Simulation of pseudostationary radical polymerization, 3. Periodic modulation of the termination process for termination by disproportionation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the termination rate constant, considering termination by disproportionation. Applying some (hypothetical) field which suppresses — or at least diminishes — the termination rate constant periodically, results in step-function-like chain-length distributions. In principle, the same information may be obtained as in the case of periodical variation of the rate of initiation.     

Automated phase correction via maximization of the real signal

Due to improved quantification capabilities and enhanced signal-to-noise ratio (SNR), phase-corrected real reconstruction in magnetic resonance imaging is superior to the common magnitude reconstruction, especially at low SNR. This requires the development of an automated phase-correction algorithm. Existing methods are not well suited for multiple unconnected regions of very low SNR. For this situation, a method based on the real-signal maximization is implemented, in which the experimental image phase is approximated by a three-dimensional polynomial of up to third order. The presented implementation was successfully applied to data originating from different samples and pulse sequences.     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

A computational study of the effect of an external electric field on the geometry of selected donor–acceptor complexes

To understand the effect of Au and thiol atoms in octane molecule, a structural and charge density analysis has been carried out by high level ab initio quantum chemical calculations using MP2 and B3PW91 methods with the basis sets 6-311G(d,p) and LANL2DZ. The optimized geometries, specifically, the geometry obtained from both levels reveal the effect of S- and Au-atoms in octane molecule. An introduction of sulfur atom in octane molecule lengthen its backbone C–C bond distances, and further adding of Au-atom at the terminals of octane dithiolate stabilizes these distances. The bond densities of the C–C bonds of octane are 1.6 eÅ⁻³, these values are decreased significantly and the charges are largely depleted, when thiol and Au-atoms added in the octane molecule. The presence of negative Laplacian ²ρ(r) at bond critical points of C–C and C–H bonds, indicate, the charges are concentrated in these bonds, confirm that these bonds exhibit an open shell type interaction. The moderate values of density and the negative Laplacian of S–C bonds confirm the covalent character. The positive ²ρ(r) value of Au–S bonds, characterize, the bonding interaction is a closed shell interaction. The combined observed low value of electron density and the positive Laplacian of Au–S bond comprises, the gold and S interaction is not a covalent interaction, but it is a very weak coordination bond interaction. The small positive value of total energy density in Au–S bond indicates, the charges in these bonds are highly depleted and this is further confirmed by the Laplacian of bond characterization.     

Orbits of parabolic subgroups on metabelian ideals

Let k be an algebraically closed field, t∈Z?1, and let B be the Borel subgroup of GLt(k) consisting of upper-triangular matrices. Let Q be a parabolic subgroup of GLt(k) that contains B and such that the Lie algebra qu of the unipotent radical of Q is metabelian, i.e. the derived subalgebra of qu is abelian. For a dimension vector with , we obtain a parabolic subgroup P(d) of GLn(k) from B by taking upper-triangular block matrices with (i,j) block of size di×dj. In a similar manner we obtain a parabolic subgroup Q(d) of GLn(k) from Q. We determine all instances when P(d) acts on qu(d) with a finite number of orbits for all dimension vectors d. Our methods use a translation of the problem into the representation theory of certain quasi-hereditary algebras. In the finite cases, we use Auslander-Reiten theory to explicitly determine the P(d)-orbits; this also allows us to determine the degenerations of P(d)-orbits.