491 research outputs found
The first order convergence law fails for random perfect graphs
We consider first order expressible properties of random perfect graphs. That
is, we pick a graph uniformly at random from all (labelled) perfect
graphs on vertices and consider the probability that it satisfies some
graph property that can be expressed in the first order language of graphs. We
show that there exists such a first order expressible property for which the
probability that satisfies it does not converge as .Comment: 11 pages. Minor corrections since last versio
Mapping of 2+1-dimensional Kardar-Parisi-Zhang growth onto a driven lattice gas model of dimer
We show that a 2+1 dimensional discrete surface growth model exhibiting
Kardar-Parisi-Zhang (KPZ) class scaling can be mapped onto a two dimensional
conserved lattice gas model of directed dimers. In case of KPZ height
anisotropy the dimers follow driven diffusive motion. We confirm by numerical
simulations that the scaling exponents of the dimer model are in agreement with
those of the 2+1 dimensional KPZ class. This opens up the possibility of
analyzing growth models via reaction-diffusion models, which allow much more
efficient computer simulations.Comment: 5 pages, 4 figures, final form to appear in PR
19th century real analysis, forward and backward
19th century real analysis received a major impetus from Cauchy's work.
Cauchy mentions variable quantities, limits, and infinitesimals, but the
meaning he attached to these terms is not identical to their modern meaning.
Some Cauchy historians work in a conceptual scheme dominated by an assumption
of a teleological nature of the evolution of real analysis toward a preordained
outcome. Thus, Gilain and Siegmund-Schultze assume that references to limite in
Cauchy's work necessarily imply that Cauchy was working with an Archi-medean
continuum, whereas infinitesimals were merely a convenient figure of speech,
for which Cauchy had in mind a complete justification in terms of Archimedean
limits. However, there is another formalisation of Cauchy's procedures
exploiting his limite, more consistent with Cauchy's ubiquitous use of
infinitesimals, in terms of the standard part principle of modern infinitesimal
analysis.
We challenge a misconception according to which Cauchy was allegedly forced
to teach infinitesimals at the Ecole Polytechnique. We show that the debate
there concerned mainly the issue of rigor, a separate one from infinitesimals.
A critique of Cauchy's approach by his contemporary de Prony sheds light on the
meaning of rigor to Cauchy and his contemporaries. An attentive reading of
Cauchy's work challenges received views on Cauchy's role in the history of
analysis, and indicates that he was a pioneer of infinitesimal techniques as
much as a harbinger of the Epsilontik.Comment: 28 pages, to appear in Antiquitates Mathematica
Detecting Candida albicans in Human Milk
Procedures for diagnosis of mammary candidosis, including laboratory confirmation, are not well defined. Lactoferrin present in human milk can inhibit growth of Candida albicans, thereby limiting the ability to detect yeast infections. The inhibitory effect of various lactoferrin concentrations on the growth of C. albicans in whole human milk was studied. The addition of iron to the milk led to a two- to threefold increase in cell counts when milk contained 3.0 mg of lactoferrin/ml and markedly reduced the likelihood of false-negative culture results. This method may provide the necessary objective support needed for diagnosis of mammary candidosis
Dispersive estimates for Schr\"odinger operators with point interactions in
The study of dispersive properties of Schr\"odinger operators with point
interactions is a fundamental tool for understanding the behavior of many body
quantum systems interacting with very short range potential, whose dynamics can
be approximated by non linear Schr\"odinger equations with singular
interactions. In this work we proved that, in the case of one point interaction
in , the perturbed Laplacian satisfies the same
estimates of the free Laplacian in the smaller regime . These
estimates are implied by a recent result concerning the boundedness of
the wave operators for the perturbed Laplacian. Our approach, however, is more
direct and relatively simple, and could potentially be useful to prove optimal
weighted estimates also in the regime .Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and
Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM
series 201
Ordering intermetallic alloys by ion irradiation: a way to tailor magnetic media
Combining He ion irradiation and thermal mobility below 600K, we both trigger
and control the transformation from chemical disorder to order in thin films of
an intermetallic ferromagnet (FePd). Kinetic Monte Carlo simulations show how
the initial directional short range order determines order propagation.
Magnetic ordering perpendicular to the film plane was achieved, promoting the
initially weak magnetic anisotropy to the highest values known for FePd films.
This post-growth treatment should find applications in ultrahigh density
magnetic recording.Comment: 7 pages, 3 Figure
Comparison of Different Parallel Implementations of the 2+1-Dimensional KPZ Model and the 3-Dimensional KMC Model
We show that efficient simulations of the Kardar-Parisi-Zhang interface
growth in 2 + 1 dimensions and of the 3-dimensional Kinetic Monte Carlo of
thermally activated diffusion can be realized both on GPUs and modern CPUs. In
this article we present results of different implementations on GPUs using CUDA
and OpenCL and also on CPUs using OpenCL and MPI. We investigate the runtime
and scaling behavior on different architectures to find optimal solutions for
solving current simulation problems in the field of statistical physics and
materials science.Comment: 14 pages, 8 figures, to be published in a forthcoming EPJST special
issue on "Computer simulations on GPU
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