fragmentation functions