Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤ q < ∞, or the -norm of the gradient of the vorticity with 3/p + 2/q ≤ 4, 1 ≤ q, 1 ≤ p, is sufficiently small near z.     

On particle multiplicities in three-jet events

A thorough verification of the distinct differences in the properties of quark and gluon jets is considered as one of the most instructive tests of the basic ideas of QCD. In the real life experiments such a comparison appears to be quite a delicate task and various subtle issues require further theoretical efforts. In this paper we discuss in detail the possibility to extract the theoretically adequate information from the particle multiplicity patterns in three-jet events in annihilation. Received: 8 June 1999 / Published online: 14 October 1999     

Dynamic Stability and Instability of Pinned Fundamental Vortices

We study the dynamic stability and instability of pinned fundamental ±1 vortex solutions to the Ginzburg–Landau equations with external potential in ℝ². For sufficiently small external potentials, there exists a perturbed vortex solution centered near each non-degenerate critical point of the potential. With respect to both dissipative and Hamiltonian dynamics, we show that perturbed vortex solutions which are concentrated near local maxima (resp. minima) are orbitally stable (resp. unstable). In the dissipative case, the stability is in the stronger “asymptotic” sense. The research of S. Gustafson partially supported by a grant from NSERC. The research of F. Ting on this paper was supported by NSERC under grant N298724.     

Ultrafast study of p-biphenylyldiazomethane and p-biphenylylcarbene

p-Biphenylyldiazomethane was excited by femtosecond pulses of UV light in acetonitrile, in cyclohexane, and in methanol. Ultrafast photolysis produces a singlet excited state of p-biphenylyldiazomethane with lambdamax = 490 nm, and lifetimes of less than 300 fs in acetonitrile, in cyclohexane, and in methanol. The decay of the excited state is accompanied by the growth of transient absorption with lambdamax = 360 nm. The carrier of this transient absorption is attributed to singlet p-biphenylylcarbene, a result that is consistent with the predictions of TD-DFT calculations. The singlet carbene lifetimes are 200 and 77 ps in acetonitrile and cyclohexane, respectively, and are controlled by intersystem crossing to the lower energy triplet state. The transient absorption does not decay to baseline in acetonitrile, because of the formation of nitrile ylide. The equilibrium mixture of singlet and triplet p-biphenylylcarbene reacts with acetonitrile to form a nitrile ylide (lambdamax = 370 nm), and with cyclohexane by C-H insertion 1-20 ns after the laser pulse. The singlet carbene lifetime is only 7.9 ps in methanol, owing to a rapid reaction with the solvent. Reaction with the solvent gives rise, in part, to a p-biphenylylbenzyl cation (lambdamax = 450 nm, tau = 6.3 ps) in methanol.     

Reversible formation of a PdC(x) phase in Pd nanoparticles upon CO and O2 exposure

The structure and chemical composition of Pd nanoparticles exposed to pure CO and mixtures of CO and O(2) at elevated temperatures have been studied in situ by a combination of X-ray Diffraction and X-ray Photoelectron Spectroscopy in pressures ranging from ultra high vacuum to 10 mbar and from room temperature to a few hundred degrees celsius. Our investigation shows that under CO exposure, above a certain temperature, carbon dissolves into the Pd particles forming a carbide phase. Upon exposure to CO and O(2) mixtures, the carbide phase forms and disappears reversibly, switching at the stoichiometric ratio for CO oxidation. This finding opens new scenarios for the understanding of catalytic oxidation of C-based molecules.     

Detection of the singlet and triplet MM δδ* states in quadruply bonded dimetal tetracarboxylates (M = Mo, W) by time-resolved infrared spectroscopy

The compounds M(2)(O(2)C(t)Bu)(4) and M(2)(O(2)CC(6)H(5))(4), where M = Mo or W, have been examined by femtosecond time-resolved IR (fs-TRIR) spectroscopy in tetrahydrofuran with excitation into the singlet metal-to-ligand charge-transfer ((1)MLCT) band. In the region from 1500 to 1600 cm(-1), a long-lived excited state (>2 ns) has been detected for the compounds M(2)(O(2)C(t)Bu)(4) and Mo(2)(O(2)C-C(6)H(5))(4) with an IR absorption at ~1540 cm(-1) assignable to the asymmetric CO(2) stretch, ν(as)(CO(2)), of the triplet metal-metal δ-δ star ((3)MM δδ*) state. The fs-TRIR spectra of W(2)(O(2)C-C(6)H(5))(4) are notably different and are assigned to decay of the MLCT states. In (3)MM δδ*, the removal of an electron from the δ orbital reduces MM δ to CO(2) π* back-bonding and causes a shift of ν(as)(CO(2)) to higher energy by ~30-60 cm(-1), depending on the metal. TRIR spectroscopy also provides evidence for M(2)(O(2)C(t)Bu)(4), where M = Mo or W, having MM δδ* S(1) states with ν(as)(CO(2)) distinct from those of the (3)MM δδ* states.     

On local parton-hadron duality

The multiplicity measure on colour-connected partonic states introduced in [1] is further generalized and we show how to partition the properties of the final state hadronic multiplicity distributions into one part depending upon the partonic cascade and one depending upon the fragmentation inside the Lund model framework. We also show the stability of the measure with respect to variations in the energy and the possible cascade cutoffs and investigate the approximations made in the analytical formulas by means of Monte Carlo simulated events.