A route to chaos in a nonlinear oscillator with delay

Summary The paper presents an analysis of the transition from regular to chaotic motion in a Van der Pol-Duffing's oscillator with delay after a Hopf bifurcation. The conditions for the occurrence of the Hopf bifurcation have been determined by means of the approximate method. For the parameters near the bifurcation point a computer simulation of the vibrating system had been performed and the evolution of the system from regular motion to chaos has been analysed at the decrease of the value of the dimensionless damping coefficient.With 2 Figures     

The incorporation of yield surface distortion into a unified constitutive model,part 2: Predictive capabilities

Summary The MATMOD-4V-DISTORTION model has been derived [1] with the intent of improving the MATMOD-4V model by adding the capability to predict distortions of small strain offset yield surfaces. This model is compared against a variety of experimental data to verify its behavior. Model simulations are compared with experimental data for proportional and nonproportional prestress histories and the effect of yield definition is also investigated. Finally, the same model which predicts a flattening of the yield surface in space is used to predict a rotation of the yield surface in ₁-₂ coordinates.With 9 Figures     

Stromdichte- und Magnetfeldverteilung bei einer Anordnung aus Platten und vielen parallelen Stromleitern

Übersicht Die vorliegende Arbeit befaßt sich mit der gesamten Stromdichte- und Magnetfeldverteilung in vielen flachen leitenden Platten konstanter Permeabilität, die bei einer Anordnung aus diesen Platten und vielen parallelen stromführenden Leitern angeordnet in mehreren Lagen entsteht. Unter Anwendung der Maxwellschen Differentialgleichungen und durch Einführung des Vektorpotentials werden allgemeine Gleichungen für die Komponenten der magnetischen Induktion im zweidimensionalen Feldraum aufgestellt. Die Stromdichteverteilung in den leitenden Platten, in denen Wirbelströme entstehen, wird aus dem Vektorpotential hergeleitet. Zunächst werden die Platten unendlich lang angenommen und die entsprechenden Gleichungen in Integralform aufgestellt, für deren Lösung die Gauss-Laguerresche Methode angewandt wird. Dann werden die Platten beiderseits durch Eisenwände begrenzt, womit die Gleichungen unter Berücksichtigung der Randbedingungen in Summenform ausgedrückt werden.

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Distribution of current and magnetic field density in flat conductive plates in an array composed from plates and many parallel conductors

Contents In the present research work the overall distribution of current and magnetic field density in many flat plates of constant magnetic permeability has been investigated, which applies to an array composed from the flat plates and many parallel conductors installed in many layers. Use of Maxwell's differential equations and vector potential results in general equations for the components of magnetic density in two dimensional field space. The distribution of current density in the conductive plates, where eddy currents are taken into account, is obtained from the vector potential. Initially the flat plates are considered being of infinite length, and with appropriate arrangement of the boundary conditions, the model applies to flat plates limited to both sides by iron partitions. Examples are given for both cases, where for the plates of infinite length the Gauss-Laguerre method is applied.

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Liste der Symbole A Vektorpotential - B Magnetische Induktion - I ₁ Stromstärke eines Leiters - N ₁ Anzahl der parallelen Leiter - N ₂ Anzahl der parallelen Platten - Permeabilität des Plattenmaterials - _r Relative Permeabilitätskonstante des Plattenmaterials - Leitfähigkeit - b Breite des Hauptstreukanals - i Stromdichte der Platten samt Wirbelströme - h ₁ Höhe der Leiter - a ₁ Breite der Leiterlagen - a Plattendicke - s Breite des Nebenstreukanals - c Abstand der letzten Platte von der Eisenwand - g Plattenhöhe - x, z, , Dimensionen - Q, K Integrationskonstanten - k ganze Zahl     

A combinatorial study of the rigidity of planar structures

Summary A combinatorial method is presented for examining the rigidity of planar structures. In this approach, an expansion process is used for the formation of a statically determinate substructure, known as a -tree of a structure. The algorithm of Lováz and Yemini, and the method of Sugihara are employed for the recognition of the elementary subgraphs, during this process.With 4 Figures     

Acoustic waves in solids with random cavities,II: Energy density considerations

Summary The propagation of acoustic plane and line-polarized waves in an isotropic solid containing random cavities is studied theoretically and experimentally. The effect of the cavities on the energy density and macroscopic propagation parameters of the acoustic waves is considered and the relationships between the cavities volume concentration, their average dynamic shape factor and the dynamic overall stiffness moduli of the solid are derived in the long wave approximation.     

From Natural Methylation to Versatile Alkylations Using Halide Methyltransferases

Halide methyltransferases (HMTs) enable the enzymatic synthesis of S-adenosyl-l -methionine (SAM) from S-adenosyl-l -homocysteine (SAH) and methyl iodide. Characterisation of a range of naturally occurring HMTs and subsequent protein engineering led to HMT variants capable of synthesising ethyl, propyl, and allyl analogues of SAM. Notably, HMTs do not depend on chemical synthesis of methionine analogues, as required by methionine adenosyltransferases (MATs). However, at the moment MATs have a much broader substrate scope than the HMTs. Herein we provide an overview of the discovery and engineering of promiscuous HMTs and how these strategies will pave the way towards a toolbox of HMT variants for versatile chemo- and regioselective biocatalytic alkylations.     

Eco‐friendly durable press finishing of cellulose‐containing fabrics

To impart easy‐care properties to cellulose‐containing fabrics along with avoiding any harmful effects of formaldehyde on both the health and the environment, attempts have been made to use citric acid (CA) as an ester crosslinking agent along with different catalytic systems in the absence and presence of certain additives. Further, fixation conditions, type of crosslinking agent, as well as type of substrate have been studied. Results revealed that the enhancement in carboxyl content, performance properties, and the decrease in tear strength (TS) as well as in whiteness indices (WI) of the finished fabric samples were increased by increasing CA concentration up to 80 g/L and by raising thermofixation temperature from 140 up to 180°C for 90 s. Inclusion of triethanolamine hydrochloride (TEA. HCl), decreased the carboxyl content, TS, color strength K/S, as well as oily stain release rating (SRR) of the finished fabric samples along with an increase in bound nitrogen (%N), wrinkle recovery angle WRA, and an improvement in WI without affecting the durable press rating (DP). Within the range examined (0–30 g/L), increasing PEG‐600 concentration improved the wet resiliency, TS, as well as WI properties of the finished samples. Increasing DMDHEU ratio in the CA/DMDHEU crosslinking system gave rise to an increase in %N, WRA (dry and wet), DP, as well as in free CH₂O of finished fabrics, along with a slight improvement in WI values. On the other hand, the TS, carboxyl content, K/S, SRR values of the finished fabric samples were lower at a higher DMDHEU ratio. Increase in carboxyl content, %N, WRA (dry and wet), DP and SRR, as well as extent of post dyeing (K/S) of the treated fabric samples upon using different ester crosslinking agents followed the descending order: citric acid > pyromellitic dianhydride. The opposite holds true for the TS, and WI values. Among the esterifying catalysts used, and for a given set of finishing conditions, NaH₂PO₂ · H₂O proved to be the most effective one, and the following order of effectiveness may be drawn: NaH₂PO₂ · H₂O > K₂HPO₄ > Na₃–citrate > Na₂–tartrate. Inclusion of silicone softener in the finishing formulation brought about an improvement in softeness degree, WRA, %N, DP, TS as well as K/S values along with a decrease in carboxyl content, SRR, and WI values of the treated fabric samples, regardless of the used silicone softener.The performance properties of the finished fabric samples were determined by the type and nature of the substrate. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2243–2253, 2002     

Synthesis,characterization, and thermal properties of phosphorus‐containing,wholly aromatic thermotropic copolyesters

A series of phosphorus‐containing, wholly aromatic thermotropic copolyesters from acetylated 2‐(6‐oxide‐6H‐dibenz〈c,e〉〈1,2〉oxa phosphorin‐6‐yl)‐1,4‐dihydroxy phenylene, p‐acetoxybenzoic acid, terephthalic acid, and isophthalic acid were prepared by melting polycondensation. The structure and basic properties of the polymers, such as the glass‐transition temperature (T_g), melting temperature (T_m), thermal stability, crystallinity, and liquid crystallinity, were investigated with Fourier transform infrared, elemental analysis, differential scanning calorimetry (DSC), thermogravimetric analysis, wide‐angle X‐ray diffraction, and hot‐stage polarizing optical microscopy. The copolyesters had relatively high T_g values ranging from 183 to 192°C. The T_m values obtained from DSC curves for samples P‐20 and P‐25 were 290 and 287°C, respectively (where the number in the sample name indicates the molar fraction of the phosphorus‐containing monomer in the reactants). The initial flow temperatures of other samples observed with hot‐stage polarizing microscopy were 271–290°C. The 5% degradation temperatures in nitrogen ranged from 431 to 462°C, and the char yields at 640°C were 41–52%. All the copolyesters, except P‐40, were thermotropic and nematic. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1278–1284, 2002     

Antimicrobial protection of cotton and cotton/polyester fabrics by radiation and thermal treatments. I. Effect of ZnO formulation on the mechanical and dyeing properties

Cotton and cotton/polyester fabrics were treated against microbial attack by applying a formulation based essentially on ZnO under high‐energy radiation and thermal curing. To achieve the homogeneity and the reactivity of the treating formulation, a binder (Impron MTP) and a dispersing agent (Setamol WS) were used with ZnO. The antimicrobial property of the fabrics was evaluated, in terms of mechanical properties, by a soil burial test. Moreover, the effect of antimicrobial finishing on the dyeing properties in terms of color strength was investigated. It was found that the best composition that affords the best antimicrobial protection to cotton fabrics contains 2% ZnO, 2% binder, and 1% dispersing agents. For the cotton/polyester blend, the best results were achieved at the same conditions except the ZnO was 1%. It was found that the treatment under the effect of electron‐beam irradiation is better than that of gamma irradiation and thermal curing. The results showed that when the finishing process was carried out before dyeing with a reactive dye, it affects the color strength rather than performing the finishing after the dyeing process. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1129–1137, 2003