Zero Modes of Rotationally Symmetric Generalized Vortices and Vortex Scattering

Zero modes of rotationally symmetric vortices in a hierarchy of generalized Abelian Higgs models are studied. Under the finite-energy and the smoothness condition, it is shown, that in all models, $n$ self-dual vortices superimposed at the origin have $2n$ modes. The relevance of these modes for vortex scattering is discussed, first in the context of the slow-motion approximation. Then a corresponding Cauchy problem for an all head-on collision of $n$ vortices is formulated. It is shown that the solution of this Cauchy problem has a $\frac{\pi}{n}$ symmetry.Comment: 12 pages. late

Aircraft Fuel Consumption - Estimation and Visualization

In order to uncover the best kept secret in today's commercial aviation, this project deals with the calculation of fuel consumption of aircraft. With only the reference of the aircraft manufacturer's information, given within the airport planning documents, a method is established that allows computing values for the fuel consumption of every aircraft in question. The aircraft's fuel consumption per passenger and 100 flown kilometers decreases rapidly with range, until a near constant level is reached around the aircraft's average range. At longer range, where payload reduction becomes necessary, fuel consumption increases significantly. Numerical results are visualized, explained, and discussed. With regard to today's increasing number of long-haul flights, the results are investigated in terms of efficiency and viability. The environmental impact of burning fuel is not considered in this report. The presented method allows calculating aircraft type specific fuel consumption based on publicly available information. In this way, the fuel consumption of every aircraft can be investigated and can be discussed openly

The Optical Soliton Contents of some Special Input Pulses

The optical soliton contents of some special input pulses and their Galilei transforms will be determined by solving the linear eigenvalue problem associated with the non-linear Schrödinger equation. The special cases discussed are the initial envelope function of width a and height β, the initial envelope function —iβ*exp(—α|x|) and the super-Gaussian initial pulse. Throughout, we compare our problem to the Korteweg-de Vries problem where a good understanding can be gained through Sturm-Liouville theory

Statics and Dynamics of Classical Yang-Mills-Higgs Systems: Some Recent Developments

Some classical Yang-Mills-Higgs solutions, all characterized by an underlying nontrivial topology, are studied. First, the explicit construction of magnetic n-pole solutions is briefly reviewed. Second, theories which allow for noncontractible loops and static saddle points which result from this type of nontrivial topology are exhibited. We then turn to time-dependent solutions. Here, we first state the underlying ideas for the description of the scattering of slowly-moving monopoles. Finally, Segal’s theorem is discussed and the existence proofs for time-dependent vortices and monopoles, which apply to the equations of motion without any approximation, are outlined

Time Dependent Vortices and Monopoles

We discuss the relevance of global existence proofs. The underlying mathematical theory is outlined, and it is shown how additional problems in the case of vortices and monopoles can be overcome. Ways of building on the existence proofs are indicated

EC56-110 Pasture Balance for Eastern Nebraska

Extension Circular 56-110: This is about pasture balance for Eastern Nebraska. It is a guide for planning and analyzing your farm pasture program

EC56-113 Pasture Balance for Panhandle and Southwestern Nebraska

Extension Circular 56-113: This is about pasture balance for Panhandle and Southwestern Nebraska. It is a guide for planning and analyzing your farm pasture program

4-H Range Management and Conservation Club Manual : Extension Circular 1-31-2

Achievement in range management based on the identification and evaluation of Imported plants

EC56-110 Pasture Balance for Eastern Nebraska

Extension Circular 56-110: This is about pasture balance for Eastern Nebraska. It is a guide for planning and analyzing your farm pasture program