33,300 research outputs found
The angular momentum transport by standard MRI in quasi-Kepler cylindric Taylor-Couette flows
The instability of a quasi-Kepler flow in dissipative Taylor-Couette systems
under the presence of an homogeneous axial magnetic field is considered with
focus to the excitation of nonaxisymmetric modes and the resulting angular
momentum transport. The excitation of nonaxisymmetric modes requires higher
rotation rates than the excitation of the axisymmetric mode and this the more
the higher the azimuthal mode number m. We find that the weak-field branch in
the instability map of the nonaxisymmetric modes has always a positive slope
(in opposition to the axisymmetric modes) so that for given magnetic field the
modes with m>0 always have an upper limit of the supercritical Reynolds number.
In order to excite a nonaxisymmetric mode at 1 AU in a Kepler disk a minimum
field strength of about 1 Gauss is necessary. For weaker magnetic field the
nonaxisymmetric modes decay. The angular momentum transport of the
nonaxisymmetric modes is always positive and depends linearly on the Lundquist
number of the background field. The molecular viscosity and the basic rotation
rate do not influence the related {\alpha}-parameter. We did not find any
indication that the MRI decays for small magnetic Prandtl number as found by
use of shearing-box codes. At 1 AU in a Kepler disk and a field strength of
about 1 Gauss the {\alpha} proves to be (only) of order 0.005
On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers
We present an efficient quantum algorithm for the exact evaluation of either
the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function
Z for a family of graphs related to irreducible cyclic codes. This problem is
related to the evaluation of the Jones and Tutte polynomials. We consider the
connection between the weight enumerator polynomial from coding theory and Z
and exploit the fact that there exists a quantum algorithm for efficiently
estimating Gauss sums in order to obtain the weight enumerator for a certain
class of linear codes. In this way we demonstrate that for a certain class of
sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon)
graphs, quantum computers provide a polynomial speed up in the difference
between the number of edges and vertices of the graph, and an exponential speed
up in q, over the best classical algorithms known to date
Symbolic computation with finite biquandles
A method of computing a basis for the second Yang-Baxter cohomology of a
finite biquandle with coefficients in Q and Z_p from a matrix presentation of
the finite biquandle is described. We also describe a method for computing the
Yang-Baxter cocycle invariants of an oriented knot or link represented as a
signed Gauss code. We provide a URL for our Maple implementations of these
algorithms.Comment: 8 pages. Version 2 has typo corrections and changes suggested by
referee. To appear in J. Symbolic Compu
Discriminated Belief Propagation
Near optimal decoding of good error control codes is generally a difficult
task. However, for a certain type of (sufficiently) good codes an efficient
decoding algorithm with near optimal performance exists. These codes are
defined via a combination of constituent codes with low complexity trellis
representations. Their decoding algorithm is an instance of (loopy) belief
propagation and is based on an iterative transfer of constituent beliefs. The
beliefs are thereby given by the symbol probabilities computed in the
constituent trellises. Even though weak constituent codes are employed close to
optimal performance is obtained, i.e., the encoder/decoder pair (almost)
achieves the information theoretic capacity. However, (loopy) belief
propagation only performs well for a rather specific set of codes, which limits
its applicability.
In this paper a generalisation of iterative decoding is presented. It is
proposed to transfer more values than just the constituent beliefs. This is
achieved by the transfer of beliefs obtained by independently investigating
parts of the code space. This leads to the concept of discriminators, which are
used to improve the decoder resolution within certain areas and defines
discriminated symbol beliefs. It is shown that these beliefs approximate the
overall symbol probabilities. This leads to an iteration rule that (below
channel capacity) typically only admits the solution of the overall decoding
problem. Via a Gauss approximation a low complexity version of this algorithm
is derived. Moreover, the approach may then be applied to a wide range of
channel maps without significant complexity increase
Discrete Distributions in the Tardos Scheme, Revisited
The Tardos scheme is a well-known traitor tracing scheme to protect
copyrighted content against collusion attacks. The original scheme contained
some suboptimal design choices, such as the score function and the distribution
function used for generating the biases. Skoric et al. previously showed that a
symbol-symmetric score function leads to shorter codes, while Nuida et al.
obtained the optimal distribution functions for arbitrary coalition sizes.
Later, Nuida et al. showed that combining these results leads to even shorter
codes when the coalition size is small. We extend their analysis to the case of
large coalitions and prove that these optimal distributions converge to the
arcsine distribution, thus showing that the arcsine distribution is
asymptotically optimal in the symmetric Tardos scheme. We also present a new,
practical alternative to the discrete distributions of Nuida et al. and give a
comparison of the estimated lengths of the fingerprinting codes for each of
these distributions.Comment: 5 pages, 2 figure
Weight distributions of cyclic codes with respect to pairwise coprime order elements
Let be an extension of a finite field with . Let
each be of order in and for .
We define a cyclic code over by
where
and . In this paper,
we present a method to compute the weights of . Further, we determine the weight distributions of the cyclic codes
and .Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1306.527
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