A new approach to spontaneously broken conformal symmetry

In this paper we present a new method for constructing theories of gravitation which exhibit spontaneously broken conformal symmetry. It does not require introducing nongeometric terms (i.e., auxiliary gauge fields or potential terms for the conformal field) into the Lagrangian. It is based on a theory which initially is locally both Lorentz invariant and Weyl gauge invariant inD dimensions. It is shown that, if the field Lagrangian contains terms quadratic in curvature in addition to the Ricci scalar, then the field equations allow both the dilation field and some connection components to have nonvanishing vacuum values. Both Lorentz and Weyl symmetries are thereby broken simultaneously.     

Study of 169Hf at high rotational frequency

High-spin properties of the nucleus ¹⁶⁹Hf have been studied through the fusion evaporation reaction ⁹⁶Zr(⁷⁶Ge,3n)¹⁶⁹Hf at a beam energy of 310 MeV. The known rotational bands have been extended considerably and 6 new bands have been established, four of which form coupled bands with pronounced M1 connections. Quasiparticle assignments are suggested for the new band structures, and it appears that coupling to vibrational degrees of freedom plays a role. Both coupled bands involve the excitation of quasiprotons. In the region of highest spin, a large alignment gain is interpreted in terms of a mixed crossing where an h _9/2 and an h _11/2 quasiproton provide the two signatures of the aligning configuration. Received: 23 March 2001 / Accepted: 20 September 2001     

Preparation of polymandelide by reaction of α-bromophenylacetic acid and triethylamine

Polymandelide was prepared in 77% yield by reaction of α-bromophenylacetic acid and triethylamine. The product was characterized by ¹H- and ¹³C-NMR and IR spectra and isolation and identification of mandelic acid from hydrolysis of the polymer. The NMR spectra indicate the presence of tacticity at CH in the polymer. Molecular weights were determined by GPC and viscosity measurements; n values of 12–20 are comparable to those reported for polymandelides prepared by other methods. The x-ray powder diffraction pattern showed the product to be completely amorphous. Thermal decomposition was studied using DSC.     

Temperature-programmed synthesis of micron-sized multi-responsive microgels

A new synthetic protocol for the synthesis of large diameter (2.5 to 5 μm), temperature-, and pH-responsive microgels via aqueous surfactant-free radical precipitation copolymerization is presented. We have found that in this size range, which is not typically attainable using traditional dispersion polymerization approaches, excellent monodispersity and size control are achieved when the synthesis employs a programmed temperature ramp from 45 to 65 °C during the nucleation stage of the polymerization. A combined kinetic and thermodynamic hypothesis for large particle formation under these conditions is described. Particle sizes, volume phase transition temperatures, and pH responsivity were characterized by particle tracking and photon correlation spectroscopy to illustrate their similar behavior to particles made via more traditional routes. These particles have been enabling for various studies in our group where microscopic visualization of the particles is required.     

Existence theory for spatially competitive network facility location models

Models for locating a firm's production facilities while simultaneously determining production levels at these facilities and shipping patterns so as to maximize the firm's profits are presented. In these models, existing firms, are assumed to act in accordance with an appropriate model of spatial equilibrium. A proof of existence of a solution to the combined location-equilibrium problem is provided.     

Weyl gauging and spontaneously broken Lorentz symmetry: Some alternative models

Some new effective actions are suggested for theories in which the affine connection is not completely specified by the metric. The new actions lead to models in which the metric, torsion, and Weyl vector fields all propagate. The dimensionally reduced versions do not contain third derivatives of the gauge potentials in the field equation. Some simple models which exhibit simultaneous breaking of Weyl andD-dimensional Lorentz symmetry are investigated. It is shown that it is possible for this effect to occur in any model in which the field action contains the Einstein-Hilbert term. This is due to the fact that the contortion occurs in this object as part of an indefinite quadratic form.     

VERIFICATION OF SMOM AND QMOM POPULATION BALANCE MODELING IN CFD CODE USING ANALYTICAL SOLUTIONS FOR BATCH PARTICULATE PROCESSES

For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics （CFD） simulation. In this work, a CFD based population balance model is tested using a batch crystallization reactor. In this CFD model, the population balance is solved by the standard method of moments （SMOM） and the quadrature method of moments （QMOM）. The results of these simulations are compared to analytical solutions for the population balance in a batch tank where 1） nucleation, 2） growth, 3） aggregation, and 4） breakage are taking place separately. The results of these comparisons show that the first 6 moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage at all times.