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#### Faculty / Organisational entity

A new method is used to investigate the tunneling between two weakly-linked Bose-Einstein con- densates confined in double-well potential traps. The nonlinear interaction between the atoms in each well contributes to a finite chemical potential, which, with consideration of periodic instantons, leads to a remarkably high tunneling frequency. This result can be used to interpret the newly found Macroscopic Quantum Self Trapping (MQST) effect. Also a new kind of first-order crossover between different regions is predicted.

Phase velocities of surface acoustic waves in several boron nitride films were investigated by Brillouin light scattering. In the case of films with predominantly hexagonal crystal structure, grown under conditions close to the nucleation threshold of cubic BN, four independent elastic constants have been determined from the dispersion of the Rayleigh and the first Sezawa mode. The large elastic anisotropy of up to c11/c33 = 0.1 is attributed to a pronounced texture with the c-axes of the crystallites parallel to the film plane. In the case of cubic BN films the dispersion of the Rayleigh wave provides evidence for the existence of a more compliant layer at the substrate-film interface. The observed broadening of the Rayleigh mode is identified to be caused by the film morphology.

A pure Yang-Mills theory extended by addition of a quartic term is considered in order to study the transition from the quantum tunneling regime to that of classical, i.e. thermal, behaviour. The periodic field confiurations are found, which interpolate between the vacuum and sphaleron field configurations. It is shown by explicit calculation that only smooth second order transitions occur for all permissible values of the parameter A introduced with the quartic term. The theory is one of the rare cases which canbe handled analytically.

Power-ordered sets are not always lattices. In the case of distributive lattices we give a description by disjoint of chains. Finite power-ordered sets have a polarity. We introduct the leveled lattices and show examples with trivial tolerance. Finally we give a list of Hasse diagrams of power-ordered sets.

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.

In this chapter, the quantitative numerical simulation of the behavior of deformable linear objects, such as hoses, wires and leaf springs is studied. We first give a short review of the physical approach and the basic solution principle. Then, we give a more detailed description of some key aspects: We introduce a novel approach concerning dynamics based on an algorithm very similar to the one used for (quasi-) static computation. Then, we look at the plastic workpiece deformation, involving a modified computation algorithm and a special representation of the workpiece shape. Then, we give alternative solutions for two key aspects of the algorithm, and investigate the problem of performing the workpiece simulation efficiently, i.e., with desired precision in a short time. In the end, we introduce the inverse modeling problem which must be solved when the gripper trajectory for a given task shall be generated.

Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unline the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used delta-function repulsive potential in the limit of a width parameter d going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a delta-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of d gives rise to a predictionof swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a delta-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution, which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is used to explore long chain rheological properties by extrapolating results obtained numerically for finite chains, to the limit of infinite chain length.

Abstract: Standard methods of nonlinear dynamics are used to investigate the stability of particles, branes and D-branes of abelian Born-Infeld theory. In particular the equation of small fluctuations about the D-brane is derived and converted into a modified Mathieu equation and - complementing earlier low-energy investigations in the case of the dilaton-axion system - studied in the high-energy domain. Explicit expressions are derived for the S-matrix and absorption and reflection amplitudes of the scalar fluctuation in the presence of the D-brane. The results confirm physical expectations and numerical studies of others. With the derivation and use of the (hitherto practically unknown) high energy expansion of the Floquet exponent our considerations also close a gap in earlier treatments of the Mathieu equation.