Ghost fields in classical gauge theories

It is shown that ghost fields, characterized as unphysical entities, are a valuable tool in finding numerical solutions of the Euler-Lagrange equations of gauge field theories.     

Shear-induced smectic ordering in the melt of isotactic polypropylene

We report an unusual shear-induced smectic phase of high-molecular-mass isotactic polypropylene at temperatures well above its melting point. The necessary stiffness in the polymer chain is provided by shear-induced coil-helix transitions. Coupling between the conformational ordering and the density generates the smectic layering. The periodicity of about 4 nm is built up from a rigid helical sequence of at least 11 monomers and a random-coil part of about 1.4 nm. These results also provide new clues to the question of preordering before polymer crystallization.     

Transitions driven by a missing frequency

We demonstrate an intricate combination of strong and weak interactions of a broadband half-cycle pulse with Rydberg atoms. A transition, which is resonant with a frequency that was taken out of the frequency spectrum, can be enhanced. In the experiment, the broadband ultrashort terahertz half-cycle pulse propagates through water vapor, which absorbs on discrete lines in the spectrum, thus removing frequencies from the spectrum. The resulting pulse interacts with a rubidium Rydberg atom, which has a resonant transition with one of the missing frequencies. Under certain conditions, the transition probability is enhanced although the associated frequency was missing in the spectrum.     

Constrained stochastic simulation—generation of time series around some specific event in a normal process

The method of so-called constrained stochastic simulation is introduced. This method specifies how to efficiently generate time series around some specific event in a normal process. All events which can be expressed by means of a linear condition (constraint) can be dealt with. Two examples are given in the paper: the generation of stochastic time series around local maxima and the generation of stochastic time series around a combination of a local minimum and maximum with a specified time separation. The constrained time series turn out to be a combination of the original process and several correction terms which includes the autocorrelation function and its time derivatives. For the application concerning local maxima it is shown that the presented method is in line with properties of a normal process near a local maximum as found in literature. The method can e.g. be applied to generate wind gusts in order to assess the extreme loading of wind turbines. AMS 2000 Subject Classification Primary—60G15, 60G70, 62G32; Secondary—62P30     

Subcritical finite-amplitude solutions for plane Couette flow of viscoelastic fluids

Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation is sufficient to create a secondary flow, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases. The results suggest a scenario for weakly turbulent viscoelastic flow which is similar to the one for Newtonian fluids as a function of Reynolds number.     

Products of idempotent matrices over Hermite domains

Communicated by F. Pastijn     

On the uniqueness of roots in virtually nilpotent groups

After revisiting the concept of the torsion subgroup of a group with respect to a set of prime numbers P (as introduced by Ribenboim), we show that, for all p in P, p-th roots are unique in a virtually nilpotent group if and only if P-roots are unique in both its Fitting subgroup and its Fitting quotient. This more general notion of torsion also turns out to be sufficient to understand completely the kernel of the P-localization homomorphism of a virtually nilpotent group. Using this result, we characterize the finitely generated virtually nilpotent groups such that, when dividing out the P-torsion subgroup, P-roots exist and are unique in the resulting quotient. Received March 10, 1998; in final form July 10, 1998