Re-Pair Compression of Inverted Lists

Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers. In this paper we explore a completely different alternative: We use Re-Pair compression of those differences. While Re-Pair by itself offers fast decompression at arbitrary positions in main and secondary memory, we introduce variants that in addition speed up the operations required for inverted list intersection. We compare the resulting data structures with several recent proposals under various list intersection algorithms, to conclude that our Re-Pair variants offer an interesting time/space tradeoff for this problem, yet further improvements are required for it to improve upon the state of the art

Contribution of One-Time Pair Correlation Function to Kinetic Phenomena in Nonequilibrium Gas

It has been established in nineteen seventies that in nonequilibrium case the pair collisions generate non-zero two-particle correlations which are non-diagonal in momentum space and give the essential contribution to the current fluctuations of hot electrons. It is shown here that this correlations give also a contribution to the collision integral, i.e., to kinetic properties of nonequilibrium gas. The expression for electron energy loss rate P via phonons is re-derived in detail from this point of view. The contribution of the non-diagonal part of the nonequilibrium pair correlator to phonon-electron collision integral and to P is obtained and explicitly calculated in the electron temperature approximation. It is shown that these results can be obtained from stochastic non-linear kinetic equation with Langevin fluctuation force. Such an approach allows to formulate the simple general conditions under that a contribution of two-particle correlations might be essential in kinetics. The contribution obtained does not contain the extra powers of small gas parameter unlike the equilibrium virial decompositions.Comment: 6 pages, based on the report presented at the conference ``Progress in Nonequilibrium Green's Functions'', Dresden, Germany, 19.-22. August 200

Radiation Reaction Kinetics and Collective QED Signatures

Observing collective effects originating from the interplay between quantum electrodynamics and plasma physics might be achieved in upcoming experiments. In particular, the generation of electron-positron pairs and the observation of their collective dynamics could be simultaneously achieved in a collision between an intense laser and a highly relativistic electron beam through a laser frequency shift driven by an increase in the plasma density increase. In this collision, the radiation of high energy photons will serve a dual purpose: first, in seeding the cascade of pair generation; and, second, in decelerating the created pairs for detection. The deceleration results in a detectable shift in the plasma frequency. This deceleration was previously studied considering only a small sample of individual pair particles. However, the highly stochastic nature of the quantum radiation reaction in the strong field regime limits the descriptive power of the average behavior to the dynamics of pair particles. Here, we examine the full kinetic evolution of generated pairs in order to more accurately model the relativistically adjusted plasma density. As we show, the most effective pair energy for creating observable signatures occurs at a local minimum, obtained at finite laser field strength due to the tradeoff between pair deceleration and the relativistic particle oscillation at increasing laser intensity. For a small number of laser cycles, the quantum radiation reaction may re-arrange the generated pairs into anisotropic distributions in momentum space, although, in the one dimensional simulations considered here, this anisotropy quickly decreases

Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders

Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as $Re$ is increased from weakly chaotic flow at $Re=40$ to a chaotic state dominated by a domain-filling vortex pair at $Re=400$. The highly accurate embeddings allow us to visualise the evolving structure of state space and are interpretable using `latent Fourier analysis' (Page {\em et. al.}, \emph{Phys. Rev. Fluids} \textbf{6}, 2021). Individual latent Fourier modes decode into vortical structures with a streamwise lengthscale controlled by the latent wavenumber, $l$, with only a small number $l \lesssim 8$ required to accurately represent the flow. Latent Fourier projections reveal a detached class of bursting events at $Re=40$ which merge with the low-dissipation dynamics as $Re$ is increased to $100$. We use doubly- ($l=2$) or triply- ($l=3$) periodic latent Fourier modes to generate guesses for UPOs (unstable periodic orbits) associated with high-dissipation events. While the doubly-periodic UPOs are representative of the high-dissipation dynamics at $Re=40$, the same class of UPOs move away from the attractor at $Re=100$ -- where the associated bursting events typically involve larger-scale ($l=1$) structure too. At $Re=400$ an entirely different embedding structure is formed within the network in which no distinct representations of small-scale vortices are observed; instead the network embeds all snapshots based around a large-scale template for the condensate. We use latent Fourier projections to find an associated `large-scale' UPO which we believe to be a finite-$Re$ continuation of a solution to the Euler equations

A Magnetically-Switched, Rotating Black Hole Model For the Production of Extragalactic Radio Jets and the Fanaroff and Riley Class Division

A model is presented in which both Fanaroff and Riley class I and II extragalactic jets are produced by magnetized accretion disk coronae in the ergospheres of rotating black holes. While the jets are produced in the accretion disk itself, the output power still is an increasing function of the black hole angular momentum. For high enough spin, the black hole triggers the magnetic switch, producing highly-relativistic, kinetic-energy-dominated jets instead of Poynting-flux-dominated ones for lower spin. The coronal mass densities needed to trigger the switch at the observed FR break power are quite small ($\sim 10^{-15} g cm^{-3}$), implying that the source of the jet material may be either a pair plasma or very tenuous electron-proton corona, not the main accretion disk itself. The model explains the differences in morphology and Mach number between FR I and II sources and the observed trend for massive galaxies to undergo the FR I/II transition at higher radio power. It also is consistent with the energy content of extended radio lobes and explains why, because of black hole spindown, the space density of FR II sources should evolve more rapidly than that of FR I sources. If the present model is correct, then the ensemble average speed of parsec-scale jets in sources distinguished by their FR I morphology (not luminosity) should be distinctly slower than that for sources with FR II morphology. The model also suggests the existence of a population of high-redshift, sub-mJy FR I and II radio sources associated with spiral or pre-spiral galaxies that flared once when their black holes were formed but were never again re-kindled by mergers.Comment: 14 pages, 2 figures, final version to appear in Sept Ap

Common vacuum conservation amplitude in the theory of the radiation of mirrors in two-dimensional space-time and of charges in four-dimensional space-time

The action changes (and thus the vacuum conservation amplitudes) in the proper-time representation are found for an accelerated mirror interacting with scalar and spinor vacuum fields in 1+1 space. They are shown to coincide to within the multiplier e^2 with the action changes of electric and scalar charges accelerated in 3+1 space. This coincidence is attributed to the fact that the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0 as do the photons and scalar quanta emitted by charges. It is shown that the propagation of virtual pairs in 1+1 space can be described by the causal Green's function \Delta_f(z,\mu) of the wave equation for 3+1 space. This is because the pairs can have any positive mass and their propagation function is represented by an integral of the causal propagation function of a massive particle in 1+1 space over mass which coincides with \Delta_f(z,\mu). In this integral the lower limit \mu is chosen small, but nonzero, to eliminate the infrared divergence. It is shown that the real and imaginary parts of the action change are related by dispersion relations, in which a mass parameter serves as the dispersion variable. They are a consequence of the same relations for \Delta_f(z,\mu). Therefore, the appearance of the real part of the action change is a direct consequence of the causality, according to which real part of \Delta_f(z,\mu) is nonzero only for timelike and zero intervals.Comment: 23 pages, Latex, revte