Lower central series of Artin–Tits and surface braid groups

We consider algebraic and topological generalisations of braid groups and pure braid groups, namely Artin–Tits groups (of spherical type) and surface (pure) braid groups, and we determine their lower central series and related residual properties.     

Non-perturbative aspects in quantum field theory: Proceedings of Les Houches Winter Advanced Study Institute,March 1978

Until recent years field theories were only studied from standard perturbation series. These are equivalent to small fluctuation expansions around the classical ground state configurations in which the fields are space-time independent. It has been gradually realized that this procedure may miss some crucial physical features of the theory. In particular the absence of free quarks cannot be explained in quantum chromodynamics from this perturbative viewpoint. One is led to deal with the non-linearities in an essential way. This issue aims at covering the recent advances in this direction typically since 1975 and the issue 23C of Physics Reports.One way of going beyond perturbation theory is to make use of non-perturbative classical solutions which are in general very difficult to obtain. In Yang-Mills theories remarkable advances have been made in the search for self-dual solutions. They are described in the lectures (I, II) by E. Corrigan and R. Stora et al. The quantum meaning of these solutions and the technical problems raised by quantizing fluctuations around them are discussed by J.L. Gervais (III) and D. Gross (IV). The most recent topics of this subject deal with imaginary time solutions, the so-called instantons, which describe quantum tunneling in the semi-classical approximation. Other field configurations such as merons, are also discussed in relation with quark confinement. An attempt to build a general picture of strong interactions on these grounds is displayed in (IV).Recent advances concerning the solitons which are real time, classical Minkowski solutions, are discussed by D. Olive (V). These solutions describe generalized Dirac magnetic monopoles in non-Abelian gauge theories. The resulting model contains confined magnetic charges and unconfined electric charges. If the magnetic and elastic characters can be interchanged by a dual transformation, as discussed by F. Englert et al. in (VI), this would provide a model for quark confinement. This duality transformation has been spelled out in (IX) by C. Itzykson who proves the existence of a confinement phase transition in a lattice model with Z₂ gauge symmetry.Another non-linear feature of Yang-Mills theory is that no single gauge condition can be implemented over large field fluctuations. This is discussed in (VII) by Sciuto and also in (III).Another mechanism of confinement is proposed by McCoy and Wu (VIII) in which the propagator has a cut instead of a pole, as it does happen in the two-dimensional Ising model.The lectures of J. Zinn-Justin and G. Parisi, (X) and (XI) deal with the asymptotic estimation of the large order behaviour of perturbation theory, which one can obtain by semi-classical methods. The use of these methods is either to provide a way of improving practical perturbative calculations, or to characterize possible ambiguities due to vacuum tunneling. Additional problems raised in renormalizable theories are discussed in (XI).Another non-perturbative approach is to examine the large N limit of an SU(N) gauge theory. At leading order, only planar Feynman diagrams contribute. They are discussed in (XII) by E. Brézin. There are very subtle questions about the corresponding exact summation in two dimensions which are studied by T.T. Wu in (XV).In two-dimensional field theories exact solutions for the S-matrix have been recently discovered. They are discussed by Karowski in (XIII). In connection with this problem, Lüscher (XIV) has shown the existence of non-linear conserved charges which ensure the absence of particle production. These models are particularly interesting since the mass spectrum cannot be obtained from coupling constant expansion.Finally several related topics in statistical physics are discussed. D. Nelson (XVI) reviews the beautiful properties of the two-dimensional X-Y model which is an ideal example of mechanisms invoked in hadronic field theories. A. Luther (XVII) discussed an attempt to extend to a higher number of dimensions the bosonization of fermion theories which is so powerful in two dimensions. G. Toulouse (XVIII) describes modern ideas in spin glass phase transitions, a possible testing ground for gauge field theories besides its obvious intrinsic interest.     

String structure of the master field of U(∞) Yang-Mills

We argue that the internal symmetry space of the U(∞) pure Yang-Mills theory must be a functional space, actually the space of configurations of a string, in contrast with the case of the O(∞) 2-dimensional non-linear sigma-model, where it is only momentum space. We then show that the old dual-resonance model provides explicit ansätze for the classical Yang-Mills master field which is to be used to evaluate all gauge-invariant quantities; these ansätze automatically give rise to a Lorentz-invariant area-law behavior for the Wilson loop.     

On the phonon self-energy

It is reported that a specific phonon-phonon interaction process described by the sixth-order Hamiltonian can contribute to the real part of the phonon self-energy of an order which involves a quadratic dependence of the resulting frequency shift on temperature, in the high temperature limit. The possible connection between the occurrence of such a process and experimental mental results in α-quartz is discussed.     

Contrasting behavior of the 5/2 and 7/3 fractional quantum Hall effect in a tilted field

Using a tilted-field geometry, the effect of an in-plane magnetic field on the even denominator nu=5/2 fractional quantum Hall state is studied. The energy gap of the nu=5/2 state is found to collapse linearly with the in-plane magnetic field above approximately 0.5 T. In contrast, a strong enhancement of the gap is observed for the nu=7/3 state. The radically distinct tilted-field behavior between the two states is discussed in terms of Zeeman and magneto-orbital coupling within the context of the proposed Moore-Read Pfaffian wave function for the 5/2 fractional quantum Hall effect.     

Spectral Vorticity and Lagrangian Velocity Measurements in Turbulent Jets

In this paper we report an experimental investigation of various statistical properties of the spatial Fourier modes of the vorticity field in turbulent jets for a large range of Reynolds numbers (530 ≤R _λ≤ 6100). The continuous time evolution of a spatial Fourier mode of the vorticity distribution, characterized by a well-defined wavevector, is obtained from acoustic scattering measurements. The spatial enstrophy spectrum, as a function of the spatial wave-vector, is determined by scanning the incoming sound frequencies. Time-frequency analysis of the turbulent vorticity fluctuations is also performed for different length scales of the flows. Vorticity time-correlations show that the characteristic time of a Fourier mode behaves as the sweeping time. Finally, we report preliminary Lagrangian velocity measurements obtained using acoustic scattering by soap bubbles inflated with helium. Gathering a large number of passages of isolated bubbles in the scattering volume, one is able to compute the Lagrangian velocity PDF and velocity spectrum. Despite the spatial filtering due to the finite size of the bubble, the latter exhibits a power law, with the -2 exponent predicted by the Kolmogorov theory, over one decade of frequencies.     

Oxo-titanium and -zirconium diphosphines [(η-C5H5)2M(CH2PPh2]2O (with M = Ti,Az) as building blocks for heterobimetallic complexes

Oxo-titanium and -zirconium diphosphines [(η-C₅H₅)₂M(CH₂PPh₂)]₂ (with M = Ti, Zr) were synthesized and treated with [Rh(CO)₂Cl]₂ to give the heterobimetallic d⁰-d⁸ species O[(η-C₅H₅)₂M(CH₂PPh₂)]₂Rh(CO)Cl.     

Crystallization in the SiO2-Al2O3 System from Amorphous Powders

The crystallization of amorphous chemically homogeneous powders in the SiO₂.Al₂O₃ system has been studied by differential scanning calorimetry and X-ray diffraction. Up to 1300°C only one exotherm has been observed. Only mullite crystallizes for compositions ≤69 mol% Al₂O₃ and spinel for those ≤80%. The crystallizations into mullite and spinel are sharp and exothermic, with an enthalpy of 250–300 J/g. The chemical composition of the crystallized mullite regularly increases from 68 to 76 mol% Al₂O₃ with increasing bulk composition from 60 to 75 mol% Al₂O₃.     

The quantum strip: Liouville theory for open strings

The quantum group structure of 2D gravity recently put forward by one of us (J.-L. G.) is used to study quantum gravity on the strip. The boundary conditions, previously studied by A. Neveu and this author become easy to implement when one introduces the universal family of chiral operators associated withU _q (sl(2)). A general formula for inverse powers of the metric-tensor operator is thereby derived. It contains a new universal matrixA, acting in representation-space, which obeys identities involving theR matrix, the Clebsch-Gordon coefficients, and the co-products ofU _q (sl(2)). The physical meaning of these identities is to ensure that these powers of the metric are local and closed by fusion.     

Mixing study of the induction plasma reactor: Part II. Radial injection mode

A study was undertaken on the mixing pattern in am induction plasma torch and reactor system. The results presented in this part of the paper relate to the radial injection mode, in which an auxiliary gas is injected into the main plasma stream through a set of 2, 4, or 8 injection ports located in the torch nozzle at the level of the torch exit flange. A much faster mixing of the gases occurred in this mode compared to the axial injection mode investigated in Part I of this paper. As in the case of axial injection, the present study demonstrates that gas mixing, in the presence of the discharge, is considerably more difficult than under ambient temperature conditions. Lower turbulence levels exist in the plasma reactor. due to the considerably higher viscosity of the gases under plasma conditions. Results obtained with a three-point injection flange, in which the injection ports were oriented at 45° to the torch and reactor axes toward the upstream .side, mere most interesting since they achieved essentially the same degree of mixing as was obtained with the radial injection ports without the need to locate the injection ports at the exit nozzle of the plasma torch. This arrangement provides for added flexibility in reactor design.