Bifurcations of Poiseuille flow between parallel plates: Three-dimensional solutions with large spanwise wavelength

The spatial dynamics approach is applied to the analysis of bifurcations of the three-dimensional Poiseuille flow between parallel plates. In contrast to the classical studies, we impose time periodicity as well as spatial periodicity with period 2/ in the streamwise direction. However, we make no assumptions on the behavior in the spanwise direction, except the uniform closeness of the bifurcating solution to the basic flow. In an abstract setting it is shown how the dimension of the critical eigenspace of the spatial dynamics analysis can be uniquely determined from the classical linear stability problem. For the three-dimensional Poiseuille problem we are able to find all relevant coefficients from the analysis of the purely two-dimensional problem. Moreover, we are able to analyze precisely the influence of a spanwise pressure gradient and the associated spanwise mass flux. The study of the reduced problem shows that there are two different kinds of solutions (spirals and ribbons) which are 2p/ periodic in the spanwise direction, as in the Couette-Taylor problem, and both of them bifurcate in the same direction.     

Time response of a coupled atoms-cavity system

We study the time response of a quantum optical system to a step excitation. The system is composed of a collection of N two-level atoms coupled to a single mode of the electromagnetic field of an optical cavity. The size of the step excitation is not limited to the low-intensity regime. Before the system reaches steady state there is an oscillatory exchange of energy between the atoms and the cavity. We compare the experimental results quantitatively with theoretical calculations and with previous transmission spectroscopy measurements.     

Improved operation range of digital superconductive electronics by implementing passive phaseshifters

We implemented small superconducting loops containing a frozen single flux quantum in single flux quantum (SFQ) electronics. Such an element acts as a π-phaseshifter which is the missing complementary circuit element in SFQ electronics and can significantly improve the circuit reliability and robustness. We designed a four bit ripple counter including toggle flip-flops (TFF) with these π-phaseshifters. We analyzed the circuit stability by means of bit error rate (BER) measurements versus bias supply. The measured operation range of the counter in standard SFQ technique was ±14% and could be improved to ±24% for the new version utilizing π-phaseshifters. These results are a clear proof for a more robust circuit realization achieved without any additional power consumption. Furthermore, it supports the reduction of present power consumption in SFQ circuits by using smaller switching energy as well as the development of more complex circuits because of a reduced sensitivity against technological parameter spread.     

Reactions of OH and NO radicals with 1,1-dichloroethylene in argon matrices. FTIR and theoretical studies

HONO/1,1-dichloroethylene/Ar matrices were subjected to UV radiation (lambda > 340 nm) from a medium pressure mercury lamp. The products of the photolysis were studied experimentally by means of FTIR spectroscopy and theoretically using the ab initio MP2 method. Two conformers of 2-nitroso-2,2-dichloroethanol molecule have been identified as the final products of the double addition reaction of the OH, NO radicals to 1,1-dichloroethylene. The additional reactive species observed in the matrix is tentatively identified as an 1,1-dichloro-2-hydroxyethyl radical, an intermediate formed by single addition of OH to 1,1-dichloroethylene. The three photoproducts have been identified and observed for the first time. The identities of the products have been justified by comparison with the experiments with deuterated DONO and by performing concentration and annealing studies as well as by reference to the spectral data of related molecules. The results of the quantum mechanical calculations confirmed both the assignment of the new molecules and mechanism of the reaction observed in our experiment.     

Chiral Anomaly in Contorted Spacetimes

The Dirac equation in Riemann-Cartan spacetimeswith torsion is reconsidered. As is well-known, only theaxial covector torsion A, a oneform, couples to massiveDirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannianterm only the Pontrjagin type four-form dA dA doesarise additionally in the chiral anomaly, but not theNieh-Yan term d * A, as has been claimed recently.Implications for Ashtekar's canonical approach to quantumgravity are discussed.     

Final Lift Actions Associated with Topological Functors

For a topological functor U:EB, the fiber U ^–1(b), bB, is a cocomplete poset and the left action, induced by final lift, of the endomorphism monoid B(b,b) on U ^–1(b) is cocontinuous. It is shown that every cocontinuous left action of B(b,b) on any cocomplete poset can be realized as the final lift action associated to a canonically defined topological functor over B. If B is a Grothendieck topos and b=, the subobject classifier, then B(,) inherits both a monoidal and a cocomplete poset structure. In the case B= Sets, all cocontinuous left actions of B(,) on itself are explicitly described and each is shown to arise as the final lift action associated to a specific subcategory of a certain fixed category, referred to as the category of LR-spaces. Relationships between these LR-spaces and several other well known topological categories are also considered.