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 $\Omega$ from interior Current Density Imaging data obtainable using MRI measurements. We only require knowledge of the magnitude $|J|$ of one current generated by a given voltage $f$ on the boundary $\partial\Omega$. As previously shown, the corresponding voltage potential u in $\Omega$ is a minimizer of the weighted least gradient problem $$u=\hbox{argmin} \{\int_{\Omega}a(x)|\nabla u|: u \in H^{1}(\Omega), \ \ u|_{\partial \Omega}=f\},$$ with $a(x)= |J(x)|$. In this paper we present an alternating split Bregman algorithm for treating such least gradient problems, for $a\in L^2(\Omega)$ non-negative and $f\in H^{1/2}(\partial \Omega)$. 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 $J$ from knowledge of its magnitude, and of the voltage $f$ 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)