Orthogonal Polynomials and Exact Correlation Functions for Two Cut Random Matrix Models

Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support a $Z_2$ symmetric distribution is obtained. This results in an exact explicit expression for the kernel at large $N$ which determines all eigenvalue correlators. The oscillating and smooth parts of the two point correlator are extracted and the universality of local fine grained and smoothed global correlators is established.Comment: 15 pages, LaTex, a paragraph added in note added:, three references added. accepted in Nucl. Phys.

More Examples of Non-Rational Adjoint Groups

We give a recursive construction to produce examples of quadratic forms q_n in the n-th power of the fundamental ideal in the Witt ring whose corresponding adjoint groups PSO(q_n) are not stably rational. Computations of the R-equivalence classes of adjoint classical groups by A.S. Merkurjev are used to show that these groups are not R-trivial. This extends earlier results of A.S. Merkurjev and P.Gille where the forms considered have non-trivial and trivial discriminants respectively

Dean Flow Dynamics in Low-Aspect Ratio Spiral Microchannels

A wide range of microfluidic cell-sorting devices has emerged in recent years, based on both passive and active methods of separation. Curvilinear channel geometries are often used in these systems due to presence of secondary flows, which can provide high throughput and sorting efficiency. Most of these devices are designed on the assumption of two counter rotating Dean vortices present in the curved rectangular channels and existing in the state of steady rotation and amplitude. In this work, we investigate these secondary flows in low aspect ratio spiral rectangular microchannels and define their development with respect to the channel aspect ratio and Dean number. This work is the first to experimentally and numerically investigate Dean flows in microchannels for Re > 100, and show presence of secondary Dean vortices beyond a critical Dean number. We further demonstrate the impact of these multiple vortices on particle and cell focusing. Ultimately, this work offers new insights into secondary flow instabilities for low-aspect ratio, spiral microchannels, with improved flow models for design of more precise and efficient microfluidic devices for applications such as cell sorting and micromixing

Graphene with wedge disclination in the presence of intrinsic and Rashba spin orbit couplings

In this article, the modified Kane-Mele Hamiltonian is derived for graphene with wedge disclination and spin orbit couplings (intrinsic and Rashba). The wedge disclination changes the flat lattice into the conical lattice and hence modifies the spin orbit couplings. The Hamiltonian is exactly solved for the intrinsic spin orbit interaction and perturbatively for the Rashba spin orbit interaction. It is shown that there exists the Kramer's degenerate midgap localized spin separated fluxon states around the defect. These zero energy spin separated states occur at the external magnetic flux value $\Phi\pm\Delta\Phi$. The external magnetic flux $\Phi$ is introduced to make the wave-function periodic when the electron circulates around the defect. It is found that this separation occurs due to the effect of the conical curvature on the spin orbit coupling. Further, we find these results are robust to the addition of the Rashba spin orbit interaction which is important for the application to spintronics and nanoelectronics.Comment: 6 pages ,3 figures ,Change in titl

Rassismus in Deutschland. Kein Thema bei der UN?

Ein beträchtlicher Teil der Klient/inn/en der Sozialen Arbeit erlebt diverse Formen von Rassismus in Deutschland. Diese zu erkennen, sie als solche zu benennen - vor allen Dingen aber gegen sie vorzugehen erfordert Mut und Ressourcen auf Seiten der Betroffenen genauso wie Wissen und Ressourcen auf Seiten der Sozialarbeitenden. Eine Durchsicht der Beschwerden über rassistische Diskriminierung in verschiedenen europäischen Ländern macht deutlich, dass rassistische Vorkommnisse nur in den seltensten Fälle einen rein nationalen Bezug haben; vielmehr handelt es sich häufig um Fallkonstellationen, die ohne weiteres auch in Deutschland vorkommen bzw. vorstellbar sind. Daher kann das Wissen um diese Fälle als mächtige Ressource der Sozialen Arbeit gewertet werden, die dazu dienen kann Sozialarbeitenden eine effektive Machtquelle an die Hand zu geben, wenn es darum geht - im Einzelfall sowie auch strukturell - effektiv gegen rassistische Diskriminierung vorzugehen. (DIPF/Orig.)Large numbers of clients of social work are affected by diverse forms of racism in Germany. To be able to identify these and to effectively create actions against racism needs courage and resources - on the part of groups affected as well as on the part of social workers. Observing the individual complaints of racist discrimination in various European countries, it becomes obvious that racist incidents rarely apply to a single national context. Rather they often deal with cases that can be found in diverse countries including Germany. Therefore, social workers can use their knowledge on human rights based instruments against racism as a powerful resource to effectively overcome racist discrimination at individual level as well as on a structural level. (DIPF/Orig.