Poloidal inhomogenity of the particle fluctuation induced fluxes near the LCFS at lower hybrid heating and improved confinement transition at the FT-2 tokamak

This paper deals with the new spectral and microturbulence experimental data and their analysis, which show that the radial electric field E _r generated at the lower hybrid heating (LHH) in the FT-2 is high enough to form the transport barriers. The ETB is formed when LHH is switched off. The radial fluctuation-induced E × B drift flux densities near LCFS in SOL are measured at two different poloidal angles. For this purpose two Langmuir probes located at low and high field sides of the torus are used. Registration of the poloidal and radial components of the electric field and density fluctuations at the same time during one discharge permits to measure the poloidal asymmetry of the transport reduction mechanism of the radial and poloidal particle fluxes in the SOL. The absolute fluctuation levels show dependence on the sign of E _r shear. The modification of the microscale turbulence by the poloidal E _r × B rotation shear _{E × B} at the L-H transition near LCFS is also studied by X-mode fluctuation reflectometry. The new data were obtained by spatial spectroscopic technique.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

The mathematics of perfect shuffles

There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle O leaves the original top card on top. The in shuffle I leaves the original top card second from the top. Applications to the design of computer networks and card tricks are reviewed. The main result is the determination of the group 〈 I, O 〉 generated by the two shuffles, for all n. If 2n is not a power of 2, and if 2n ≠ 12,24, then 〈 I, O 〉 has index 1, 2, or 4 in the Weyl group B_n (the group of all 2ⁿn! signed n × n permutation matrices). If 2n = 2^k, then 〈 I, O 〉 is isomorphic to a semi-direct product of Z₂^k and Z_k. When 2n = 24, 〈 I, O 〉 is isomorphic to a semi-direct product of Z₂¹¹ and M₁₂, the Mathieu group of degree 12. When 2n = 12, 〈 I, O 〉 is isomorphic to a semi-direct product of Z₂⁶ and the group PGL(2,5) of all linear fractional transformations over GF(5).     

Symplectic semifield planes and -linear codes

There are lovely connections between certain characteristic 2 semifields and their associated translation planes and orthogonal spreads on the one hand, and -linear Kerdock and Preparata codes on the other. These inter-relationships lead to the construction of large numbers of objects of each type. In the geometric context we construct and study large numbers of nonisomorphic affine planes coordinatized by semifields; or, equivalently, large numbers of non-isotopic semifields: their numbers are not bounded above by any polynomial in the order of the plane. In the coding theory context we construct and study large numbers of -linear Kerdock and Preparata codes. All of these are obtained using large numbers of orthogonal spreads of orthogonal spaces of maximal Witt index over finite fields of characteristic 2.

We also obtain large numbers of ``boring' affine planes in the sense that the full collineation group fixes the line at infinity pointwise, as well as large numbers of Kerdock codes ``boring' in the sense that each has as small an automorphism group as possible.

The connection with affine planes is a crucial tool used to prove inequivalence theorems concerning the orthogonal spreads and associated codes, and also to determine their full automorphism groups.

     

Computational simulation of the molecular ordering of 3,6-bis(4-butylphenyl)[1,2,4,5]tetrazine at the phase transition temperatures

Computational simulation of 3,6-bis(4-butylphenyl)[1,2,4,5]tetrazine was carried out. Based on the energy of intermolecular interactions of dimers was determined the probability of each configuration (stacking, in-plane and terminal). It was revealed that in the 3,6-bis(4-butylphenyl)[1,2,4,5]tetrazine dimers the sliding of the molecules relative to each other is energetically allowed in the narrow range of distances that provides retaining orientation of the molecules in the mesophase. The relationship between the translational rigidity of the molecules in the dimer and nematic properties was revealed.