Number and length of attractors in a critical Kauffman model with connectivity one

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.     

Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite

Ultrafast charge carrier dynamics in graphite has been investigated by time-resolved terahertz spectroscopy. Analysis of the transient dielectric function and model calculations show that more than 90% of the initially deposited excitation energy is transferred to a few strongly coupled lattice vibrations within 500 fs. These hot optical phonons also substantially contribute to the striking increase of the Drude relaxation rate observed during the first picosecond after photoexcitation. The subsequent cooling of the hot phonons yields a lifetime estimate of 7 ps for these modes.     

A superlinearly convergent predictor-corrector method for degenerate LCP in a wide neighborhood of the central path with -iteration complexity

An interior point method for monotone linear complementarity problems acting in a wide neighborhood of the central path is presented. The method has -iteration complexity and is superlinearly convergent even when the problem does not possess a strictly complementary solution. Mathematics Subject Classification (2000): 49M15, 65K05, 90C33 Work supported by the National Science Foundation under Grant No. 0139701. An erratum to this article is available at.     

Decoherence and multipartite entanglement

We study the dynamics of multipartite entanglement under the influence of decoherence. A suitable generalization of concurrence reveals distinct scaling of the entanglement decay rate of Greenberger-Horne-Zeilinger and W states, for various environments.     

Monosaccharides as silicon chelators: pentacoordinate bis(diolato)(phenyl)silicates with the cis-furanose isomers of common pentoses and hexoses

Five-coordinate phenylsilicates are formed from the reaction of trimethoxy(phenyl)silane with monosaccharides in methanol in the presence of a stoichiometric amount of base. Five complexes have been isolated and characterized with two ketoses and three aldopentoses. The silicon central atom in [K([18]crown-6)][PhSi(beta-D-Fruf 2,3H-2)2].MeOH (1, Fru=fructose) is part of two chelate rings, with the ligands being beta-D-fructofuranose-O2,O3 dianions. The beta-furanose isomer is best suited for silicon ligation because it exhibits a torsion angle close to 0 degrees for the most acidic diol function, thus assuring a flat chelate ring. The same structural principles are also found in [K([18]crown-6)][PhSi(beta-D-Araf1,2H-2)2].2 MeOH (2, Ara=arabinose), [K([18]crown-6)][PhSi(alpha-D-Ribf1,2H-2)2] (3, Rib=ribose), [K([18]crown-6)][PhSi(alpha-D-Xylf1,2H-2)2]. acetone (4, Xyl=xylose), and [K([18]crown-6)][PhSi(alpha-D-Rulf2,3H-2)2] (5, Rul=ribulose).     

An Inequality Involving Tight Closure and Parameter Ideals

An inequality is established involving colengths of the tightclosure of ideals of systems of parameters in local rings withsome mild conditions. As an application, a proof is given ofa result due to Goto and Nakamura (first conjectured by Watanabeand Yoshida), which states that the Hilbert–Samuel multiplicityof a parameter ideal is greater than or equal to the colengthof the tight closure of the ideal. The result is also furtherrefined. 2000 Mathematics Subject Classification 13D40, 13A35,13H15.     

Widely tunable sub-30-fs pulses from a compact erbium-doped fiber source

Coupling femtosecond light pulses from an all-fiber Er:laser system into a dispersion-shifted and highly non-linear fiber, we generate output spectra exhibiting two broadband and mutually coherent maxima. Depending on the chirp of the input pulse, the spectral separation is easily tunable over a wide range up to values exceeding 100 THz. In this way, the source provides access to an ultrabroadband wavelength interval from 1130 to 1950 nm. Because of soliton effects, the long-wave component exhibits a transform-limited pulse width of 40 fs directly after the nonlinear element. The high-frequency part propagating in the dispersive regime is recompressed to pulse durations as short as 24 fs with an optimized prism sequence.     

Shear-induced sponge-to-lamellar phase transition studied by rheo-birefringence

We report on the shear induced transition from the L₃- to the L-phase studied by means of flow birefringence using the system pentaethyleneglycol monododecylether (C₁₂E₅), decane, water. The dependence of the critical shear rate, at which the transition from the isotropic state to the anisotropic takes place, on membrane volume fraction was studied in temperature ramp experiments at different constant shear rates and in isothermal shear ramp experiments. These results are compared with relaxation experiments from the shear aligned state back to the isotropic. For all these experiments power law exponents in the membrane volume fraction between 1.6 and 2.8 were found, which are rather low compared to values of current theories. The values found for the inverse critical shear rate and the decay times from the relaxation experiments differ by four orders of magnitude.     

Rovibrational product state distribution for inelastic H+D2 collisions

Experimental measurements of rovibrational product state distributions for the inelastic scattering process H + D2(nu=0,j)-->H + D2(nu' = 1,2,j') are presented and compared with the results of quasiclassical and quantum mechanical calculations. Agreement between theory and experiment is almost quantitative. Two subtle trends are found: the relative amount of energy in product rotational excitation decreases slightly with increasing collision energy and increases slightly with increasing product vibrational excitation. These trends are the reverse of what has been found for reactive scattering in which the opposite trends are much more pronounced.