116 research outputs found
Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models
We demonstrate that the invaded cluster algorithm, recently introduced by
Machta et al, is a fast and reliable tool for determining the critical
temperature and the magnetic critical exponent of periodic and aperiodic
ferromagnetic Ising models in two dimensions. The algorithm is shown to
reproduce the known values of the critical temperature on various periodic and
quasiperiodic graphs with an accuracy of more than three significant digits. On
two quasiperiodic graphs which were not investigated in this respect before,
the twelvefold symmetric square-triangle tiling and the tenfold symmetric
T\"ubingen triangle tiling, we determine the critical temperature. Furthermore,
a generalization of the algorithm to non-identical coupling strengths is
presented and applied to a class of Ising models on the Labyrinth tiling. For
generic cases in which the heuristic Harris-Luck criterion predicts deviations
from the Onsager universality class, we find a magnetic critical exponent
different from the Onsager value. But also notable exceptions to the criterion
are found which consist not only of the exactly solvable cases, in agreement
with a recent exact result, but also of the self-dual ones and maybe more.Comment: 15 pages, 5 figures; v2: Fig. 5b replaced, minor change
Symmetries and reversing symmetries of toral automorphisms
Toral automorphisms, represented by unimodular integer matrices, are
investigated with respect to their symmetries and reversing symmetries. We
characterize the symmetry groups of GL(n,Z) matrices with simple spectrum
through their connection with unit groups in orders of algebraic number fields.
For the question of reversibility, we derive necessary conditions in terms of
the characteristic polynomial and the polynomial invariants. We also briefly
discuss extensions to (reversing) symmetries within affine transformations, to
PGL(n,Z) matrices, and to the more general setting of integer matrices beyond
the unimodular ones.Comment: 34 page
Compilation on Synthesis, Characterization and Properties of Silicon and Boron Carbonitride Films
During the last years the interest in silicon and boron carbonitrides developed remarkably. This interest is mainly based on the extraordinary properties, expected from theoretical considerations. In this time significant improvements were made in the synthesis of silicon
carbonitride SiCxNy and boron carbonitride BCxNy films by both physical and chemical methods.
In the Si–C–N and B-C-N ternary systems a set of phases is situated, namely diamond, SiC, -Si3N4, c-BN, B4C, and -C3N4, which have important practical applications. SiCxNy has drawn considerable interest due to its excellent new properties in comparison with the Si3N4 and SiC binary phases. The silicon carbonitride coatings are of importance because they can potentially be used in wear and corrosion protection, high-temperature oxidation resistance, as a good moisture barrier for high-temperature industrial as well as strategic applications. Their properties are low electrical conductivity, high hardness, a low friction coefficient, high photosensitivity in the UV region, and good field emission characteristics. All these characteristics have led to a rapid increase in research activities on the synthesis of SiCxNy compounds. In addition to these properties, low density and good thermal shock resistance are very important requirements for future aerospace and automobile parts applications to
enhance the performance of the components. SiCxNy is also an important material in micro- and nano-electronics and sensor technologies due to its excellent mechanical and electrical properties. The material possesses good optical transmittance properties. This is very useful for membrane applications, where the support of such films is required (Fainer et al., 2007, 2008; Mishra, 2009; Wrobel, et al., 2007, 2010; Kroke et al., 2000). The structural similarity between the allotropic forms of carbon and boron nitride
(hexagonal BN and graphite, cubic BN and diamond), and the fact that B-N pairs are isoelectronic to C-C pairs, was the basis for predictions of the existence of ternary BCxNy
compounds with notable properties (Samsonov et al., 1962; Liu et al., 1989; Lambrecht & Segall, 1993; Zhang et al., 2004). This prediction has stimulated intensive research in the last 40 years towards the synthesis of ternary boron carbonitride. BCxNy compounds are interesting in both the cubic (c-BCN) and hexagonal (h-BCN) structure. On the one hand, the ..
Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices
We study various aspects of the dynamics induced by integer matrices on the
invariant rational lattices of the torus in dimension 2 and greater. Firstly,
we investigate the orbit structure when the toral endomorphism is not
invertible on the lattice, characterising the pretails of eventually periodic
orbits. Next we study the nature of the symmetries and reversing symmetries of
toral automorphisms on a given lattice, which has particular relevance to
(quantum) cat maps.Comment: 29 pages, 3 figure
Mutation, selection, and ancestry in branching models: a variational approach
We consider the evolution of populations under the joint action of mutation
and differential reproduction, or selection. The population is modelled as a
finite-type Markov branching process in continuous time, and the associated
genealogical tree is viewed both in the forward and the backward direction of
time. The stationary type distribution of the reversed process, the so-called
ancestral distribution, turns out as a key for the study of mutation-selection
balance. This balance can be expressed in the form of a variational principle
that quantifies the respective roles of reproduction and mutation for any
possible type distribution. It shows that the mean growth rate of the
population results from a competition for a maximal long-term growth rate, as
given by the difference between the current mean reproduction rate, and an
asymptotic decay rate related to the mutation process; this tradeoff is won by
the ancestral distribution.
Our main application is the quasispecies model of sequence evolution with
mutation coupled to reproduction but independent across sites, and a fitness
function that is invariant under permutation of sites. Here, the variational
principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure
Coincidence isometries of a shifted square lattice
We consider the coincidence problem for the square lattice that is translated
by an arbitrary vector. General results are obtained about the set of
coincidence isometries and the coincidence site lattices of a shifted square
lattice by identifying the square lattice with the ring of Gaussian integers.
To illustrate them, we calculate the set of coincidence isometries, as well as
generating functions for the number of coincidence site lattices and
coincidence isometries, for specific examples.Comment: 10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool
Error Thresholds on Dynamic Fittness-Landscapes
In this paper we investigate error-thresholds on dynamics fitness-landscapes.
We show that there exists both lower and an upper threshold, representing
limits to the copying fidelity of simple replicators. The lower bound can be
expressed as a correction term to the error-threshold present on a static
landscape. The upper error-threshold is a new limit that only exists on dynamic
fitness-landscapes. We also show that for long genomes on highly dynamic
fitness-landscapes there exists a lower bound on the selection pressure needed
to enable effective selection of genomes with superior fitness independent of
mutation rates, i.e., there are distinct limits to the evolutionary parameters
in dynamic environments.Comment: 5 page
On rotational excitations and axial deformations of BPS monopoles and Julia-Zee dyons
It is shown that Julia-Zee dyons do not admit slowly rotating excitations.
This is achieved by investigating the complete set of stationary excitations
which can give rise to non-vanishing angular momentum. The relevant zero modes
are parametrized in a gauge invariant way and analyzed by means of a harmonic
decomposition. Since general arguments show that the solutions to the
linearized Bogomol'nyi equations cannot contribute to the angular momentum, the
relevant modes are governed by a set of electric and a set of non self-dual
magnetic perturbation equations. The absence of axial dipole deformations is
also established.Comment: 22 pages, Revtex, no figure
Critical domain walls in the Ashkin-Teller model
We study the fractal properties of interfaces in the 2d Ashkin-Teller model.
The fractal dimension of the symmetric interfaces is calculated along the
critical line of the model in the interval between the Ising and the
four-states Potts models. Using Schramm's formula for crossing probabilities we
show that such interfaces can not be related to the simple SLE, except
for the Ising point. The same calculation on non-symmetric interfaces is
performed at the four-states Potts model: the fractal dimension is compatible
with the result coming from Schramm's formula, and we expect a simple
SLE in this case.Comment: Final version published in JSTAT. 13 pages, 5 figures. Substantial
changes in the data production, analysis and in the conclusions. Added a
section about the crossing probability. Typeset with 'iopart
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