Vortex Interaction in a Ducted Flow

The objective of this study is to describe the structure of pipe flow by considering it as a superposition of many axisymmetric vortex rings. In knowing the unsteady gross feature of pipe flow, the investigation on vortex interactions is important. As a first step to the goal, we investigate the nonlinear interaction among vortex rings whose number is three at most. The interaction among vortex rings of equal circulation is here investigated. Momentum and energy conservation of the present vortex ring system are also discussed to know a better understanding of the perturbed pipe flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Director reorientation and order reconstruction: competing mechanisms in a nematic cell

We propose a model to explore the competition between two mechanisms possibly at work in a nematic liquid crystal confined within a flat cell with strong uniaxial planar conditions on the bounding plates and subject to an external field. To obtain an electric field perpendicular to the plates, a voltage is imposed across the cell; no further assumption is made on the electric potential within the cell, which is therefore calculated together with the nematic texture. The Landau-de Gennes theory of liquid crystals is used to derive the equilibrium nematic order tensor Q. When the voltage applied is low enough, the equilibrium texture is nearly homogeneous. Above a critical voltage, there exist two different possibilities for adjusting the order tensor to the applied field within the cell: plain director reorientation, i.e., the classical Freedericksz transition, and order reconstruction. The former mechanism entails the rotation of the eigenvectors of Q and can be described essentially by the orientation of the ordinary uniaxial nematic director, whilst the latter mechanism implies a significant variation of the eigenvalues of Q within the cell, virtually without any rotation of its eigenvectors, but with the intervention of a wealth of biaxial states. Either mechanism can actually occur, which yields different nematic textures, depending on material parameters, temperature, cell thickness and the applied potential. The equilibrium phase diagram illustrating the prevailing mechanism is constructed for a significant set of parameters.      

Organophosphorus insecticides extraction and heterogeneous oxidation on column for analysis with an acetylcholinesterase (AChE) biosensor

This paper presents an analysis method for organophosphorus insecticides based on AChE biosensors coupled with a preconcentration and oxidation on a solid phase column. Three organic solvents, acetonitrile (ACN), ethanol and methanol were tested for their influence on AChE activity, insecticide inhibition and their ability to elute the adsorbed insecticides. Our results showed that ACN in a concentration of 5% (v/v) had the less negative effect on biosensor analysis and was the most appropriate organic solvent for the column elution. The presence of the organic solvent in the incubation media of the biosensor was found to induce a reduction of the inhibition percentages. The inhibition of the biosensors was performed in phosphate buffer with 5% (v/v) ACN, while the initial and remaining response of the biosensors were measured in PBS. In these conditions, the LODs of paraoxon and dichlorvos were measured with or without a preconcentration step. The LODs of the AChE biosensor without sample preconcentration were 8 × 10⁻⁸ M for paraoxon and 1 × 10⁻⁷ M dichlorvos and the LOD obtained after the preconcentration step were 2.5 × 10⁻⁸ M for paraoxon and 2.5 × 10⁻⁸ M for dichlorvos. Moreover, the use of the column allowed the heterogeneous oxidation of organophosphorus insecticides for improved LOD.     

Smectic-A edge dislocations in a very thin cell

We study stable “bookshelf” smectic-A structures within a very thin plane-parallel cell of thickness L in which the mismatch between surface preferred (d _s) and intrinsic (d₀) smectic layer thicknesses occurs. The Landau-Ginzburg approach based on a complex smectic order parameter is used. For a weak enough smectic positional anchoring strength W smectic layers adopt the modified bookshelf profile. In a thick enough cell with increasing W a lattice of edge dislocations is continuously formed at the confining surfaces and then depinned from them. The structure with dislocations is formed when the condition d ₀/( d ₀/d _s - 1) ∼ 2 is fulfilled, where is the positional surface anchoring extrapolation length. If the cell is thin enough the dislocations formed at opposite cell plates annihilate and consequently the smectic layers adopt a locked bookshelf structure. This transition is discontinuous and takes place when d ₀/(L d ₀/d _s - 1) ∼ 5 is realized. To observe these transitions in a cell of thickness L∼ 1μm the conditions W∼ 10^-6 J/m ² and d ₀/d _s - 1∼ 5 ^. 10^-4 have to be fulfilled. All the three qualitatively different structures coexist at the triple point. Received 21 February 2002     

Nef dimension of minimal models

We reduce the Abundance Conjecture in dimension 4 to the following numerical statement: if the canonical divisor K is nef and has maximal nef dimension, then K is big. From this point of view, we classify in dimension 2 nef divisors which have maximal nef dimension, but which are not big.Mathematics Subject Classification (2000): 14E30, 14J10, 14N30Revised version: 2 March 2004     

Norm estimates of almost Mathieu operators

We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C^*-algebra . In the process, we prove for every λ∈R and the inequality

     

Saari's conjecture for the collinear -body problem

In 1970 Don Saari conjectured that the only solutions of the Newtonian -body problem that have constant moment of inertia are the relative equilibria. We prove this conjecture in the collinear case for any potential that involves only the mutual distances. Furthermore, in the case of homogeneous potentials, we show that the only collinear and non-zero angular momentum solutions are homographic motions with central configurations.

     

The Correlations of Farey Fractions

It is proved that all correlations of the sequence of Fareyfractions exist and explicit formulas are provided for the correlationmeasures.     

Reversing the training effect in exchange biased CoO/Co bilayers

We performed a detailed study of the training effect in exchange biased CoO/Co bilayers. High-resolution measurements of the anisotropic magnetoresistance (AMR) display an asymmetry in the first magnetization reversal process and training in the subsequent reversal processes. Surprisingly, the AMR measurements as well as magnetization measurements reveal that it is possible to partially reinduce the untrained state by performing a hysteresis measurement with an in-plane external field perpendicular to the cooling field. Indeed, the next hysteresis loop obtained in a field parallel to the cooling field resembles the initial asymmetric hysteresis loop, but with a reduced amount of spin rotation occurring at the first coercive field. This implies that the antiferromagnetic domains, which are created during the first reversal after cooling, can be partially erased.     

Preparation of phthalamic acid derivatives and ring closure to phthalimidobarbituric acids

Phthalamic acid derivatives with a barbiturate moiety were prepared from 5‐amino‐5‐ethylbarbituric acids. To circumvent an undesired acetylation in glacial acetic acid during the preparation of phthalimidobarbituric acids, two routes were proven exemplarily. On the one hand, a phthalamic acid ( 6a ) was isolated and subsequently cyclized with acetic anhydride to the corresponding phthalimide 2a . On the other hand, a phthalamic acid tert‐butyl ester ( 5b ) was successively treated with trifluoroacetic acid and trifluoroacetic anhydride to achieve heterocyclization to the phthalimide 2b . These routes might be useful for the preparation of other phthalimides derived from sterically hindered primary amines.