4,283 research outputs found
Higher ramification and varieties of secant divisors on the generic curve
For a smooth projective curve, the cycles of e-secant k-planes are among the
most studied objects in classical enumerative geometry and there are well-known
formulas due to Castelnuovo, Cayley and MacDonald concerning them. Despite
various attempts, surprisingly little is known about the enumerative validity
of such formulas. The aim of this paper is to completely clarify this problem
in the case of the generic curve C of given genus. Using degeneration
techniques and a few facts about the birational geometry of moduli spaces of
stable pointed curves we determine precisely under which conditions the cycle
of e-secant k-planes in non-empty and we compute its dimension. We also
precisely determine the dimension of the variety of linear series on C carrying
e-secant k-planes. In a different direction, in the last part of the paper we
study the distribution of ramification points of the powers of a line bundle on
C having prescribed ramification at a given point.Comment: 25 pages. Numerous changes suggested by the referee, several proofs
explained in more detail. To appear in the Journal of the London Mathematical
Societ
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
We formulate, and in some cases prove, three statements concerning the purity
or, more generally the naturality of the resolution of various rings one can
attach to a generic curve of genus g and a torsion point of order l in its
Jacobian. These statements can be viewed an analogues of Green's Conjecture and
we verify them computationally for bounded genus. We then compute the
cohomology class of the corresponding non-vanishing locus in the moduli space
R_{g,l} of twisted level l curves of genus g and use this to derive results
about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3}
is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is
greater than or equal to 19. In the last section we explain probabilistically
the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the
statement of Prop 2.
Magnetic field control of cycloidal domains and electric polarization in multiferroic BiFeO
The magnetic field induced rearrangement of the cycloidal spin structure in
ferroelectric mono-domain single crystals of the room-temperature multiferroic
BiFeO is studied using small-angle neutron scattering (SANS). The cycloid
propagation vectors are observed to rotate when magnetic fields applied
perpendicular to the rhombohedral (polar) axis exceed a pinning threshold value
of 5\,T. In light of these experimental results, a phenomenological model
is proposed that captures the rearrangement of the cycloidal domains, and we
revisit the microscopic origin of the magnetoelectric effect. A new coupling
between the magnetic anisotropy and the polarization is proposed that explains
the recently discovered magnetoelectric polarization to the rhombohedral axis
Frictional coupling between sliding and spinning motion
We show that the friction force and torque, acting at a dry contact of two
objects moving and rotating relative to each other, are inherently coupled. As
a simple test system, a sliding and spinning disk on a horizontal flat surface
is considered. We calculate, and also measure, how the disk is slowing down,
and find that it always stops its sliding and spinning motion at the same
moment. We discuss the impact of this coupling between friction force and
torque on the physics of granular materials.Comment: 4 pages, 5 figures; submitte
Systematically extending classical nucleation theory
The foundation for any discussion of first-order phse transitions is
Classical Nucleation Theory(CNT). CNT, developed in the first half of the
twentieth century, is based on a number of heuristically plausible assumtptions
and the majority of theoretical work on nucleation is devoted to refining or
extending these ideas. Ideally, one would like to derive CNT from a more
fundamental description of nucleation so that its extension, development and
refinement could be developed systematically. In this paper, such a development
is described based on a previously established (Lutsko, JCP 136:034509, 2012 )
connection between Classical Nucleation Theory and fluctuating hydrodynamics.
Here, this connection is described without the need for artificial assumtions
such as spherical symmetry. The results are illustrated by application to CNT
with moving clusters (a long-standing problem in the literature) and the
constructrion of CNT for ellipsoidal clusters
Cosmetics Alter Biologically-Based Factors of Beauty: Evidence from Facial Contrast
The use of cosmetics by women seems to consistently increase their attractiveness. What factors of attractiveness do cosmetics alter to achieve this? Facial contrast is a known cue to sexual dimorphism and youth, and cosmetics exaggerate sexual dimorphisms in facial contrast. Here, we demonstrate that the luminance contrast pattern of the eyes and eyebrows is consistently sexually dimorphic across a large sample of faces, with females possessing lower brow contrasts than males, and greater eye contrast than males. Red-green and yellow-blue color contrasts were not found to differ consistently between the sexes. We also show that women use cosmetics not only to exaggerate sexual dimorphisms of brow and eye contrasts, but also to increase contrasts that decline with age. These findings refine the notion of facial contrast, and demonstrate how cosmetics can increase attractiveness by manipulating factors of beauty associated with facial contrast
Systematic Improvement of Classical Nucleation Theory
We reconsider the applicability of classical nucleation theory (CNT) to the
calculation of the free energy of solid cluster formation in a liquid and its
use to the evaluation of interface free energies from nucleation barriers.
Using two different freezing transitions (hard spheres and NaCl) as test cases,
we first observe that the interface-free-energy estimates based on CNT are
generally in error. As successive refinements of nucleation-barrier theory, we
consider corrections due to a non-sharp solid-liquid interface and to a
non-spherical cluster shape. Extensive calculations for the Ising model show
that corrections due to a non-sharp and thermally fluctuating interface account
for the barrier shape with excellent accuracy. The experimental solid
nucleation rates that are measured in colloids are better accounted for by
these non-CNT terms, whose effect appears to be crucial in the interpretation
of data and in the extraction of the interface tension from them.Comment: 20 pages (text + supplementary material
Bioelectronic DNA detection of human papillomaviruses using eSensorâ„¢: a model system for detection of multiple pathogens
BACKGROUND: We used human papillomaviruses (HPV) as a model system to evaluate the utility of a nucleic acid, hybridization-based bioelectronic DNA detection platform (eSensorâ„¢) in identifying multiple pathogens. METHODS: Two chips were spotted with capture probes consisting of DNA oligonucleotide sequences specific for HPV types. Electrically conductive signal probes were synthesized to be complementary to a distinct region of the amplified HPV target DNA. A portion of the HPV L1 region that was amplified by using consensus primers served as target DNA. The amplified target was mixed with a cocktail of signal probes and added to a cartridge containing a DNA chip to allow for hybridization with complementary capture probes. RESULTS: Two bioelectric chips were designed and successfully detected 86% of the HPV types contained in clinical samples. CONCLUSIONS: This model system demonstrates the potential of the eSensor platform for rapid and integrated detection of multiple pathogens
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