Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

Determination of Surface Functional Groups in Lignocellulosic Materials by Chemical Derivatization and ESCA Analysis

Simple and convenient methods for determining surface chemical composition of lignocellulosic materials are described. The methods are based on vapor phase fluorine surface derivatization with either trifluoro acetic anhydride (TFAA), tri-fluoro ethanol (TFE) or pentafluorophenyl hydrazine (PFPH) and subsequent Electron Spectroscopy for Chemical Analysis (ESCA). Model cellulosic surfaces with well defined functionalities were used to optimize the derivatization reaction conditions. Detection and accessibility of surface hydroxyl functional groups were investigated in cotton and regenerated cellulose as models. Carboxymethyl cellulose (CMC) was used as a model surface for detection and quantification of carboxylic acid groups. Theoretical conversion curves for derivatization reactions were calculated and used to evaluate the extent of the reactions on the model surfaces. It was found that the conversion was higher for the regenerated cellulose and CMC than for cotton. The protocols developed using the model surfaces were applied to a case study on wood fibers with different degrees of complexity, namely dissolving and chemithermomechanical (CTMP) pulp. Untreated and oxygen-plasma modified pulps were compared with respect to the surface composition of functional groups. According to the derivatization reactions, functionalities containing oxygen were significantly increased on the plasma-treated samples. The effect of the treatment was found to be dependent on the type of pulp. Fluorine derivatization is shown to be an unambiguous method for clear assessment of the chemical functionalities of cellulosic surfaces.     

A locally computed suboptimal control strategy for a class of interconnected systems

In this paper, a locally computed suboptimal control strategy for a class of interconnected systems is introduced. First, optimal statefeedback control equations are derived for a finite-horizon quadratic cost. Then, the control for each subsystem is separated into two portions. The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions. To achieve a locally calculable control, an approximation to the optimal control equations is introduced, and two iterative suboptimal control algorithms are developed. In the first algorithm, the initial conditions of subsystems are assumed to be known; in the second algorithm, this information is replaced by statistical distributions. The orders of errors in the iterations of the algorithm and in the suboptimality are given in terms of interconnections. An example with comparisons is also included to show the performance of the approach.     

A finite cutting plane method for facial disjunctive programs

This paper shows that any linear disjunctive program with a finite number of constraints can be transformed into an equivalent facial program. Based upon linear programming technique, a new, finite cutting plane method is presented for the facial programs.

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Zusammenfassung Die Arbeit zeigt, daß jedes lineare disjunktive Optimierungsproblem mit endlich vielen Restriktionen in ein äquivalentes Fazetten-Problem transformiert werden kann. Auf der Grundlage von linearer Optimierungstechnik wird für das Fazetten-Problem ein neues, endliches Schnittebenenverfahren vorgestellt.

     

On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

Properties of isolated DNA bases, base pairs and nucleosides examined by laser spectroscopy

The vibronic spectra of laser desorbed and jet cooled guanine (G) adenine (A), and cytosine (C) consist of bands from four, two and two major tautomers respectively, as revealed by UV-UV and IR-UV double resonance spectroscopy. The vibronic spectrum of adenine around 277 nm consists of weak nπ^* and strong ππ^* transitions, based on IR-UV and deuteration experiments. Precise ionization potentials of G and A were determined with 2-color, 2-photon ionization. We also measured vibronic and IR spectra of several base pairs. GC exhibits a HNH ^... OH/NH ^... N/C=O ^... HNH bonding similar to the Watson-Crick GC base pair but with C as enol tautomer. One GG isomer exhibits non-symmetric hydrogen bonding with HNH ^... N/NH ^... N/C=O ^... HNH interactions. A second observed GG isomer has a symmetrical hydrogen bond arrangement with C=O ^... NH/NH ^... O=C bonding. Two CC isomers were observed with symmetrical C=O ^... NH/NH ^... O=C bonding and nonsymmetrical C=O ^... HNH/NH ^... N interaction, respectively. Guanosine (Gs), 2-DeoxyGs und 3-DeoxyGs each exhibit only one isomer in the investigated wavelength range around 290 nm with a strong intramolecular sugar(5-OH) ^... enolguanine(3-N) hydrogen bond. Received 16 June 2002 / Received in final form 15 July 2002 Published online 13 September 2002     

Studies on pre-hump and main fractions of cellulose-2,5-acetate in acetone

Technical cellulose-2.5-acetates (CA 2.5) were characterized regarding their carbohydrate composition in comparison to the raw material. The association of the CA 2.5 samples in acetone was studied by size exclusion chromatography (SEC) using various acetone grades and styrene divinylbenzene copolymer columns. In HPLC grade acetone with and without addition of 1% water up to three different pre-humps eluted in front of the main fraction of the polymer. The evaluation of the main peak by light scattering measurements resulted in high molar masses indicating that for these technical CA 2.5 samples even the main fraction is not dissolved without association. No pre-humps or association phenomena were observed after addition of 1 ppm LiBr to HPLC grade acetone or with p.a. grade acetone. In addition pre-hump enriched and pre-hump free fractions were isolated by fractionated precipitation. The carbohydrate composition of these fractions was determined and correlated with their association pattern in SEC investigations.