Nash equilibrium mapping vs Hamiltonian dynamics vs Darwinian evolution for some social dilemma games in the thermodynamic limit

How cooperation evolves and manifests itself in the thermodynamic or infinite player limit of social dilemma games is a matter of intense speculation. Various analytical methods have been proposed to analyse the thermodynamic limit of social dilemmas. In a previous work [Chaos Solitons and fractals 135, 109762(2020)] involving one among us, two of those methods, Hamiltonian Dynamics(HD) and Nash equilibrium(NE) mapping were compared. The inconsistency and incorrectness of HD approach vis-a-vis NE mapping was brought to light. In this work we compare a third analytical method, i.e, Darwinian evolution(DE) with NE mapping and a numerical agent based approach. For completeness, we give results for HD approach as well. In contrast to HD which involves maximisation of payoffs of all individuals, in DE, payoff of a single player is maximised with respect to its nearest neighbour. While, HD utterly fails as compared to NE mapping, DE method gives a false positive for game magnetisation -- the net difference between the fraction of cooperators and defectors -- when payoffs obey the condition a+d=b+c, wherein a, d represent the diagonal elements and b, c the off diagonal elements in symmetric social dilemma games. When either a+d =/= b+c or, when one looks at average payoff per player, DE method fails much like the HD approach. NE mapping and numerical agent based method on the other hand agree really well for both game magnetisation as well as average payoff per player for the social dilemmas in question, i.e., Hawk-Dove game and Public goods game. This paper thus bring to light the inconsistency of the DE method vis-a-vis both NE mapping as well as a numerical agent based approach.Comment: 15 pages, 4 figures, 2 table

Black Hole Lightning from the Peculiar Gamma-Ray Loud Active Galactic Nucleus IC 310

The nearby active galaxy IC 310, located in the outskirts of the Perseus cluster of galaxies is a bright and variable multi-wavelength emitter from the radio regime up to very high gamma-ray energies above 100 GeV. Originally, the nucleus of IC 310 has been classified as a radio galaxy. However, studies of the multi-wavelength emission showed several properties similarly to those found from blazars as well as radio galaxies. In late 2012, we have organized the first contemporaneous multi-wavelength campaign including radio, optical, X-ray and gamma-ray instruments. During this campaign an exceptionally bright flare of IC 310 was detected with the MAGIC telescopes in November 2012 reaching an averaged flux level in the night of up to one Crab above 1 TeV with a hard spectrum over two decades in energy. The intra-night light curve showed a series of strong outbursts with flux-doubling time scales as fast as a few minutes. The fast variability constrains the size of the gamma-ray emission regime to be smaller than 20% of the gravitational radius of its central black hole. This challenges the shock acceleration models, commonly used to explain gamma-ray radiation from active galaxies. Here, we will present more details on the MAGIC data and discuss several possible alternative emission models.Comment: 8 pages, 5 figures, Proceedings of the 34th International Cosmic Ray Conference, 30 July - 6 August, 2015, The Hague, The Netherland

Insights into the particle acceleration of a peculiar gamma -ray radio galaxy IC 310

IC 310 has recently been identified as a gamma-ray emitter based on observations at GeV energies with Fermi-LAT and at very high energies (VHE, E > 100 GeV) with the MAGIC telescopes. Despite IC 310 having been classified as a radio galaxy with the jet observed at an angle > 10 degrees, it exhibits a mixture of multiwavelength properties of a radio galaxy and a blazar, possibly making it a transitional object. On the night of 12/13th of November 2012 the MAGIC telescopes observed a series of violent outbursts from the direction of IC 310 with flux-doubling time scales faster than 5 min and a peculiar spectrum spreading over 2 orders of magnitude. Such fast variability constrains the size of the emission region to be smaller than 20% of the gravitational radius of its central black hole, challenging the shock acceleration models, commonly used in explanation of gamma-ray radiation from active galaxies. Here we will show that this emission can be associated with pulsar-like particle acceleration by the electric field across a magnetospheric gap at the base of the jet.Comment: 2014 Fermi Symposium proceedings - eConf C14102.

Families of spherical caps: spectra and ray limit

We consider a family of surfaces of revolution ranging between a disc and a hemisphere, that is spherical caps. For this family, we study the spectral density in the ray limit and arrive at a trace formula with geodesic polygons describing the spectral fluctuations. When the caps approach the hemisphere the spectrum becomes equally spaced and highly degenerate whereas the derived trace formula breaks down. We discuss its divergence and also derive a different trace formula for this hemispherical case. We next turn to perturbative corrections in the wave number where the work in the literature is done for either flat domains or curved without boundaries. In the present case, we calculate the leading correction explicitly and incorporate it into the semiclassical expression for the fluctuating part of the spectral density. To the best of our knowledge, this is the first calculation of such perturbative corrections in the case of curvature and boundary.Comment: 28 pages, 7 figure

A portable neutron spectroscope (NSPECT) for detection, imaging and identification of nuclear material

We have developed, fabricated and tested a prototype imaging neutron spectrometer designed for real-time neutron source location and identification. Real-time detection and identification is important for locating materials. These materials, specifically uranium and transuranics, emit neutrons via spontaneous or induced fission. Unlike other forms of radiation (e.g. gamma rays), penetrating neutron emission is very uncommon. The instrument detects these neutrons, constructs images of the emission pattern, and reports the neutron spectrum. The device will be useful for security and proliferation deterrence, as well as for nuclear waste characterization and monitoring. The instrument is optimized for imaging and spectroscopy in the 1-20 MeV range. The detection principle is based upon multiple elastic neutron-proton scatters in organic scintillator. Two detector panel layers are utilized. By measuring the recoil proton and scattered neutron locations and energies, the direction and energy spectrum of the incident neutrons can be determined and discrete and extended sources identified. Event reconstruction yields an image of the source and its location. The hardware is low power, low mass, and rugged. Its modular design allows the user to combine multiple units for increased sensitivity. We will report the results of laboratory testing of the instrument, including exposure to a calibrated Cf-252 source. Instrument parameters include energy and angular resolution, gamma rejection, minimum source identification distances and times, and projected effective area for a fully populated instrument

Bells as memorials in South Africa to the Great (1914-18) War

The contribution of South Africa to the allied cause in the Great War, and the sacrifice of so many lives of the White and Coloured populations, is memorialised on bells of the Cape Town carillon, on ringing, and on clock and other bells. The contribution of the Black population awaits recognition. Restoration of the Cape Town carillon so that it can again be played effectively, would be a fitting memorial to those who lost their lives in the non-combative roles that were open to the majority population of South Africa. Completion of the ring at what is now Queenstown cathedral would also be a fitting tribute to the bravery and unstinting service of so many South Africans during the Great War.Colin Lewis was Professor of Geography at Rhodes University, Grahamstown, South Africa from 1989 until his retirement at the end of 2007. In 1990, with the strong support of the incumbent Vice-Chancellor, Dr Derek Henderson, he instigated the Certificate in Change Ringing (Church Bell Ringing) in the Rhodes University Department of Music and Musicology - the first such course to be offered in Africa. Since that date he has lectured in the basic theory, and taught the practice of change ringing. He is the Ringing Master of the Cathedral of St Michael and St George, Grahamstown, South Africa

The Beagle 2 microscope

The Beagle 2 microscope provides optical images of the Martian surface at a resolution 5x higher than any other experiment currently planned. By using a novel illumination system it images in three colors and can also detect fluorescent materials