5,325 research outputs found

    The B36/S125 "2x2" Life-Like Cellular Automaton

    Full text link
    The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution and the existence of a natural diagonal glider, the individual objects that the rule contains generally look very different from their Life counterparts. In this article, a history of notable discoveries in the 2x2 rule is provided, and the fundamental patterns of the automaton are described. Some theoretical results are derived along the way, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular automaton that 2x2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 x 2 blocks are analyzed and used to show that there exist oscillators with period 2^m(2^k - 1) for any integers m,k \geq 1.Comment: 18 pages, 19 figure

    Finite temperature properties of the two-dimensional SU(2) Kondo-necklace

    Full text link
    We analyse several thermodynamic properties of the two-dimensional Kondo necklace using finite-temperature stochastic series expansion. In agreement with previous zero-temperature findings the model is shown to exhibit a quantum critical point (QCP), separating an antiferromagnetic from a paramagnetic dimerized state at a critical Kondo exchange-coupling strength Jc1.4J_{c}\approx 1.4. We evaluate the temperature dependent uniform and staggered structure factors as well as the uniform and staggered susceptibilities and the local 'impurity' susceptibility close to the QCP as well as in the ordered and quantum disordered phase. The crossover between the classical, renormalized classical, and quantum critical regime is analyzed as a function of temperature and Kondo coupling.Comment: 4.2 pages, 6 figure

    On computational irreducibility and the predictability of complex physical systems

    Full text link
    Using elementary cellular automata (CA) as an example, we show how to coarse-grain CA in all classes of Wolfram's classification. We find that computationally irreducible (CIR) physical processes can be predictable and even computationally reducible at a coarse-grained level of description. The resulting coarse-grained CA which we construct emulate the large-scale behavior of the original systems without accounting for small-scale details. At least one of the CA that can be coarse-grained is irreducible and known to be a universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR

    The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing

    Full text link
    The probability density function (PDF) of the gas density in turbulent supersonic flows is investigated with high-resolution numerical simulations. In a systematic study, we compare the density statistics of compressible turbulence driven by the usually adopted solenoidal forcing (divergence-free) and by compressive forcing (curl-free). Our results are in agreement with studies using solenoidal forcing. However, compressive forcing yields a significantly broader density distribution with standard deviation ~3 times larger at the same rms Mach number. The standard deviation-Mach number relation used in analytical models of star formation is reviewed and a modification of the existing expression is proposed, which takes into account the ratio of solenoidal and compressive modes of the turbulence forcing.Comment: 5 pages, 3 figures, accepted to ApJL, simulation movies available at http://www.ita.uni-heidelberg.de/~chfeder/videos.shtml?lang=e

    Max-plus analysis on some binary particle systems

    Full text link
    We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.Comment: 24 pages, 5 figures, submitted to J. Phys.

    Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks

    Full text link
    We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show a significantly larger density contrast, a more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments on large scales, we derive a model that describes this behaviour.Comment: 24 pages, 13 figures, Journal of Fluid Mechanics in pres

    Testing the Peculiar Velocity Field predicted from Redshift Surveys

    Full text link
    The reconstruction of the peculiar velocity field from the 1.936~Jy iras selected sample of galaxies is compared to a similar reconstruction from an optically selected sample. A general method for combining different samples to reconstruct a self-consistent density and peculiar velocity field is presented. The method is applied to determine how sensitive the derived peculiar velocity field is to the characteristics of the sample used. The possibility that the iras galaxies do not trace the general galaxy population is explored adopting a simple model of linear biasing between the iras and optical samples. We find that the velocity fields derived from the two samples are consistent, within the estimated shot noise error, for the case of no relative bias. This result suggests that the predicted peculiar velocity field based on iras samples is not sensitive to the sampling properties of iras galaxies. Combined with previous suggestion of a relative biasing of iras galaxies on small scales (about 5 h^-1Mpc), this result suggests scale dependent biasing.Comment: tar-compressed and uudecoded postscript files, 12 pages+8 figure

    A Mathematica Package for Computing N=2 Superfield Operator Product Expansions

    Full text link
    We describe a general purpose Mathematica package for computing Superfield Operator Product Expansions in meromorphic N=2N=2 superconformal field theory. Given the SOPEs for a set of ``basic" superfields, SOPEs of arbitrarily complicated composites can be computed automatically. Normal ordered products are always reduced to a standard form. It is possible to check the Jacobi identities, and to compute Poisson brackets (``classical SOPEs''). We present two explicit examples: a construction of the ``small'' N=4N=4 superconformal algebra in terms of N=2N=2 superfields, and a realisation of the N=2N=2 superconformal algebra in terms of chiral and antichiral fermionic superfields.Comment: 15 pages, LaTeX. Minor corrections, particularly to Mathematica output Out[6],Out[9] in section 4. Available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers

    Audible Axions

    Full text link
    Conventional approaches to probing axions and axion-like particles (ALPs) typically rely on a coupling to photons. However, if this coupling is extremely weak, ALPs become invisible and are effectively decoupled from the Standard Model. Here we show that such invisible axions, which are viable candidates for dark matter, can produce a stochastic gravitational wave background in the early universe. This signal is generated in models where the invisible axion couples to a dark gauge boson that experiences a tachyonic instability when the axion begins to oscillate. Incidentally, the same mechanism also widens the viable parameter space for axion dark matter. Quantum fluctuations amplified by the exponentially growing gauge boson modes source chiral gravitational waves. For axion decay constants f1017f \gtrsim 10^{17} GeV, this signal is detectable by either pulsar timing arrays or space/ground-based gravitational wave detectors for a broad range of axion masses, thus providing a new window to probe invisible axion models.Comment: 8 pages, 4 figures. References added, version submitted to JHE
    corecore