60 research outputs found
Ultrastable lasers based on vibration insensitive cavities
We present two ultra-stable lasers based on two vibration insensitive cavity
designs, one with vertical optical axis geometry, the other horizontal.
Ultra-stable cavities are constructed with fused silica mirror substrates,
shown to decrease the thermal noise limit, in order to improve the frequency
stability over previous designs. Vibration sensitivity components measured are
equal to or better than 1.5e-11 per m.s^-2 for each spatial direction, which
shows significant improvement over previous studies. We have tested the very
low dependence on the position of the cavity support points, in order to
establish that our designs eliminate the need for fine tuning to achieve
extremely low vibration sensitivity. Relative frequency measurements show that
at least one of the stabilized lasers has a stability better than 5.6e-16 at 1
second, which is the best result obtained for this length of cavity.Comment: 8 pages 12 figure
On the Size Complexity of Non-Returning Context-Free PC Grammar Systems
Improving the previously known best bound, we show that any recursively
enumerable language can be generated with a non-returning parallel
communicating (PC) grammar system having six context-free components. We also
present a non-returning universal PC grammar system generating unary languages,
that is, a system where not only the number of components, but also the number
of productions and the number of nonterminals are limited by certain constants,
and these size parameters do not depend on the generated language
Stable Determination of the Electromagnetic Coefficients by Boundary Measurements
The goal of this paper is to prove a stable determination of the coefficients
for the time-harmonic Maxwell equations, in a Lipschitz domain, by boundary
measurements
Computing Volume Bounds of Inclusions by EIT Measurements
The size estimates approach for Electrical Impedance Tomography (EIT) allows
for estimating the size (area or volume) of an unknown inclusion in an
electrical conductor by means of one pair of boundary measurements of voltage
and current. In this paper we show by numerical simulations how to obtain such
bounds for practical application of the method. The computations are carried
out both in a 2D and a 3D setting.Comment: 20 pages with figure
Reaction Front in an A+B -> C Reaction-Subdiffusion Process
We study the reaction front for the process A+B -> C in which the reagents
move subdiffusively. Our theoretical description is based on a fractional
reaction-subdiffusion equation in which both the motion and the reaction terms
are affected by the subdiffusive character of the process. We design numerical
simulations to check our theoretical results, describing the simulations in
some detail because the rules necessarily differ in important respects from
those used in diffusive processes. Comparisons between theory and simulations
are on the whole favorable, with the most difficult quantities to capture being
those that involve very small numbers of particles. In particular, we analyze
the total number of product particles, the width of the depletion zone, the
production profile of product and its width, as well as the reactant
concentrations at the center of the reaction zone, all as a function of time.
We also analyze the shape of the product profile as a function of time, in
particular its unusual behavior at the center of the reaction zone
The stability for the Cauchy problem for elliptic equations
We discuss the ill-posed Cauchy problem for elliptic equations, which is
pervasive in inverse boundary value problems modeled by elliptic equations. We
provide essentially optimal stability results, in wide generality and under
substantially minimal assumptions. As a general scheme in our arguments, we
show that all such stability results can be derived by the use of a single
building brick, the three-spheres inequality.Comment: 57 pages, review articl
Simulating eddy current sensor outputs for blade tip timing
Blade tip timing is a contactless method used to monitor the vibration of blades in rotating machinery. Blade vibration and clearance are important diagnostic features for condition monitoring, including the detection of blade cracks. Eddy current sensors are a practical choice for blade tip timing and have been used extensively. As the data requirements from the timing measurement become more stringent and the systems become more complicated, including the use of multiple sensors, the ability to fully understand and optimize the measurement system becomes more important. This requires detailed modeling of eddy current sensors in the blade tip timing application; the current approaches often rely on experimental trials. Existing simulations for eddy current sensors have not considered the particular case of a blade rotating past the sensor. Hence, the novel aspect of this article is the development of a detailed quasi-static finite element model of the electro-magnetic field to simulate the integrated measured output of the sensor. This model is demonstrated by simulating the effect of tip clearance, blade geometry, and blade velocity on the output of the eddy current sensor. This allows an understanding of the sources of error in the blade time of arrival estimate and hence insight into the accuracy of the blade vibration measurement
A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data
We consider the hybrid problem of reconstructing the isotropic electric
conductivity of a body from interior Current Density Imaging data
obtainable using MRI measurements. We only require knowledge of the magnitude
of one current generated by a given voltage on the boundary
. As previously shown, the corresponding voltage potential u in
is a minimizer of the weighted least gradient problem
with . In this paper we present an
alternating split Bregman algorithm for treating such least gradient problems,
for non-negative and . We
give a detailed convergence proof by focusing to a large extent on the dual
problem. This leads naturally to the alternating split Bregman algorithm. The
dual problem also turns out to yield a novel method to recover the full vector
field from knowledge of its magnitude, and of the voltage on the
boundary. We then present several numerical experiments that illustrate the
convergence behavior of the proposed algorithm
Cardiac telocytes — their junctions and functional implications
Telocytes (TCs) form a cardiac network of interstitial cells. Our previous studies have shown that TCs are involved in heterocellular contacts with cardiomyocytes and cardiac stem/progenitor cells. In addition, TCs frequently establish ‘stromal synapses’ with several types of immunoreactive cells in various organs (www.telocytes.com). Using electron microscopy (EM) and electron microscope tomography (ET), we further investigated the interstitial cell network of TCs and found that TCs form ‘atypical’ junctions with virtually all types of cells in the human heart. EM and ET showed different junction types connecting TCs in a network (puncta adhaerentia minima, processus adhaerentes and manubria adhaerentia). The connections between TCs and cardiomyocytes are ‘dot’ junctions with nanocontacts or asymmetric junctions. Junctions between stem cells and TCs are either ‘stromal synapses’ or adhaerens junctions. An unexpected finding was that TCs have direct cell–cell (nano)contacts with Schwann cells, endothelial cells and pericytes. Therefore, ultrastructural analysis proved that the cardiac TC network could integrate the overall ‘information’ from vascular system (endothelial cells and pericytes), nervous system (Schwann cells), immune system (macrophages, mast cells), interstitium (fibroblasts, extracellular matrix), stem cells/progenitors and working cardiomyocytes. Generally, heterocellular contacts occur by means of minute junctions (point contacts, nanocontacts and planar contacts) and the mean intermembrane distance is within the macromolecular interaction range (10–30 nm). In conclusion, TCs make a network in the myocardial interstitium, which is involved in the long-distance intercellular signaling coordination. This integrated interstitial system appears to be composed of large homotropic zones (TC–TC junctions) and limited (distinct) heterotropic zones (heterocellular junctions of TCs)
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