Palm pairs and the general mass-transport principle

We consider a lcsc group G acting properly on a Borel space S and measurably on an underlying sigma-finite measure space. Our first main result is a transport formula connecting the Palm pairs of jointly stationary random measures on S. A key (and new) technical result is a measurable disintegration of the Haar measure on G along the orbits. The second main result is an intrinsic characterization of the Palm pairs of a G-invariant random measure. We then proceed with deriving a general version of the mass-transport principle for possibly non-transitive and non-unimodular group operations first in a deterministic and then in its full probabilistic form.Comment: 26 page

Irradiation test program for FFTF

Four unique deisgn features are described which make the Fast Flux Test Facility eminently suitable for irradiation test programs. These features are a fast flux level of 7 x 10/sup 15/ neutrons/cm/sup 2//sec, a 36-inch reference (breeder reactor) core height, test volumes suitable for testing of statistical quantities of materials, and the capability for direct (contact) or indirect (proximity) instrumentation of active core experiments

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

The neonatal sepsis is diminished by cervical vagus nerve stimulation and tracked non-invasively by ECG: a preliminary report in the piglet model

In adults, vagus nerve stimulation (VNS) reduces inflammation. In neonates, the effects of VNS are not known. An electrocardiogram (ECG)-derived heart rate variability (HRV) index reliably tracks the inflammatory response induced by low-dose lipopolysaccharide (LPS) in near-term sheep fetuses. We evaluated the VNS effect on the systemic inflammatory response induced by a high dose of LPS in neonatal piglets to mimic late-onset neonatal sepsis. Next, we tested if our HRV inflammatory index tracks inflammation in piglets. Following anesthesia, electrodes were attached to the left vagal nerve; ECG and blood pressure (BP) were recorded throughout the experiment. Following baseline, the piglets were administered LPS as 2mg/kg IV bolus. In the VNS treated piglet, the vagus nerve was stimulated for 10 minutes prior to and 10 min after the injection of LPS. In both groups, every 15 min post LPS, the arterial blood sample was drawn for blood gas, metabolites, and inflammatory cytokines. At the end of the experiment, the piglets were euthanized. BP and HRV measures were calculated. The piglets developed a potent inflammatory response to the LPS injection with TNF-alpha, IL-1beta, IL-6 and IL-8 peaking between 45 and 90 min post-injection. VNS diminished the LPS-induced systemic inflammatory response varying across the measured cytokines from two to ten-fold. The HRV index tracked accurately the cytokines' temporal profile. This novel model allows manipulating and tracking neonatal sepsis: The HRV inflammatory index 1) applies across species pre- and postnatally and 2) performs well at different degrees of sepsis (i.e., nanogram and milligram doses of LPS); 3) the present VNS paradigm effectively suppresses LPS-induced inflammation, even at high doses of LPS. The potential of early postnatal VNS to counteract sepsis and of HRV monitoring to early detect and track it deserve further study

Azbel-Hofstadter model on triangular lattice revisited

In the present paper, the mean of Lyapunov exponents for the Azbel-Hofstadter model on the triangular lattice is calculated. It is recently proposed that [Phys. Rev. Lett. {\bf 85}, 4920 (2000)], for the case of the square lattice, this quantity can be related to the logarithm of the partition function of the two dimensional Ising model and has a connection to the asymptotic bandwidth. We find that the correspondence of this quantity to the logarithm of the partition function of the two dimensional Ising model is not complete for the triangular lattice. Moreover, the detailed connection between this quantity and the asymptotic bandwidth is not valid. Thus the conclusions for the mean of Lyapunov exponents suggested previously depend on the lattice geometry.Comment: RevTeX, 4 page, no figur

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense

Space-based research in fundamental physics and quantum technologies

Space-based experiments today can uniquely address important questions related to the fundamental laws of Nature. In particular, high-accuracy physics experiments in space can test relativistic gravity and probe the physics beyond the Standard Model; they can perform direct detection of gravitational waves and are naturally suited for precision investigations in cosmology and astroparticle physics. In addition, atomic physics has recently shown substantial progress in the development of optical clocks and atom interferometers. If placed in space, these instruments could turn into powerful high-resolution quantum sensors greatly benefiting fundamental physics. We discuss the current status of space-based research in fundamental physics, its discovery potential, and its importance for modern science. We offer a set of recommendations to be considered by the upcoming National Academy of Sciences' Decadal Survey in Astronomy and Astrophysics. In our opinion, the Decadal Survey should include space-based research in fundamental physics as one of its focus areas. We recommend establishing an Astronomy and Astrophysics Advisory Committee's interagency ``Fundamental Physics Task Force'' to assess the status of both ground- and space-based efforts in the field, to identify the most important objectives, and to suggest the best ways to organize the work of several federal agencies involved. We also recommend establishing a new NASA-led interagency program in fundamental physics that will consolidate new technologies, prepare key instruments for future space missions, and build a strong scientific and engineering community. Our goal is to expand NASA's science objectives in space by including ``laboratory research in fundamental physics'' as an element in agency's ongoing space research efforts.Comment: a white paper, revtex, 27 pages, updated bibliograph

Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics

We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of a U-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for such U-statistics of the Gibbs particle process. A byproduct of our approach is a new uniqueness result for Gibbs particle processes

Ferroelectric and Incipient Ferroelectric Properties of a Novel Sr_(9-x)PbxCe2Ti2O36 (x=0-9) Ceramic System

Sr_(9-x)PbxCe2Ti12O36 system is derived from the perovskite SrTiO3 and its chemical formula can be written as (Sr_(1-y)Pby)0.75Ce0.167TiO3. We investigated dielectric response of Sr_(9-x)PbxCe2Ti12O36 ceramics (x = 0-9) between 100 Hz and 100 THz at temperatures from 10 to 700 K using low- and high-frequency dielectric, microwave (MW), THz and infrared spectroscopy. We revealed that Sr9Ce2Ti12O36 is an incipient ferroelectric with the R-3c trigonal structure whose relative permittivity e' increases from 167 at 300 K and saturates near 240 below 30 K. The subsequent substitution of Sr by Pb enhances e' to several thousands and induces a ferroelectric phase transition to monoclinic Cc phase for x>=3. Its critical temperature Tc linearly depends on the Pb concentration and reaches 550 K for x=9. The phase transition is of displacive type. The soft mode frequency follows the Barrett formula in samples with x=3. The MW dispersion is lacking and quality factor Q is high in samples with low Pb concentration, although the permittivity is very high in some cases. However, due to the lattice softening, the temperature coefficient of the permittivity is rather high. The best MW quality factor was observed for x=1: Q*f=5800 GHz and e'=250. Concluding, the dielectric properties of Sr_(9- x)PbxCe2Ti12O36 are similar to those of Ba_(1-x)SrxTiO3 so that this system can be presumably used as an alternative for MW devices or capacitors.Comment: subm. to Chem. Mate

A Nonperturbative Eliasson's Reducibility Theorem

This paper is concerned with discrete, one-dimensional Schr\"odinger operators with real analytic potentials and one Diophantine frequency. Using localization and duality we show that almost every point in the spectrum admits a quasi-periodic Bloch wave if the potential is smaller than a certain constant which does not depend on the precise Diophantine conditions. The associated first-order system, a quasi-periodic skew-product, is shown to be reducible for almost all values of the energy. This is a partial nonperturbative generalization of a reducibility theorem by Eliasson. We also extend nonperturbatively the genericity of Cantor spectrum for these Schr\"odinger operators. Finally we prove that in our setting, Cantor spectrum implies the existence of a $G_\delta$-set of energies whose Schr\"odinger cocycle is not reducible to constant coefficients