The Fredholm index of locally compact band-dominated operators on Lp(R)L^p (R)

We establish a necessary and sufficient criterion for the Fredholmness of a general locally compact band-dominated operator $A$ on $L^p(R)$ and solve the long-standing problem of computing its Fredholm index in terms of the limit operators of $A$. The results are applied to operators of convolution type with almost periodic symbol

Occupants in manifolds

Let K be a subset of a smooth manifold M. In some cases functor calculus methods lead to a homotopical formula for M minus K in terms of the subspaces M minus S, where S runs through the finite subsets of K.Comment: There is a sequel to this paper: title "Configuration categories and homotopy automorphisms". v2: some typos corrected, v3: some errors in section 1 corrected. v4: more errors corrected and therefore number of authors increased from 1 to 2. v5: more errors corrected especially in section 3. v6: just a few typos corrected and pointers adde

Aggregation of Red Blood Cells: From Rouleaux to Clot Formation

Red blood cells are known to form aggregates in the form of rouleaux. This aggregation process is believed to be reversible, but there is still no full understanding on the binding mechanism. There are at least two competing models, based either on bridging or on depletion. We review recent experimental results on the single cell level and theoretical analyses of the depletion model and of the influence of the cell shape on the binding strength. Another important aggregation mechanism is caused by activation of platelets. This leads to clot formation which is life saving in the case of wound healing but also a major cause of death in the case of a thrombus induced stroke. We review historical and recent results on the participation of red blood cells in clot formation

Designing dark energy afterglow experiments

Chameleon fields, which are scalar field dark energy candidates, can evade fifth force constraints by becoming massive in high-density regions. However, this property allows chameleon particles to be trapped inside a vacuum chamber with dense walls. Afterglow experiments constrain photon-coupled chameleon fields by attempting to produce and trap chameleon particles inside such a vacuum chamber, from which they will emit an afterglow as they regenerate photons. Here we discuss several theoretical and systematic effects underlying the design and analysis of the GammeV and CHASE afterglow experiments. We consider chameleon particle interactions with photons, Fermions, and other chameleon particles, as well as with macroscopic magnetic fields and matter. The afterglow signal in each experiment is predicted, and its sensitivity to various properties of the experimental apparatus is studied. Finally, we use CHASE data to exclude a wide range of photon-coupled chameleon dark energy models.Comment: 29 pages, 31 figures, 1 tabl

Development of new flux splitting schemes

Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for CFD. This is especially important for solution of complex three-dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for both their capability of resolving discontinuities and their sound theoretical basis in characteristic theory for hyperbolic systems. With this in mind, two new flux splitting techniques are presented for upwind differencing