5,325 research outputs found

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

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

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 $J_{c}\approx
1.4$. 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

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

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

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

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

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

We describe a general purpose Mathematica package for computing Superfield
Operator Product Expansions in meromorphic $N=2$ 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'' $N=4$ superconformal
algebra in terms of $N=2$ superfields, and a realisation of the $N=2$
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

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 $f \gtrsim 10^{17}$ 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

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