962 research outputs found
Experimental verification of a zero-dimensional model of the ionization kinetics of XeCl discharges
An improved 0-dimensional model for XeCl high-pressure glow discharges is presented. Calculated discharge voltages are compared with precise measurements at a small, very homogeneous discharge. Excellent agreement in a wide parameter field demonstrates that this model may serve as a reference for simpler models describing the ionization kinetics
Derivatives of Knots and Second-order Signatures
We define a set of "second-order" L^(2)-signature invariants for any
algebraically slice knot. These obstruct a knot's being a slice knot and
generalize Casson-Gordon invariants, which we consider to be "first-order
signatures". As one application we prove: If K is a genus one slice knot then,
on any genus one Seifert surface, there exists a homologically essential simple
closed curve of self-linking zero, which has vanishing zero-th order signature
and a vanishing first-order signature. This extends theorems of Cooper and
Gilmer. We introduce a geometric notion, that of a derivative of a knot with
respect to a metabolizer. We also introduce a new equivalence relation,
generalizing homology cobordism, called null-bordism.Comment: 40 pages, 22 figures, typographical corrections, to appear in Alg.
Geom. Topolog
LRRC8/VRAC anion channels are required for late stages of spermatid development in mice
Spermatogenesis is a highly complex developmental process that occurs primarily in seminiferous tubules of the testes and requires additional maturation steps in the epididymis and beyond. Mutations in many different genes can lead to defective spermatozoa and hence to male infertility. Some of these genes encode for ion channels and transporters that play roles in various processes such as cellular ion homeostasis, signal transduction, sperm motility, and the acrosome reaction. Here we show that germ cell-specific, but not Sertoli cell-specific, disruption of Lrrc8a leads to abnormal sperm and male infertility in mice. LRRC8A (leucine-rich repeat containing 8 A) is the only obligatory subunit of heteromeric volume-regulated VRAC anion channels. Its ablation severely compromises cell volume regulation by completely abolishing the transport of anions and osmolytes through VRAC. Consistent with impaired volume regulation, the cytoplasm of late spermatids appeared swollen. These cells failed to properly reduce their cytoplasm during further development into spermatozoa and later displayed severely disorganized mitochondrial sheaths in the midpiece region as well as angulated or coiled flagella. These changes, which progressed in severity on the way to the epididymis, resulted in dramatically reduced sperm motility. Our work shows that VRAC, probably through its role in cell volume regulation, is required in a cell-autonomous manner for proper sperm development and explains the male infertility of Lrrc8a(-/-) mice and the spontaneous mouse mutant ébouriffé
Effects of non-resonant interaction in ensembles of phase oscillators
We consider general properties of groups of interacting oscillators, for
which the natural frequencies are not in resonance. Such groups interact via
non-oscillating collective variables like the amplitudes of the order
parameters defined for each group. We treat the phase dynamics of the groups
using the Ott-Antonsen ansatz and reduce it to a system of coupled equations
for the order parameters. We describe different regimes of co-synchrony in the
groups. For a large number of groups, heteroclinic cycles, corresponding to a
sequental synchronous activity of groups, and chaotic states, where the order
parameters oscillate irregularly, are possible.Comment: 21 pages, 7 fig
Thermal noise of folding mirrors
Current gravitational wave detectors rely on the use of Michelson interferometers. One crucial limitation of their sensitivity is the thermal noise of their optical components. Thus, for example fluctuational deformations of the mirror surface are probed by a laser beam being reflected from the mirrors at normal incidence. Thermal noise models are well evolved for that case but mainly restricted to single reflections. In this work we present the effect of two consecutive reflections under a non-normal incidence onto mirror thermal noise. This situation is inherent to detectors using a geometrical folding scheme such as GEO\,600. We revise in detail the conventional direct noise analysis scheme to the situation of non-normal incidence allowing for a modified weighting funtion of mirror fluctuations. An application of these results to the GEO\,600 folding mirror for Brownian, thermoelastic and thermorefractive noise yields an increase of displacement noise amplitude by 20\% for most noise processes. The amplitude of thermoelastic substrate noise is increased by a factor 4 due to the modified weighting function. Thus the consideration of the correct weighting scheme can drastically alter the noise predictions and demands special care in any thermal noise design process
The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with
(twisted) coefficients in any associative ring with unit.Comment: 33 pages; final version; to appear in Invent. Mat
On Turing dynamical systems and the Atiyah problem
Main theorems of the article concern the problem of M. Atiyah on possible
values of l^2-Betti numbers. It is shown that all non-negative real numbers are
l^2-Betti numbers, and that "many" (for example all non-negative algebraic)
real numbers are l^2-Betti numbers of simply connected manifolds with respect
to a free cocompact action. Also an explicit example is constructed which leads
to a simply connected manifold with a transcendental l^2-Betti number with
respect to an action of the threefold direct product of the lamplighter group
Z/2 wr Z. The main new idea is embedding Turing machines into integral group
rings. The main tool developed generalizes known techniques of spectral
computations for certain random walk operators to arbitrary operators in
groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio
Rayleigh scattering in fused silica samples for gravitational wave detectors
Laser interferometer gravitational wave detectors require very high optical quality test masses. We report the bulk Rayleigh scattering in high quality fused silica samples. Results show that the scattering of the high quality fused silica is similar for various grades of fused silica from Heraeus. The total integrated scattering is about 0.7 ppm cm− 1at 1064 nm wavelength, which agrees with the theoretical value calculated using known fused silica parameters. All samples show Rayleigh scattering ratio inhomogeneity of ~ 4%
Knot Concordance and Higher-Order Blanchfield Duality
In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} of
the classical knot concordance group C. The filtration is important because of
its strong connection to the classification of topological 4-manifolds. Here we
introduce new techniques for studying C and use them to prove that, for each
natural number n, the abelian group F_n/F_{n.5} has infinite rank. We establish
the same result for the corresponding filtration of the smooth concordance
group. We also resolve a long-standing question as to whether certain natural
families of knots, first considered by Casson-Gordon and Gilmer, contain slice
knots.Comment: Corrected Figure in Example 8.4, Added Remark 5.11 pointing out an
important strengthening of Theorem 5.9 that is needed in a subsequent pape
Analytic and Reidemeister torsion for representations in finite type Hilbert modules
For a closed Riemannian manifold we extend the definition of analytic and
Reidemeister torsion associated to an orthogonal representation of fundamental
group on a Hilbert module of finite type over a finite von Neumann algebra. If
the representation is of determinant class we prove, generalizing the
Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal.
In particular, this proves the conjecture that for closed Riemannian manifolds
with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister
torsions are equal.Comment: 78 pages, AMSTe
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