Spectral flow of monopole insertion in topological insulators

Inserting a magnetic flux into a two-dimensional one-particle Hamiltonian leads to a spectral flow through a given gap which is equal to the Chern number of the associated Fermi projection. This paper establishes a generalization to higher even dimension by inserting non-abelian monopoles of the Wu-Yang type. The associated spectral flow is then equal to a higher Chern number. For the study of odd spacial dimensions, a new so-called `chirality flow' is introduced which, for the insertion of a monopole, is then linked to higher winding numbers. This latter fact follows from a new index theorem for the spectral flow between two unitaries which are conjugates of each other by a self-adjoint unitary.Comment: title changed; final corrections before publication; to appear in Commun. Math. Phy

Comet P/Tempel: Some highlights and conclusions from the 1988 apparition

From the brightness development and a sequence of imaging observations of the coma activity onset of comet P/Tempel 2 in 1988, it is concluded that there might have happened eruptive events of strong dust and gas outbursts during May and June 1988. A comparison of dust coma modeling calculations with CCD observations of the coma widely confirms Sekanina's nucleus model for the comet

High performance structures

Materials selection, structural geometry, proof testing and statistical screening, prestressing, and system energy as tools for designing optimum trusses and other high performance structure

Studies in prestressed and segmented brittle structures

Application of nonlinear bending theory to prestressed and segmented brittle structure

Multiphoton Bloch-Siegert shifts and level-splittings in spin-one systems

We consider a spin-boson model in which a spin 1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch-Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch-Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed.Comment: 14 pages, 3 figure

Laboratory studies on cometary crust formation: The importance of sintering

It is demonstrated by experiments and theoretical considerations that sintering processes, so far used to describe the densification of metal and ceramic powders, are relevant for icy materials and therefore probably also for comets. A theoretical model is presented which describes the evolution of so called sinter necks, the contact zone between ice particles. With this model the strength increase of a porous, loosley packed icy body is calculated in which the sinter necks grow by evaporation and condensation of water vapor at a constant temperature. Experiments with ice powders validate the model qualitatively. An increase in strength up to a factor of four is observed during isothermal sintering. In order to check the relevance of the experimental results and the basic theoretical ideas with respect to real comets, more exact theories and improved experiments taking into account additional mass transport mechanisms are needed

Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe or hexagon patterns are linearly stable, whereas square patterns and patterns involving more than three modes are unstable. In the case of hexagon patterns up- and down-hexagons can be simultaneously stable. The third-order, weakly nonlinear analysis predicts stable square patterns and super-hexagons for larger amplitudes. Direct simulations show, however, that in this regime the third-order weakly nonlinear analysis is insufficient, and these patterns are, in fact unstable

On Keller Theorem for Anisotropic Media

The Keller theorem in the problem of effective conductivity in anisotropic two-dimensional (2D) many-component composites makes it possible to establish a simple inequality $\sigma_{{\sf is}}^e(\sigma^{-1}_i)\cdot \sigma_{{\sf is}}^e(\sigma_k)> 1$ for the isotropic part $\sigma_{{\sf is}}^e(\sigma_k)$ of the 2-nd rank symmetric tensor ${\widehat \sigma}_{i,j}^e$ of effective conductivity.Comment: 1 page, 1 figur