Ten microseconds in the life of a superhelix

Dynamic light scattering measurement data of DNA topoisomers are compared with two different computer models: a Monte Carlo model and a Brownian dynamics model. First results on the kinetics of formation of a superhelix and on the influence of curved sequences on the dynamics of superhelical DNA are reported.To whom correspondence should be addressed     

K-Loops, gyrogroups and symmetric spaces

In this paper we present a new class of K-Loops consisting of homogeneous symmetric spaces of the noncompact type. The most famous physical example of a representative of this class is found in special relativity: The set of all relativistically admissible velocities, R _c ³:= {υ ∈ R3: ¦v¦< c} (c the speed of light), together with the relativistic velocity composition law forms a K-Loop, as was already shown by A. Ungar in 1988. The set of the corresponding boosts turns out to be the effective homogeneous symmetric space SO (1,3)⁰/SO(3), where SO(1,3)⁰ denotes the proper orthochronous Lorentz group and SO(3) the subgroup of proper rotations in three dimensions, which is also found to be the set of fixed points of an automorphism σ: SO(1,3)⁰ → SO(1,3)⁰, whose action on a matrix A in the defining representation is given by σ(A) = (AT)?1. Moreover, the triple (so(l,3),so(3),s) consisting of the Lie algebras of SO(1,3) and SO(3) and the induced automorphism s = (dσ)e is an orthogonal symmetric Lie algebra of the noncompact type. This property of the Lie algebra makes SO(l, 3)/SO(3) an (effective) homogeneous symmetric space of the noncompact type. The method of exact decomposition allows endowing each homogeneous symmetric space of the noncompact type with the structure of a K-Loop in a similar manner. Finally, we treat some alternative approaches which lead to K-Loops that are isomorphic to the one described above.     

Source-Region Electromagnetic Field in an Affinely Transformable AUBM

We derive expressions for the source–region electromagnetic field in an affinely transformable Axially Uniaxial Bianisotropic Medium (AUBM) by employing a technique originally developed by Fikioris for free space (i.e., vacuum). The obtained results may be used to determine the scattering response of an electrically small bianisotropic particle embedded in an affinely transformable AUBM. They can therefore be further used to homogenize a wide class of particulate composites.     

Synthesis and thermotropic properties of new discotic 1,3,5-trisubstituted s-triazinetriones obtained by cyclotrimerization of isocyanates

The synthesis of a number of s-triazine-2,4,6-triones (isocyanurates) by cyclotrimerization of 4-monoalkoxy-, 3,4-dialkoxy-, or 3,4,5-trialkoxyphenyl-, benzyl-, or styryl-isocyanates is reported. The thermal and phase behaviour of the novel compounds were investigated by optical polarized light microscopy and thermal analysis. No mesophase could be observed for any of the precursors except 4-decyloxybenzoic acid. Mesophases of the isocyanurates were observed only in the series containing 3,4-dialkoxyphenyl moieties. A vinylene group between the inner s-triazine ring and the outer phenylene rings gives low melting points and enantiotropic mesophases for C₈ and longer alkyl chains. The phenylisocyanurates may exhibit a monotropic mesophase and normally have the highest melting points of the three types, whereas a methylene spacer suppresses formation of a mesophase. According to the textures observed, the mesophases are hexagonal columnar. This will have to be confirmed by X-ray scattering techniques.     

Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

Diode laser frequency stabilisation for water-vapour differential absorption sensing

We describe a low-power continuous-wave laser system for water-vapour sensing applications in the 935-nm region. The system is based on extended-cavity diode lasers and distributed-feedback lasers and delivers four single-mode frequency-stabilised optical signals. Three lasers are locked to three water-vapour absorption lines of different strengths, whereas the fourth lies outside any absorption line. On-line stabilisation is performed by wavelength-modulation spectroscopy using compact water-vapour reference cells. An offset-locking technique implemented around an electrical filter is applied for the stabilisation of the off-line slave laser to an on-line master laser at a frequency detuning of 18.8 GHz. Stabilities in the order of 15 MHz over one day were observed for the strongest lines, at the detection limit of the measurement instrumentation. The developed techniques and schemes can be applied to other wavelength ranges and molecular species. Differential absorption lidar instrumentation can in particular benefit from such a system when the stabilised lasers serve as injection seeders to pulsed power oscillators. PACS 42.62.Fi; 42.72.-g; 42.68.Wt     

CAS in general mathematics education

A rational discussion of the use of Computer algebra systems (CAS) in mathematics teaching in general education needs an explicit image of (general) mathematics education, an explication of global perspectives and goals on mathematics teaching focusing on general education (chapter 1). The conception of general education according to the «ability of communication with experts» described in chapter 2 can be such an orientation for analysing, considering, classifying and assessing the didactical possibilities of using CAS. CAS are materialised mathematics allowing for more or less exhaustive outsourcing of operative (also symbolically) knowledge and skills to the machine. This frees up space of time as well as mental space for the development of those competences being in our view relevant for general mathematics education. In chapter 3 the idea of outsourcing and the role of CAS for it is discussed more detailed as well as consequences being possible for the CAS-supported teaching of mathematics. Beyond, CAS can be didactically used and reflected as a model of communication between (mathematical) experts and lay-persons (chapter 4). Chapter 5 outlines some research perspectives.     

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.     

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