Choosing the maximum from a sequence with a discount function

Choosing the maximum value from a sequence ofN independent values is a well known problem often called the candidate problem or secretary problem. This paper treats the above problem with a discount penalty (0<<1) for each additional observation taken. It is shown that asN increases indefinitely, the optimal stopping policy is bounded although the maximum expected payoff goes to zero, and that there exists a sequence 0= ₀<₁<₂<<1, such that the asymptotic optimal stopping rule is the same for all _i–1<_i.     

The Morphology of Liquid-Crystalline Polymers and the Possible Consequences for their Rheological Behaviour

Abstract

Polymer liquid crystals can occur as polydomain materials where the domain size may be tens of microns. While the material within each domain may be characterized by a common order parameter, the directors of the domains can be more or less randomly distributed. Since the transition from polydomain to monodomain material only involves the removal of grain boundaries and the alignment of directors, the free energy change must necessarily be small. Such a transition can readily be achieved, therefore, by the action of any external field: electrical, magnetic, stress or surface. In this work optical photomicrographs of polymeric liquid crystals with widely varying and in some cases well controlled morphologies are presented. Probable dependence of rheological behaviour on morphology is also discussed. Such dependence is expected to be considerable under certain conditions. Due to experimental and sample limitations, however, direct correlations of rheology and morphology are sparse. Morphological consequences for the rheology of liquid-crystalline materials can be exemplified by the following possibilities. In contrast to the case of isotropic melts, wall effects can be non-negligible. Zero shear rate rheological parameters are not expected to be uniquely defined quantities since the domain sizes are large and the director may not be effectively averaged over typical sample dimensions. Non-zero shear-rate measurements of rheological parameters is effected by the propensity of: (1) individual domain directors to align under the influence of a stress field and (2) flow alignment to dominate surface-induced alignment above some critical shear rate. The effects might be manifested by a non-newtonian regime as well as yield stress behaviour and thixotropy. The kinetics of relaxation from mono- to poly-domain material has implications for the dynamic response and rheological hysterises of the material.     

Measurements Of Biogenic Hydrocarbons And Their Atmospheric Degradation In Forests

Abstract

An analytical procedure for the sampling and quantitative determination of biogenic hydrocarbons in the atmosphere is presented. The method is based on the adsorptive preconcentration of the hydrocarbons using Tenax TA/Carbopack B filled sampling tubes followed by thermodesorption of the trapped compounds and gas chromatographic analysis. To avoid losses of the biogenic alkenes as a consequence of their reaction with ozone on the adsorbents during the sampling step, an ozone scrubber is used in front of the adsorption tubes. Diurnal variations of the monoterpene- and ozone-concentrations are determined at different heights in and above a forest stand (coniferous and deciduous trees) in the Vosges (Col du Donon, 760 m a.s.l.) in order to elucidate the importance of terpene-oxidation reactions on the formation of peroxidic products in forest air.     

Heating and cooling effects generated by the dynamic stresses of cracked interfaces and layers in laminated composites

The temperature field generated by the sudden application of a far-field mechanical loading of a periodically layered composite with an interfacial crack or with a cracked layer parallel to the interfaces is determined. As a result of the crack’s existence, the periodicities of the structure and the thermoelastic field are lost. The complexity of the resulting problem is resolved by the combined application of the representative cell method and the full (two-way) dynamic thermomechanical equations. In the former analysis, due to the loss of periodicity the dynamic thermoelastic Green’s functions are generated, in conjunction with the double finite discrete Fourier transform. In the latter one, the transformed displacements and temperature are expressed by second-order expansions and the strong-form of the elastodynamic and energy equations together with the various interfacial and the so called Born–von Karman boundary conditions are imposed in the average sense (in the transform domain). The results exhibit the induced temperature field at any point in the plane of the crack. The generated temperature fields show the cooling and heating zones in both Mode I and Mode II deformations. In addition, the adiabatic assumption (according to which the heat conduction is a priori ignored) is assessed by comparing the computed temperature field with the corresponding one based on the full thermomechanical coupling.