A Natural Generalization of Hypoelasticity and Eulerian Rate Type Formulation of Hyperelasticity

According to the classical hypoelasticity theory, the hypoelasticity tensor, i.e. the fourth order Eulerian constitutive tensor, characterizing the linear relationship between the stretching and an objective stress rate, is dependent on the current stress and must be isotropic. Although the classical hypoelasticity in this sense includes as a particular case the isotropic elasticity, it fails to incorporate any given type of anisotropic elasticity. This implies that one can formulate the isotropic elasticity as an integrable-exactly classical hypoelastic relation, whereas one can in no way do the same for any given type of anisotropic elasticity. A generalization of classical theory is available, which assumes that the material time derivative of the rotated stress is dependent on the rotated Cauchy stress, the rotated stretching and a Lagrangean spin, linear and of the first degree in the latter two. As compared with the original idea of classical hypoelasticity, perhaps the just-mentioned generalization might be somewhat drastic. In this article, we show that, merely replacing the isotropy property of the aforementioned stress-dependent hypoelasticity tensor with the invariance property of the latter under an R-rotating material symmetry group R⋆ G ₀, one may establish a natural generalization of classical theory, which includes all of elasticity. Here R is the rotation tensor in the polar decomposition of the deformation gradient and G ₀ any given initial material symmetry group. In particular, the classical case is recovered whenever the material symmetry is assumed to be isotropic. With the new generalization it is demonstrated that any two non-integrable hypoelastic relations based on any two objective stress rates predict quite different path-dependent responses in nature and hence can in no sense be equivalent. Thus, the non-integrable hypoelastic relations based on any given objective stress rate constitute an independent constitutive class in its own right which is disjoint with and hence distinguishes itself from any class based on another objective stress rate. Only for elasticity, equivalent hypoelastic formulations based on different stress rates may be established. Moreover, universal integrability conditions are derived for all kinds of objective corotational stress rates and for all types of material symmetry. Explicit, simple, integrable-exactly hypoelastic relations based on the newly discovered logarithmic stress rate are presented to characterize hyperelasticity with any given type of material symmetry. It is shown that, to achieve the latter goal, the logarithmic stress rate is the only choice among all infinitely many objective corotational stress rates. This revised version was published online in August 2006 with corrections to the Cover Date.     

Model-independent analysis of density-matrix element measurements in multiparticle reactions

We present a general study of polarization measurement in multiparticle production processes, including a definition of experimentally observable quantities, the splitting into natural- and unnatural parity exchanges and a study of their relative phase, and information concerning the quantum numbers of a packet of particles. When only one single particle is detected in the final state (inclusive reactions for instance) we prove that the usual formalism for two-body reactions is applicable. Very interesting new information on multi-particle production can be reached when it can be asserted that another particle has been emitted above or below a given plane, parallel or perpendicular to the scattering plane.     

Chiral 1,4-dihydropyridines. Synthesis and absolute configuration.

Addition of organometallics to chiral 3-pyridyl oxazolines gave high diastereoselectivity at the 4-position of the pyridine nucleus. Absolute configuration was determined by x-ray analysis.     

On the formation of the 1,2-acetonide of (+), (−), and (±) 1,2,4-butanetriol and its corresponding aldehyde

The acetonides $\text{1}$ and $\text{3}$ are components of a 9:1 equilibrium established during their formation.     

Benzyne derived from aryloxazolines. A versatile intermediate.

The benzyne derived from m-chlorophenyl oxazoline adds nucleopiles regiospecifically producing m-substituted products. Electrophiles are also trapped furnishing 1,2,3-trisubstituted benzenes.     

Selective adsorption of 4He on clean LiF (001) surfaces

The selective adsorption of ⁴He on in-situ cleaved LiF surfaces has been studied under improved resolution. The main results are as follows: (1) There are four bound states in the surface potential well, at energies of ?5.8, ?2.2, ?0.6 and ?0.1 meV. The lowest three levels were reported previously. (2) Most of the structure previously designated as “fine structure” is due either to transitions to these four levels via various small reciprocal lattice vectors or to the opening of diffraction channels. (3) The transitions involving the [01] and [01?] reciprocal lattice vectors (i.e., the ones nearly perpendicular to the incident wave vector) are strong; as much as 85% of the specular intensity may be removed. Transitions via the other small reciprocal lattice vectors are much weaker. (4) The widths of the lines are consistent with the velocity distribution, which has a half-width of about 2%. (5) The observed energies agree fairly well with those calculated by Tsuchida for a zeta-function potential, but are not consistent with a Morse potential.