Approximate analysis of coupled non-linear non-conservative systems subjected to step-function excitation

The paper deals with the approximate analysis of non-linear non-conservative systems oftwo degrees of freedom subjected to step-function excitation. The method of averaging of Krylov and Bogoliubov is used to arrive at the approximate equations for amplitude and phase. An example of a spring-mass-damper system is presented to illustrate the method and a comparison with numerical results brings out the validity of the approach.

Identification of a class of non-linear systems

This paper considers the on-line identification of a non-linear system in terms of a Hammerstein model, with a zero-memory non-linear gain followed by a linear system. The linear part is represented by a Laguerre expansion of its impulse response and the non-linear part by a polynomial. The identification procedure involves determination of the coefficients of the Laguerre expansion of correlation functions and an iterative adjustment of the parameters of the non-linear gain by gradient methods. The method is applicable to situations involving a wide class of input signals. Even in the presence of additive correlated noise, satisfactory performance is achieved with the variance of the error converging to a value close to the variance of the noise. Digital computer simulation establishes the practicability of the scheme in different situations.

Linear description of electrical networks for computer analysis

A parentheses-free code is suggested for the description of two-terminal electrical networks for computer analysis.

Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

A note on the period of oscillation of non-linear systems

This paper deals with two approximate methods of finding the period of oscillations of non-linear conservative systems excited by step functions. The first method is an extension of the analysis presented by Jonckheere [4] and the second one is based on a weighted bilinear approximation of the non-linear characteristic. An example is presented and the approximate results are compared with the exact results

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Syntheses and Self-Assembling Characteristics of Amphiphilic Star Diblock Copolymers

Uusien polymeeripohjaisten teknologioiden ja materiaalien myötä räätälöityjen polymeerien tarve on kasvanut. Viime vuosituhannen lopussa kehitetyt kontrolloidut polymerointimenetelmät ovat avanneet uusia mahdollisuuksia paitsi monimutkaisten polymeerien synteesiin, myös itsejärjestyvyyteen perustuvien funktionaalisten nanorakenteiden suunnitteluun ja valmistukseen. Nämä voivat jäljitellä luonnossa esiintyviä rakenteita, joita muodostavat esimerkiksi lipidit ja proteiinit. Itsejärjestyvät molekyylit ovat usein amfifiilisiä eli ne koostuvat hydrofiilisistä ja hydrofobisista osista ja polymeereissä nämä osat voivat olla omina lohkoinaan, jolloin puhutaan amfifiilisistä lohko- tai blokkikopolymeereistä. Riippuen järjestyneiden rakenteiden koostumuksesta ja muodosta, amfifiilisiä blokkikopolymeerejä on tutkittu tai jo käytetty nanoteknologiassa, elastomeereissä, voiteluaineissa, pinta-aktiivisina aineina, lääkkeenannostelussa, maaleissa, sekä elektroniikka-, kosmetiikka- ja elintarviketeollisuudessa. Tavallisimmin käytetyt amfifiiliset blokkikopolymeerit ovat olleet lineaarisia, mutta viime aikoina tutkimus on suuntautunut kohti monimutkaisempia rakenteita. Tällaisia ovat esimerkiksi tähtipolymeerit. Tähtimäisissä polymeereissä miselleille tyypillinen ydin-kuori-rakenne säilyy hyvin alhaisissakin polymeerikonsentraatioissa, koska polymeeriketjut ovat kiinni toisissaan yhdessä pisteessä. Siten ne ovat erityisen kiinnostavia tutkimuskohteita erilaisten hydrofobisten orgaanisten yhdisteiden sitomiseksi ja vapauttamiseksi. Tässä työssä on tarkasteltu amfifiilisten tähtipolymeerien itsejärjestymistä vesiliuoksissa sekä kokeellisesti ja tietokonesimulaatioin. Työ koostuu kahdesta osasta: tähtipolymeerien synteesistä makrosyklisillä initiaattoreilla ja amfifiilisten tähtimäisten blokkikopolymeerien ominaisuuksien tutkimisesta.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

Molecular Interactions Chlorin Assemblies and NMR Separations

Photosynthesis is a chemical process in which the energy of the light quanta is transformed into chemical energy. Chlorophyll (Chl) molecules play a key role in photosynthesis; they function in the antennae systems and in the photosynthetic reaction center where the primary charge separation (CS) takes place. Bio-inspired mimicry of the CS is an essential unit in dye-sensitized solar cells. Aim of this study was to design and develop electron donor-acceptor (EDA) pairs from Chls and fullerenes (C60) or carbon nanotubes (CNT). The supramolecular approach was chosen, as long synthetic sequences required by the covalent approach lead to long reaction schemes and low yields. Here, a π-interaction between soluble CNTs and Chl was used in EDA construction. Also, a beta-face selective two-point bound Chl-C60 EDA was introduced. In addition, the photophysical properties of the supramolecular EDA dyads were analyzed. In organic chemistry, nuclear magnetic resonance (NMR) spectroscopy is the most vital analytical technique in use. Multi-dimensional NMR experiments have enabled a structural analysis of complex natural products and proteins. However, in mixture analysis NMR is still facing difficulties. In many cases overlapping signals can t be resolved even with the help of multi-dimensional experiments. In this work, an NMR tool based on simple host-guest chemistry between analytes and macromolecules was developed. Diffusion ordered NMR spectroscopy (DOSY) measures the mobilities of compounds in an NMR sample. In a liquid state NMR sample, each of the analytes has a characteristic diffusion coefficient, which is proportional to the size of the analyte. With normal DOSY experiment, provided that the diffusion coefficients of the analytes differ enough, individual spectra of analytes can be extracted. When similar sized analytes differ chemically, an additive can be introduced into the sample. Since macromolecules in a liquid state NMR sample can be considered practically stationary, even faint supramolecular interaction can change the diffusion coefficient of the analyte sufficiently for a successful resolution in DOSY. In this thesis, polyvinylpyrrolidone and polyethyleneglycol enhanced DOSY NMR techniques, which enable mixture analysis of similar in size but chemically differing natural products, are introduced.

Preparation of Industrially Important Hydroxy Acids and Diacids from 2,2-Disubstituted Propane-1,3-Diols and Linear Primary Diols by Green Chemistry Methods

Environmentally benign and economical methods for the preparation of industrially important hydroxy acids and diacids were developed. The carboxylic acids, used in polyesters, alkyd resins, and polyamides, were obtained by the oxidation of the corresponding alcohols with hydrogen peroxide or air catalyzed by sodium tungstate or supported noble metals. These oxidations were carried out using water as a solvent. The alcohols are also a useful alternative to the conventional reactants, hydroxyaldehydes and cycloalkanes. The oxidation of 2,2-disubstituted propane-1,3-diols with hydrogen peroxide catalyzed by sodium tungstate afforded 2,2-disubstituted 3-hydroxypropanoic acids and 1,1-disubstituted ethane-1,2-diols as products. A computational study of the Baeyer-Villiger rearrangement of the intermediate 2,2-disubstituted 3-hydroxypropanals gave in-depth data of the mechanism of the reaction. Linear primary diols having chain length of at least six carbons were easily oxidized with hydrogen peroxide to linear dicarboxylic acids catalyzed by sodium tungstate. The Pt/C catalyzed air oxidation of 2,2-disubstituted propane-1,3-diols and linear primary diols afforded the highest yield of the corresponding hydroxy acids, while the Pt, Bi/C catalyzed oxidation of the diols afforded the highest yield of the corresponding diacids. The mechanism of the promoted oxidation was best described by the ensemble effect, and by the formation of a complex of the hydroxy and the carboxy groups of the hydroxy acids with bismuth atoms. The Pt, Bi/C catalyzed air oxidation of 2-substituted 2-hydroxymethylpropane-1,3-diols gave 2-substituted malonic acids by the decarboxylation of the corresponding triacids. Activated carbon was the best support and bismuth the most efficient promoter in the air oxidation of 2,2-dialkylpropane-1,3-diols to diacids. In oxidations carried out in organic solvents barium sulfate could be a valuable alternative to activated carbon as a non-flammable support. In the Pt/C catalyzed air oxidation of 2,2-disubstituted propane-1,3-diols to 2,2-disubstituted 3-hydroxypropanoic acids the small size of the 2-substituents enhanced the rate of the oxidation. When the potential of platinum of the catalyst was not controlled, the highest yield of the diacids in the Pt, Bi/C catalyzed air oxidation of 2,2-dialkylpropane-1,3-diols was obtained in the regime of mass transfer. The most favorable pH of the reaction mixture of the promoted oxidation was 10. The reaction temperature of 40°C prevented the decarboxylation of the diacids.

Schiff Base Complexes and their Assemblies on Surfaces

Schiff bases and their transition metal complexes are of significant current interest even though they have been prepared for decades. They have been used in various applications such as catalysis, corrosion protection, and molecular sensors. In this study, N-aryl Schiff base ketimine ligands as well as numerous new, differently substituted salen and salophen-type ligands and their cobalt(II), copper(II), iron(II), manganese(II), and nickel(II) complexes were synthesised. New solid state structures of the above compounds and the dioxygen coordination properties of cobalt(II) complexes and catalytic properties of three synthesised binuclear complexes were examined. The prepared complexes were applied in the formation of self-assembled layers on a polycrystalline gold surface and liquid-graphite interface. The effect of metal ion and ligand structure on the as-formed patterns was studied. When studying gold surfaces, a unique thiol-assisted dissolution of elemental gold was observed and a new thin gold foil preparation method was introduced. In the summary, synthesis, structures, and properties of Schiff base ligands and their transition metal complexes are described in detail and the applications of these reviewed. Assemblies of other complexes on a liquid-graphite interface and on a gold surface are also presented, and the surface characterisation methods and surfaces employed are described.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Comments on a decentralized control of linear multivariable systems

A strongly connected decentralized control system may be made single channel controllable and observable with respect to any channel by decentralized feedbacks. It is noted here that the system example considered by Corfmat and Morse to illustrate this fact is already single channel controllable and observable, with respect to one of the channels. An alternate example which fits into the situation is presented in this item.