On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

High temperature stability of maghemite in partially oxidized basalt lava

Mössbauer spectroscopy of basalt lava samples, exhibiting reversible thermal magnetization (J_S-T) curves with Curie temperatures of about 580°C, has revealed considerable amounts of maghemite (γ-Fe₂O₃) in many samples. In view of the expected instability, of maghemite at temperatures above 350°C, this reversibility is rather surprising. Here we report Mössbauer studies on heated lava samples, showing high content of maghemite. The samples were kept at 600°C in oxidizing, reducing, and inactive atmospheres, respectively, for different lengths of time, and then analyzed with Mössbauer spectroscopy at room temperature. The Mössbauer spectra showed that maghemite is stable in the oxidizing atmosphere for at least several hours. In the inactive atmosphere a considerable amount of maghemite still exists after two hours heating. In the reducing atmosphere maghemite had transformed to magnetite after only 30 minutes.     

Rates of redox reactions in basaltic melts determined by Mössbauer spectroscopy

Mössbauer spectroscopy has been widely used for determining the ferric/ferrous ratio in amorphous rock samples to reveal the oxygen pressure in the melt. In the present investigation, Mössbauer spectroscopy in conjunction with melting experiments at controlled oxygen pressures was used to determine the rates of redox reactions in basaltic melts at 1300°C. The samples were kept at a fixed oxygen pressure long enough to reach equilibrium at a well established ferric/ferrous ratio. Then, the oxygen fugacity in the furnace was changed abruptly and the samples were kept for different lengths of time, from 15 min, to 4 hrs, at the new condition. At the end of each run the samples were quenched and the ferric/ferrous ratio analyzed by Mössbauer spectroscopy. A geological corollary of our results is that natural volcanic glasses, representing quenched melts, retain and reflect the oxidation state in the melt immediately prior to eruption, and hence the oxygen fugacity in the magma.     

Solutions for the storage and handling of SPINE standard pucks

Currently there is no rack system for the long‐term storage of SPINE pucks in spite of their commercial availability and heavy usage at the ESRF. The only way to store pucks is in transport dewar canisters which presents a number of limitations and drawbacks. Here a simple affordable rack for storing SPINE pucks is described, which we believe is accessible to not only synchrotrons but also both academic and industrial research laboratories.     

Mössbauer spectroscopy for determining phase stability in the ferrosilicon system

We present studies of phase dynamics of the silicon rich part of the Fe?Si system performed with Mössbauer spectroscopy. Standard spectra are obtained in very pure samples and these are applied to the studies of commercial 75& ferrosilicon. We find that the semistable high temperature alpha phase, known for considerable concentration of vacancies, needs multiple quadrupole doublets to fit the data. Finally it is shown how the Mössbauer effect can be applied to quality control in ferrosilicon production.     

The Phase Transition in Statistical Models Defined on Farey Fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C [ ln² ]^–1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.     

Phase Transitions of Ruthenium-Doped Iron Oxide Studied by 57Fe Mössbauer Spectroscopy at Elevated Temperatures

Hyperfine Interactions - The 57Fe Mössbauer spectra recorded in situ from 5% ruthenium-doped maghemite show parameters typical for maghemite up to 600 K and a hyperfine field distribution...