Elastic model for simulating ultrasonic inspection of smooth and rough defects

A model is presented for the scattering of ultrasonic waves from smooth and randomly rough defects. The model uses Kirchhoff theory and is elastic, such that mode-conversion between compressional and shear waves is included in the formulation. The model is designed to simulate ultrasonic non-destructive testing situations, by specifying the location and orientation of a defect within an isotropic material, together with transmitter and receiver locations on an inspection surface. Results are presented for the scattering of both monochromatic waves and of pulses. It is shown how small levels of roughness can affect echodynamic curves and how diffracted signals may become lost due to scatter from the rough faces of defects. It is also shown that the usual rules for coupling between waves of all three modes no longer hold when roughness is present. In particular, roughness leads to coupling between horizontally polarized shear (SH) waves and the other two wave modes. The model predictions are also compared with an earlier acoustic model, indicating the importance of mode-conversion effects when considering rough defects embedded within solids.     

Formation of muonium and a muonic radical in fullerene

Three distinct electronic states were detected for positive muons (⁺) after implantation into a C₆₀ powder sample. About 40% of the ⁺ remained in the bare (diamagnetic) state, essentially an interstitial charged point particle. The rest of the muons were found to thermalize predominantly in two muonium (Mu=⁺ e^–) atomic species. A vacuum Mu state, with hyperfine coupling close to that of free Mu, most likely at the molecular center, and a muonic substituted radical, i.e. a hydrogen-like Mu addition to double bonds on the carbon rings. This opens up a rich subfield of fullerene spectroscopy using muons.     

To the relation between energies of molecular soliton and extended states in chains

A standard statement is that in the interacting electron (exciton) — phonon systems in molecular chains and on the level of the standard quantum mechanics, the formation of localised solition states is energetically more advantageous than the formation of extended (plane--wave-like or polaron) states (see e.g. /1/ for a review). The question about validity of this statement is not yet finally settled /2/. We are going to question this assertion using trivial variational arguments here. For arbitrary localized standing-soliton state (having its energy lower than the states describing running solitons irrespective of technique used to derive them), we are able to prove the existence of an intermediate or large polaron state whose energy is still lower. Hence, the energy arguments are not sufficient to explain the anomalous soliton stability.     

On solutions of truncated Kramers-Moyal expansions; continuum approximations to the Poisson process

We discuss the solutions of a Kramers-Moyal-expansion-type master equation for a discrete Poisson process, truncated at an arbitrary orderM. As was shown some time ago solutions withM=3, 7, 11 are in better agreement with the exact solution than the solution truncated atM=2. If a δ function is used as an initial condition, the solutions start to oscillate very rapidly with increasingM leading to a δ-function behaviour at the integer points for largeM. If, however, more smooth initial conditions are used, the rapid oscillations die out for increasingM and the solutions converge to interpolations of the exact solution.     

The geodesic approximation for the Yang-Mills-Higgs equations

In this paper we consider the dynamics of the monopole solutions of Yang-Mills-Higgs theory on Minkowski space. The monopoles are solutions of the Yang-Mills-Higgs equations on three dimensional Euclidean space. It is of interest to understand how they evolve in time when considered as solutions of the Yang-Mills-Higgs equations on Minkowski space-i.e. the time dependent equations. It was suggested by Manton that in certain situations the monopole dynamics could be understood in terms of geodesics with respect to a certain, metric on the space of guage equivalence classes of monopoles-the moduli space. The metric is defined by taking theL ² inner product of tangent vectors to this space. In this paper we will prove that Manton's approximation is indeed valid in the right circumstances, which correspond to the slow motion of monopoles. The metric on the moduli space of monopoles was analysed in a book by Atiyah and Hitchin, so together with the results of this paper a detailed and rigorous understanding of the low energy dynamics of monopoles in Yang-Mills-Higgs theory is obtained. The strategy of the proof is to develop asymptotic expansions using appropriate gauge conditions, and then to use energy estimates to prove their validity. For the case of monopoles to be considered here there is a technical obstacle to be overcome-when the equations are linearised about the monopole the continuous spectrum extends all the way to the origin. This is overcome by using a norm introduced by Taubes in a discussion of index, theory for the Yang-Mills-Higgs functional.Supported by grant DMS-9214067 from the National Science Foundation.     

Generating a low-energy high-current electron beam in a gun having a plasma anode

Research has been done on major physical processes governing the scope for generating magnetized low-energy high-current electron beams in a plasma-filled system. Conditions are considered for efficient excitation of the explosive electron emission at a large-area cathode at low accelerating voltages, together with the trends in beam formation in the nonstationary double layer formed between the cathode and anode plasmas, as well as the beam transport to the collector in the inhomogeneous guiding plasma. It is found that a gun having a plasma anode enables one to generate wide-aperture electron beams of microsecond duration having a mean electron energy of 10–20 keV and an energy density of up to 20 J/cm² or more, which goes with homogeneity sufficient for technological purposes.High-Current Electronics Institute, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh, Fizika, No. 3, pp. 100–114, March, 1994.     

A high temperature Mössbauer effect study of iron-doped YBa2Cu3O7 superconductor

Superconducting YBa₂Cu_2.955Fe_0.045O₇ has been studied at temperatures between 300 and 1000 K. Spectra were recorded on a sample which was sealed as a pellet pressed with boron nitride. An atmosphere of oxygen was maintained in the sample region at all times. At temperatures up to 900 K, we observed the four iron sites A, (Cu(1) chain-site; square planar oxygen coordination with O(5) vacancy on thea-axis), B, (Cu(2) plane-site; square pyramidal oxygen coordination), C, (Cu(1) chain-site; square pyramidal oxygen coordination with O(5) site occupied) and D, (Cu(1) chain-site; quasi-tetrahedral oxygen coordination with O(4) vacancy along theb-axis). At temperatures up to 700 K, the relative area of the B and C sites remained nearly constant as the temperature was increased. However, the area of the A site decreased while, the D site area increased with increasing temperature. At all times, the total area of sites A and D remained constant, thereby indicating the possibility of oxygen atom hopping in thea-b plane. The quadrupole splitting of each site, except the B site, decreased linearly with increasing temperature.Research supported in part by the Old Dominion University Undergraduate Research Program.     

Reflections on a New Approach to Gittins Indexation

Traditional approaches to stochastic resource allocation problems (including the classical multi-armed bandit problems) have usually made use of dynamic programming (DP) methodology, perhaps buttressed by further ad hoc arguments. While such approaches seem ‘natural’ they have usually proved technically very difficult. Bertsimas and Niño-Mora have recently given a radically new account of many important results in this area which relate to Gittins indices. The key to their approach is in the characterisation of the region of achievable performance. The optimisation problems of interest are then solved as linear programs over this region. Here we exploit elements within the Bertsimas and Niño-Mora framework (in particular, its capacity to give formulae for the total return of a given policy in closed form) to obtain (i) a simple dynamic programming proof of the optimality of Gittins index policies and (ii) a range of index-based suboptimality bounds for general policies for a variety of stochastic models for resource allocation.     

A game locating a needle in a circular haystack

A complete solution of the following Hider-Seeker zero-sum game is obtained. The hider hides a needle of lengtha, 0<a2, in the closed unit dise, and the seeker tries to locate it by shooting in a straight line across the disc. The payoff to the seeker is 1 if he hits the needle and 0 otherwise.     

Sequential location-allocation problems on chains and trees with probabilistic link demands

In this paper, we consider multiperiod minisum location problems on networks in which demands can occur continuously on links according to a uniform probability density function. In addition, demands may change dynamically over time periods and at most one facility can be located per time period. Two types of networks are considered in conjunction with three behavioral strategies. The first type of network discussed is a chain graph. A myopic strategy and long-range strategy for locatingp-facilities are considered, as is a discounted present worth strategy for locating two facilities. Although these problems are generally nonconvex, effective methods are developed to readily identify all local and global minima. This analysis forms the basis for similar problems on tree graphs. In particular, we construct algorithms for the 3-facility myopic problem and the 2-facility long-range and discounted cost problems on a tree graph. Extensions and suggestions for further research on problems involving more general networks are provided.