394 research outputs found
Heegaard genus, cut number, weak p-congruence, and quantum invariants
We use quantum invariants to define a 3-manifold invariant j_p which lies in
the non-negative integers. We relate j_p to the Heegard genus, and the cut
number. We show that j_$ is an invariant of weak p-congruence.Comment: to appear in JKTR. 8pages 1 figur
Monte Carlo with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics
A class of Monte Carlo algorithms which incorporate absorbing Markov chains
is presented. In a particular limit, the lowest-order of these algorithms
reduces to the -fold way algorithm. These algorithms are applied to study
the escape from the metastable state in the two-dimensional square-lattice
nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the
agreement with theoretical predictions is very good. It is demonstrated that
the higher-order algorithms can be many orders of magnitude faster than either
the traditional Monte Carlo or -fold way algorithms.Comment: ReVTeX, Request 3 figures from [email protected]
Unconventional MBE Strategies from Computer Simulations for Optimized Growth Conditions
We investigate the influence of step edge diffusion (SED) and desorption on
Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the
solid-on-solid (SOS) model. Based on these investigations we propose two
strategies to optimize MBE growth. The strategies are applicable in different
growth regimes: During layer-by-layer growth one can exploit the presence of
desorption in order to achieve smooth surfaces. By additional short high flux
pulses of particles one can increase the growth rate and assist layer-by-layer
growth. If, however, mounds are formed (non-layer-by-layer growth) the SED can
be used to control size and shape of the three-dimensional structures. By
controlled reduction of the flux with time we achieve a fast coarsening
together with smooth step edges.Comment: 19 pages, 7 figures, submitted to Phys. Rev.
A Variable-Number Genetic Algorithm for Growth of 1-Dimensional Nanostructures into Their Global Minimum Configuration Under Radial Confinement
New distinguished classes of spectral spaces: a survey
In the present survey paper, we present several new classes of Hochster's
spectral spaces "occurring in nature", actually in multiplicative ideal theory,
and not linked to or realized in an explicit way by prime spectra of rings. The
general setting is the space of the semistar operations (of finite type),
endowed with a Zariski-like topology, which turns out to be a natural
topological extension of the space of the overrings of an integral domain,
endowed with a topology introduced by Zariski. One of the key tool is a recent
characterization of spectral spaces, based on the ultrafilter topology, given
in a paper by C. Finocchiaro in Comm. Algebra 2014. Several applications are
also discussed
Primary decomposition and the fractal nature of knot concordance
For each sequence of polynomials, P=(p_1(t),p_2(t),...), we define a
characteristic series of groups, called the derived series localized at P.
Given a knot K in S^3, such a sequence of polynomials arises naturally as the
orders of certain submodules of the sequence of higher-order Alexander modules
of K. These group series yield new filtrations of the knot concordance group
that refine the (n)-solvable filtration of Cochran-Orr-Teichner. We show that
the quotients of successive terms of these refined filtrations have infinite
rank. These results also suggest higher-order analogues of the p(t)-primary
decomposition of the algebraic concordance group. We use these techniques to
give evidence that the set of smooth concordance classes of knots is a fractal
set. We also show that no Cochran-Orr-Teichner knot is concordant to any
Cochran-Harvey-Leidy knot.Comment: 60 pages, added 4 pages to introduction, minor corrections otherwise;
Math. Annalen 201
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