Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains

It is well established that the solitary waves of FPU-type chains converge in the high-energy limit to traveling waves of the hard-sphere model. In this paper we establish improved asymptotic expressions for the wave profiles as well as an explicit formula for the wave speed. The key step in our approach is the derivation of an asymptotic ODE for the appropriately rescaled strain profile.Comment: revised version with corrected typos; 25 pages, several figure

Design, Synthesis and Analysis of Self-Assembling Triangulated Wireframe DNA Structures

The field of DNA nanotechnology offers a wide range of design strategies with which nanometer-sized structures with a desired shape, size and aspect ratio can be built. The most established techniques in the field rely on close-packed 'solid' DNA nanostructures produced with either the DNA origami or the single-stranded tile techniques. These structures depend on high-salt buffer solutions and require more material than comparable size hollow wireframe structures. This dissertation explores the construction of hollow wireframe DNA nanostructures composed of equilateral triangles. To achieve maximal material efficiency the design is restricted to use a single DNA double helix per triangle edge. As a proof of principle, the DNA origami technique is extended to produce a series of truss structures including the flat, tetrahedral, octahedral, or irregular dodecahedral truss designs. In contrast to close packed DNA origami designs these structures fold at low-salt buffer conditions. These structures have defined cavities that may in the future be used to precisely position functional elements such as metallic nanoparticles or enzymes. The design process of these structures is simplified by a custom design software. Next, the triangulated construction motif is extended to the single-stranded DNA tile technique. A collection of finite structures, as well as one-dimensional crystalline assemblies is explored. The ideal assembly conditions are determined experimentally and using molecular dynamics simulations. A custom design software is presented to simplify the design and handling of these structures. At last, the cost-effective prototyping of triangulated wireframe DNA origami structures is explored. This is achieved through the introduction of single-stranded “gap” regions along the triangle edges. These gap regions are then filled using a DNA polymerase rather than by synthetic oligonucleotides. This technique also allows the mechanical transformation of these structures, which is exemplified by the transition of a bent into a straight structure upon completion of the gap filling.:Abstract v Publications vii Acknowledgements ix Contents xi Chapter 1 A short introduction into DNA nanotechnology 1 1.1 Nanotechnology 1 1.1.1 Top down 1 1.1.2 Bottom up 3 1.2 Deoxyribonucleic acid (DNA) 4 1.3 DNA Nanotechnology 6 1.3.1 Tile based assembly 9 1.3.2 DNA origami and single-stranded tiles 10 1.3.3 Some applications of DNA nanotechnology 12 1.3.4 Wireframe structures 15 1.3.5 Computational tools and DNA nanotechnology. 17 Chapter 2 Motivation and objectives 19 Chapter 3 Design and Synthesis of Triangulated DNA Origami Trusses 20 3.1 Introduction 20 3.2 Results and Discussion 21 3.2.1 Design 21 3.2.2 Nomenclature and parameters of the tube structures 23 3.2.3 Gel electrophoreses analysis 25 3.2.4 Imaging of the purified structures 26 3.2.5 Optimizing the folding conditions 28 3.2.6 Comparison to vHelix 29 3.3 Conclusions 29 3.4 Methods 30 3.4.1 Standard DNA origami assembly reaction. 30 3.4.2 Gel purification. 30 3.4.3 AFM sample preparation. 31 3.4.4 TEM sample preparation. 31 3.4.5 Instructions for mixing the staple sets. 31 Chapter 4 Triangulated wireframe structures assembled using single-stranded DNA tiles 33 4.1 Introduction 33 4.2 Results and Discussion 35 4.2.1 Designing the structures 35 4.2.2 Synthesis of test structures 37 4.2.3 Molecular dynamics simulations of 6-arm junctions 38 4.2.4 Assembly of the finite structures 40 4.2.5 Influence of salt concentration and folding times 42 4.2.6 Molecular dynamics simulations of the rhombus structure 43 4.2.7 1D SST crystals 44 4.2.8 Controlling the crystal growth 46 4.3 Conclusions 48 4.4 Methods 49 4.4.1 SST Folding 49 4.4.2 Agarose Gel Electrophoresis 49 4.4.3 tSEM Characterization 49 4.4.4 AFM Imaging 49 4.4.5 AGE-Based Folding-Yield Estimation 49 4.4.6 Molecular Dynamics Simulations 50 Chapter 5 Structural transformation of wireframe DNA origami via DNA polymerase assisted gap-filling 52 5.1 Introduction 52 5.2 Results and Discussion 54 5.2.1 Design of the Structures 54 5.2.2 Folding of Gap-Structures 56 5.2.3 Inactivation of Polymerase. 57 5.2.4 Secondary Structures. 58 5.2.5 Folding Kinetics of Gap Origami. 60 5.3 Conclusions 61 5.4 Methods 62 5.4.1 DNA origami folding 62 5.4.2 Gap filling of the wireframe DNA origami structures 63 5.4.3 Agarose gel electrophoresis 63 5.4.4 PAGE gel analysis 63 5.4.5 tSEM characterization 64 5.4.6 AFM imaging 64 5.4.7 AGE based folding-yield estimation 64 5.4.8 Gibbs free energy simulation using mfold 65 5.4.9 List of sequence for folding the DNA origami triangulated structures 65 Chapter 6 Summary and outlook 67 Appendix 69 A.1 Additional figures from chapter 369 A.2 Additional figures from chapter 4 77 A.3 Additional figures from chapter 5 111 Bibliography 127 Erklärung 13

A uniqueness result for a simple superlinear eigenvalue problem

We study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein-Rutmann arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.Comment: revised version with enhanced introduction; 21 pages, several figure

Subsonic phase transition waves in bistable lattice models with small spinodal region

Phase transitions waves in atomic chains with double-well potential play a fundamental role in materials science, but very little is known about their mathematical properties. In particular, the only available results about waves with large amplitudes concern chains with piecewise-quadratic pair potential. In this paper we consider perturbations of a bi-quadratic potential and prove that the corresponding three-parameter family of waves persists as long as the perturbation is small and localised with respect to the strain variable. As a standard Lyapunov-Schmidt reduction cannot be used due to the presence of an essential spectrum, we characterise the perturbation of the wave as a fixed point of a nonlinear and nonlocal operator and show that this operator is contractive in a small ball in a suitable function space. Moreover, we derive a uniqueness result for phase transition waves with certain properties and discuss the kinetic relation.Comment: revised version with extended introduction, improved perturbation method, and novel uniqueness result; 20 pages, 5 figure

Langfristige Entwicklungen auf dem Markt für Energierohstoffe

Die Preise für Energierohstoffe sind derzeit auf einem historischen Höchststand. Diese Entwicklung ist wesentlich auf den Nachfrageanstieg aus den asiatischen Schwellen ländern zurückzuführen. Wird sich dieser Trend steigender Preise bei begrenzt verfügbaren Rohstoffreserven weiter fortsetzen? --

The spatial scale of organic chemicals in multimedia fate modeling: Recent developments and significance for chemical assessment

In the last years, the spatial range (SR) or characteristic travel distance (CTD) of organic chemicals has found increasing scientific interest as an indicator of the long-range transport (LRT) potential and, in combination with persistence, as a kind of ‘hazard' indicator on the exposure level. This development coincides with European debates about more effective and more preventive approaches to the chemicals assessment, and about an international, legally-binding instrument for the phase out of persistent organic pollutants (POPs). Persistence and LRT potential are important issues in these debates. Here, the development of the concept of assessing the spatial scale from early ideas in the 1970s and 1980s to recent studies in the field of multimedia fate and transport modeling is summarized. Different approaches to the modeling of environmental transport (advective and dispersive) and different methods for quantifying the SR or CTD are compared. Relationships between SR or CTD and different persistence measures are analyzed. Comparison of these relationships shows that conclusions for chemical assessment should be based on an evaluation of different persistence and spatial scale measures. The use of SR or CTD and persistence as hazard indicators in the chemicals assessment is illustrate