The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

ON AVOIDANCE ACTIVITIES IN FISHERY ENFORCEMENT MODELS

Compliance and enforcement in fisheries are important issues from an economic point of view since management measures are useless without a certain level of enforcement. These conclusions come from the well‐established theoretical literature on compliance and enforcement problems within fisheries and a common result is that, it is efficient to set fines as high as possible and monitoring as low as possible, when fines are costless and offenders are risk neutral. However, this result is sensitive to the assumption that fishermen cannot engage in avoidance activities, e.g., activities to reduce the likelihood of being detected when noncomplying. The paper presents a model of fisheries that allows the fishermen to engage in avoidance activities. The conclusions from the model are that, under certain circumstances, fines are costly transfers to society since they not only have a direct positive effect on the level of deterrence, but also an indirect negative effect in the form of increased avoidance activities to reduce the probability of detection. The paper contributes to the literature on avoidance activities by introducing the externality from the illegal behavior as an endogenous effect on other offenders. For an externality, that has an exogenous effect on other actors, Malik shows that fines are only costly transfers for conditional deterrence (when one actor is deterred while another actor is not). For fisheries, we show that fines are also costly transfers under no deterrence (when no agents are deterred).     

An investigation of the spin glass behaviour in iron antimonate by iron-57 and antimony-121 Mössbauer spectroscopy

Iron antimonate, which contains a superlattice composed of an ordered array of cations in the rutile-type structure, has been shown to undergo a spin glass transition atca. 20K which is induced by antisite atomic ordering. The iron-57 Mössbauer spectra recorded at 298 and 77K provide information on the relaxation times of short range magnetically ordered clusters identified by magnetic susceptibility measurements. The spectrum of 4K is tentatively interpreted in terms of the existence, at temperatures below the spin glass transition temperature, of a hyperfine magnetic field distribution at Fe³⁺ ions with a mean value of 487 kOe and which contains a supertransferred contribution from the nearest neighbour Fe³⁺ ions. The¹²¹Sb Mössbauer spectra are characteristic of Sb⁵⁺ and the increasing linewidths at lower temperatures are consistent with the presence of a supertransferred hyperfine magnetic field at the Sb⁵⁺ species ofca. 16^kOe.     

Orthogonal Polynomials and Second-order Differential Equations

We show that a sequence of polynomials can be eigenfunctionsof a second-order differential operator only under severe restrictions.