On the general problem of stability for impulsive differential equations

Criteria for stability, asymptotical stability and instability of the nontrivial solutions of the impulsive system

     

Towards a microchannel‐based X‐ray detector with two‐dimensional spatial and time resolution and high dynamic range

X‐ray detectors that combine two‐dimensional spatial resolution with a high time resolution are needed in numerous applications of synchrotron radiation. Most detectors with this combination of capabilities are based on semiconductor technology and are therefore limited in size. Furthermore, the time resolution is often realised through rapid time‐gating of the acquisition, followed by a slower readout. Here, a detector technology is realised based on relatively inexpensive microchannel plates that uses GHz waveform sampling for a millimeter‐scale spatial resolution and better than 100 ps time resolution. The technology is capable of continuous streaming of time‐ and location‐tagged events at rates greater than 10⁷ events per cm². Time‐gating can be used for improved dynamic range.     

Exact Solution of a Generalized ANNNI Model on a Cayley Tree

We consider the Ising model on a rooted Cayley tree of order two with nearest neighbor interactions and competing next nearest neighbor interactions restricted to spins belonging to the same branch of the tree. This model was studied by Vannimenus who found a new modulated phase, in addition to the paramagnetic, ferromagnetic, antiferromagnetic phases and a (+ + - -) periodic phase. Vannimenus’s results are based on an analysis of the recurrence equations (relating the partition function of an n ? generation tree to the partition function of its subsystems containing (n ?1) generations) and most results are obtained numerically. In this paper we analytically study the recurrence equations and obtain some exact results: critical temperatures and curves, number of phases, partition function.     

Microwave Plasmas at Atmospheric Pressure

Microwave plasmas at atmospheric pressure are used for surface treatments like for example cleaning, sterilization or decontamination purposes, for a pre‐treatment to increase the adhesion of lacquer, paint, or glue, and for the deposition of different kind of layers and coatings. Micro plasma jets can also be applied for biomedical applications and for treatment of small and complex geometries like for example the inside of capillaries. Larger plasma torches which exhibit higher gas temperatures can also be used for chemical syntheses like waste gas decomposition, methane pyrolysis, or carbon dioxide dissociation and for plasma spraying purposes. In the present publication an overview on the development and the investigation of the operating principle of two atmospheric pressure microwave plasma torches at frequencies of 2.45 GHz and 915 MHz will be presented. The plasma sources are based on a cylindrical resonator combined with coaxial structures. To explain how these plasma sources work, simulations of the electric field distribution will be discussed. Furthermore, some physical characteristics of an air and an Ar/H2 atmospheric plasma like gas temperatures, excitation temperatures and densities as well as the heating of the plasma by the microwave will be investigated. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ion-isotopic exchange reaction kinetics using Duolite ARA-9366B and Indion-AGR resins

Radiotracer isotopic technique as an effective analytical tool was used to study the kinetics of ion-isotopic exchange reactions in the nuclear- and nonnuclear-grade anion exchange resins Duolite ARA-9366B and Indion-AGR. On the basis of kinetic data, specific reaction rate (per minute), amount of ion exchanged (millimoles), initial rate of iodide ion exchange (millimoles per minute), and log K _d values were calculated for the two resins. It was observed that under identical experimental conditions of 35.0 °C, 1.000 g of ion exchange resins, and 0.002 mol/L of labeled iodide ion solution, the values calculated were 0.200 min^?1, 0.278 mmol, 0.056 mmol/min, and 9.6, respectively, for Duolite ARA-9366B resin, which were higher than 0.102 min^?1, 0.216 mmol, 0.022 mmol/min, and 5.7, respectively, for Indion-AGR resins. An identical trend was observed for the two resins during bromide ion-isotopic exchange reaction. The overall results indicate that under identical experimental conditions, Duolite ARA-9366B resins show superior performance than Indion-AGR resins. The results of the present experimental work have demonstrated that the radioanalytical technique used here can be successfully applied for the characterization of different ion exchange resins so as to evaluate their performance under various process parameters.     

Asymptotic properties of nonparametric curve estimates

We consider a class of nonparametric estimators for the regression functionm(t) in the model:y _i =m(t _i ) + _i , 1 i n, t _i [0, 1], which are linear in the observationsy _i . Several limit theorems concerning local and global stochastic and a.s. convergence and limit distributions are given.     

Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space

Using Cesari's approach, we prove the existence of optimal controls for a class of systems governed by differential inclusions on a Banach space having the Radon-Nikodym property. Theorem 3.1 gives the existence result for optimal relaxed controls under fairly general assumptions on the system and the admissible controls. This result depends on a fundamental result (Theorem 2.1) that proves the existence of mild solutions of differential inclusions on a Banach space, which has also independent interest. Further, the preparatory results, such as Lemma 3.1 and Lemma 3.2, are also useful in the study of time-optimal and terminal control problems.For illustration of the results, we present two examples, one on distributed controls for a class of systems governed by nonlinear parabolic equations and the other on boundary controls with discontinuous boundary operator.This work is supported in part by the National Science and Engineering Council of Canada under Grant No. 7109.     

X-ray difffraction studies on samarium up to one megabar pressure

Abstract

High—pressure crystal structure studies have been performed on Sm up to 100 GPa using synchrotron x-radiation and a diamond anvil cell. The structural sequence Sm-dhcp-fcc-dist.fcc has been confirmed. There is no evidence of any volume collapse. The bulk modulus and its pressure derivative have been determined (B₀ = 30.7 GPa, B₀’ = 2.5).     

Conformally Flat Hypersurfaces of E4

We consider 3-dimensional conformally flat hypersurfaces of E ⁴ with 2 different principal curvatures such that the coordinate directions are principal directions. We describe explicitly those which allow an immersion with constant mean curvature. They are shown to be in close correspondence with solutions of the nonlinear integrable sine-Gordon and sinh-Gordon equations. Conversely, this provides a geometrical characterization for this particular class of conformally flat hypersurfaces of E ⁴.     

Singularities of Euler Flow? Not Out of the Blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.