Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

Nanotechnology attempts to control matter at the nanometer scale so that new types of materials, components and devices for a wide variety of applications can be developed. There are two approaches possible. The first stems from semiconductor technology in which improvements in processing small structures have led to a drastic reduction in the size of electronic components. The inverse approach - which is used in this work - orientates itself around structures based on biological systems, in which highly dynamic nanometer size components assemble themselves.

In this thesis it is shown how defined structures with sizes ranging from nanometers to micrometres and made up of DNA molecules can self assemble. Self-assembly has four defining features: structured particles, a suitable environment, a driving force and reversible binding. DNA molecules are relatively stable and can be synthesised with arbitrary sequences of four units, diffuse freely in an aqueous buffer under Brownian motion, and can bind and unbind (using hydrogen bonding) with one another in the practical temperature range between 0 and 100°C. They are thus useful building blocks for self-assembly.

A review is provided of some physical properties of DNA, and of self-assembled DNA ‘motifs’ and devices developed to date, along with examples that have been demonstrated here in the laboratory. Such examples include DNA nanotubes, lattices, and ‘origami’ structures.

The idea of assembling structures - not by creating and breaking hydrogen bonds using temperature changes - but rather by changing the concentration of small molecules known as denaturants is introduced. The denaturants also form hydrogen bonds and can occupy the binding sites of the DNA molecules. Decreasing the concentration of denaturants frees the binding sites and allows the self-assembly of structures. This is demonstrated with successful motifs, and provides an isothermal assembly technique that allows the use of many temperature-sensitive components in DNA self-assembly.

It is shown that self-assembled motifs are useful as templates for nanoscale objects such as fluorescent molecules, which can be set out in defined geometries. Moreover, using newly developed optical super-resolution techniques, such geometries are resolved below the optical diffraction limit, providing the possibility for nanoscale optical calibration standards.

And finally the intrinsic stability of three-dimensional structures as compared to two-dimensional structures is investigated, in that the assembly and ‘melting’ of DNA nanotubes is shown to be fundamentally different to that of DNA lattices, with the closed form of the tubes providing a natural and significantly higher stability. This will be useful for designing and building stronger structures in DNA nanotechnology.

Active Galactic Nuclei (AGNs) are among the most luminous objects in the universe. At the center of an AGN, there is a SuperMassive Black Hole (SMBH) with a mass above million Solar mass, which is believed to be the engine of a huge energy output. Blazars are a subclass of AGNs, which usually have bipolar jets, one of which is pointing towards us. Markarian 421 (Mrk421) is one of the bright and nearby established TeV blazars. Its TeV emission was first discovered by the Whipple telescope in 1992 and it became one of the most studied extra-galactic objects in the TeV regime. Mrk421 shows strong variabilities in time and amplitude in different energy regimes.

The Mrk421 data collected so far from many historic multiwavelength observations is not yet sufficient to fully constrain the theoretical models. In particular, it is not yet clear whether the leptonic or hadronic processes play a decisive role inside the jets.

Due to short duty cycles and limited observation time, studies of bright TeV (E > 100 GeV) blazars are mostly restricted to flaring episodes or short time period (a few days to weeks) of multiwavelength campaigns. However, to study these objects long time monitoring is needed in order to constrain theoretical jet models. Only unbiased long-term studies are adequate for the determination of flaring states probabilities and for estimating the statistical significance of possible correlations between TeV flaring states and other observables, like X-ray or neutrinos. Besides, regular observations can also provide triggers for multiwavelength ToO observations. This is particularly necessary for identifying and studying orphan TeV flares.

MAGIC has observed Mrk421 since 2004 and then constantly monitored this source from 2006. In this thesis, the Mrk421 data taken from 2005 to 2008 will be presented. The physics results from several times of joint observations will be also discussed.

To further increase the sensitivity of the MAGIC telescope, a second telescope was built. The photosensors, PMTs, with light collectors, Winston Cones, of the second telescope were tested in order to know the performance of the new system. The different characteristics of the PMTs and their performance tests will be also described.

This thesis is concerned with two approaches on the singularity problem of the general theory of relativity. The first is of bottom-up nature. We start from Einstein's well established general relativity and make an educated guess for an asymptotically equivalent but non-singular theory. In the second approach we take the top-down perspective starting with the assumption that string theory gives the fundamental description of nature and analyse the resulting low energy effective theory.

Our bottom-up approach is an application of the limiting curvature hypothesis to anisotropic cosmologies. This extends the success for isotropic cosmologies of Brandenberger et al. Applying the LCH, they constructed a theory in which all homogeneous and isotropic solutions are singularity free. Due to the non-analytic nature of the equations we were unable repeat the proof in the anisotropic case, but analytical and numerical analysis produce circumstantial evidence for a resolution of the singularity in this case as well. Generically this resolution seems not to involve a de Sitter phase as expected. Instead it would interpolate between a contracting anisotropic universe and a universe, that time-symmetrically expands anisotropically. During this transition spacetime evolves through a nearly flat, Minkowski phase. This solution could represent an alternative to the so-called bounce solutions as they appear in pre-big-bang scenarios.

In our top-down approach we construct a simple model in type IIA super string theory. With a non-BPS D7 or D9 brane we introduce a tachyonic degree of freedom. Its potential is influenced by the compact background wrapped by the brane. In a way the mass can be tuned by the size of the compact dimension. We use a truncated action which was constructed in order to approximate the full string theory result for the dynamical creation and decay of non-BPS branes quite accurately. Taking the lowest order effective action for metric, dilaton and an effective action for the open tachyonic mode, we obtaine bounce solutions. The

bounce results from the positivity of the pressure of the tachyon field in our Lagrangian. Both curvature and time derivative of the dilaton remain small during our bounce so that the gravitational sector behaves entirely classical. Asymptotically our bounce solutions are similar to pre-big bang and post-big bang solutions respectively. Thus there remain singularities in the curvature and the dilaton before or after the bounce. These asymptotic string frame curvature singularities can be resolved by the ad hoc addition of a potential term, that might result from alpha' corrections in the open string sector. Exact calculation of the corrections would be necessary in order to give a more precise picture.

We derive predictions for Yukawa coupling ratios within Grand Unified Theories generated from operators with mass dimension four and five. These relations are a characteristic property of unified flavour models and can reduce the large number of free parameters related to the flavour sector of the Standard Model.

The Yukawa couplings of the down-type quarks and charged leptons are affected within supersymmetric models by tan beta-enhanced threshold corrections which can be sizeable if tan beta is large. In this case their careful inclusion in the renormalisation group evolution is mandatory. We analyse these corrections and give simple analytic expressions and numerical estimates for them.

The threshold corrections sensitively depend on the soft supersymmetry breaking parameters. Especially, they determine the overall sign of the corrections and therefore if the affected Yukawa couplings are enhanced or suppressed. In the minimal supersymmetric extension of the Standard Model many free parameters are introduced by supersymmetry breaking about which we make some plausible assumptions in our first simplified approach. In a second, more sophisticated approach we use three common breaking schemes in which all the soft breaking parameters at the electroweak scale can be calculated from only a handful of parameters. Within the second approach, we apply various phenomenological constraints on the supersymmetric parameters and find in this way new viable Yukawa coupling relations, for example y_mu/y_s = 9/2 or 6 or y_tau/y_b = 3/2 in SU(5).

Furthermore, we study a special class of quark mass matrix textures for small tan beta where theta_{13}^u = theta_{13}^d = 0. We derive sum rules for the quark mixing parameters and find a simple relation between the two phases delta_{12}^u and delta_{12}^d and the right unitarity triangle angle alpha which suggests a simple phase structure for the quark mass matrices where one matrix element is purely imaginary and the remaining ones are purely real.

To complement the aforementioned considerations, we give two explicit flavour models in a SU(5) context, one for large and one for small tan beta which implement the Yukawa coupling relations mentioned before. The models have interesting phenomenological consequences like, for example, quasi-degenerate neutrino masses in the case of small tan beta.