Possibilities of formation or modification of polymers by means of chemical reactions during processing (polymer processing)

The trends for polymeric engineering materials are marked by the search for defined thermomechanical, plastic-elastic stability of dimension, and surface properties. This trend is caused by the demands for higher usage values of the polymers and more efficient processing technologies. The greatest chances are granted to the chemical modification and reactive compounding of known polymers to reach the aims of this development. Thermodynamically, most of the polymers are incompatible with each other and no sufficient disperse distribution is reached by only physical mixing. During the last 10 years a good compatibility at the interfaces has been found as one supposition and the influence of the viscosity of the polymer components and of the shear rate in the mixing machine as a further supposition to reach a fine-dispersed distribution. Polymer composites with fibres and fillers are a further importent group of materials. The properties of composites are also determined by the interactions in the interfaces, by the dispersity of the fibres and fillers, and by the physical properties of the interfaces. Polymer-analogous reactions, polymer blends, and polymer composites with and without low molecular reactants in the melt are decisively influenced by the parameters of the compounding machine. The quality of mixing, distribution of the residence time and of the shear rate, and the temperature profile of the reaction mixture are essential criterions for the course of the reaction. Continuous and quasi continuous technologies as, e. g., extruders and internal mixers are preferred. The lecture will deal with the present state and technical possibilities. Polymer syntheses in screw extruders are a new trend for the future. All these possibilities offer prospective chances of development.     

Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.     

Universal properties of two-dimensional boson droplets

We consider a system of N nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for N large, but below some critical value, the properties of the N-boson bound state are universal. In particular, the ratio of the binding energies of (N+1)- and N-boson systems, B(N+1)/B(N), approaches a finite limit, approximately 8.567, at large N. We also confirm previous results that the three-body system has exactly two bound states. We find for the ground state B(0)(3)=16.522 688(1)B2 and for the excited state B(1)(3)=1.270 409 1(1)B2.     

Phase control in a coherent superposition of degenerate quantum states through frequency control

We demonstrate a controlled phase change of π in a degenerate superposition by altering a laser frequency by only 10 MHz. The method relies on the preparation of an adiabatic state involving the M = ±2 and M = 0 states of the ³P₂ (J = 2) level of metastable neon. Dependent on the frequency, the preparation proceeds either by stimulated Raman adiabatic passage (STIRAP) or by coherent population trapping (CPT). In the former case the superposition is prepared by adiabatic transfer induced in an extended tripod linkage scheme. In the latter case population is optically pumped into the Zeeman manifold of the level ³P₂. The population which does not reach a dark state decays to the ground state of neon. The amplitudes and relative phases of the dark states differ for the two cases. The phase change is monitored using the method of phase-to-population mapping.     

Operator orderings and functional formulations of quantum and stochastic dynamics

We study the connection between operator ordering schemes and thec-number formulations of quantum mechanics, which are based on generating functionals and functional integrals. We show by explicit construction that different operator ordering schemes are related to different functional and functional integral formulations of quantum mechanics. The results of these considerations are applied to classical non-linear stochastic dynamics by using the formal analogy between the Fokker-Planck equation and the Schrödinger equation.     

A mixed finite element method for solving the nonstationary stokes equation

Summary This paper deals with a mixed finite element method for approximating a fourth order initial value problem arising from the nonstationary Stokes problem. For piecewise linear shape functions error estimates are given with convergence rates similar to the elliptic case. Some numerical computations will illustrate the theoretical results.