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We consider a solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver. The frequency of parametric perturbation varies slowly and passes through a resonant value, which leads to a solution change. We obtain a new connection formula for the asymptotic solution before and after the resonance.
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t similar to s(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.
We construct a special asymptotic solution for the forced KdV equation. In the frame of the shallow water model this kind of the external driving force is related to the atmospheric disturbance. The perturbation slowly passes through a resonance and it leads to the solution exchange. The detailed asymptotic description of the process is presented.
Jüdisches Selbstverständnis im Wandel : jiddische Literatur zu Beginn des zwanzigsten Jahrhunderts
(1999)
Homopolymers of N-acryloyl glycinamide were prepared by reversible addition-fragmentation chain transfer polymerization in water. The formed macromolecules exhibit strong polymer-polymer interactions in aqueous milieu and therefore form thermoreversible physical hydrogels in pure water, physiological buffer or cell medium.
Cellulose is the most abundant biopolymer on earth. In this work it has been used, in various forms ranging from wood to fully processed laboratory grade microcrystalline cellulose, to synthesise a variety of metal and metal carbide nanoparticles and to establish structuring and patterning methodologies that produce highly functional nano-hybrids. To achieve this, the mechanisms governing the catalytic processes that bring about graphitised carbons in the presence of iron have been investigated. It was found that, when infusing cellulose with an aqueous iron salt solution and heating this mixture under inert atmosphere to 640 °C and above, a liquid eutectic mixture of iron and carbon with an atom ratio of approximately 1:1 forms. The eutectic droplets were monitored with in-situ TEM at the reaction temperature where they could be seen dissolving amorphous carbon and leaving behind a trail of graphitised carbon sheets and subsequently iron carbide nanoparticles. These transformations turned ordinary cellulose into a conductive and porous matrix that is well suited for catalytic applications. Despite these significant changes on the nanometre scale the shape of the matrix as a whole was retained with remarkable precision. This was exemplified by folding a sheet of cellulose paper into origami cranes and converting them via the temperature treatment in to magnetic facsimiles of those cranes. The study showed that the catalytic mechanisms derived from controlled systems and described in the literature can be transferred to synthetic concepts beyond the lab without loss of generality. Once the processes determining the transformation of cellulose into functional materials were understood, the concept could be extended to other metals and metal-combinations. Firstly, the procedure was utilised to produce different ternary iron carbides in the form of MxFeyC (M = W, Mn). None of those ternary carbides have thus far been produced in a nanoparticle form. The next part of this work encompassed combinations of iron with cobalt, nickel, palladium and copper. All of those metals were also probed alone in combination with cellulose. This produced elemental metal and metal alloy particles of low polydispersity and high stability. Both features are something that is typically not associated with high temperature syntheses and enables to connect the good size control with a scalable process. Each of the probed reactions resulted in phase pure, single crystalline, stable materials. After showing that cellulose is a good stabilising and separating agent for all the investigated types of nanoparticles, the focus of the work at hand is shifted towards probing the limits of the structuring and pattering capabilities of cellulose. Moreover possible post-processing techniques to further broaden the applicability of the materials are evaluated. This showed that, by choosing an appropriate paper, products ranging from stiff, self-sustaining monoliths to ultra-thin and very flexible cloths can be obtained after high temperature treatment. Furthermore cellulose has been demonstrated to be a very good substrate for many structuring and patterning techniques from origami folding to ink-jet printing. The thereby resulting products have been employed as electrodes, which was exemplified by electrodepositing copper onto them. Via ink-jet printing they have additionally been patterned and the resulting electrodes have also been post functionalised by electro-deposition of copper onto the graphitised (printed) parts of the samples. Lastly in a preliminary test the possibility of printing several metals simultaneously and thereby producing finely tuneable gradients from one metal to another have successfully been made. Starting from these concepts future experiments were outlined. The last chapter of this thesis concerned itself with alternative synthesis methods of the iron-carbon composite, thereby testing the robustness of the devolved reactions. By performing the synthesis with partly dissolved scrap metal and pieces of raw, dry wood, some progress for further use of the general synthesis technique were made. For example by using wood instead of processed cellulose all the established shaping techniques available for wooden objects, such as CNC milling or 3D prototyping, become accessible for the synthesis path. Also by using wood its intrinsic well defined porosity and the fact that large monoliths are obtained help expanding the prospect of using the composite. It was also demonstrated in this chapter that the resulting material can be applied for the environmentally important issue of waste water cleansing. Additionally to being made from renewable resources and by a cheap and easy one-pot synthesis, the material is recyclable, since the pollutants can be recovered by washing with ethanol. Most importantly this chapter covered experiments where the reaction was performed in a crude, home-built glass vessel, fuelled – with the help of a Fresnel lens – only by direct concentrated sunlight irradiation. This concept carries the thus far presented synthetic procedures from being common laboratory syntheses to a real world application. Based on cellulose, transition metals and simple equipment, this work enabled the easy one-pot synthesis of nano-ceramic and metal nanoparticle composites otherwise not readily accessible. Furthermore were structuring and patterning techniques and synthesis routes involving only renewable resources and environmentally benign procedures established here. Thereby it has laid the foundation for a multitude of applications and pointed towards several future projects reaching from fundamental research, to application focussed research and even and industry relevant engineering project was envisioned.