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We show that the anomalous decrease in the thermal conductivity of cuprates below 300 mK, as has been observed recently in several cuprate materials including Pr 2−x Ce x CuO 7−␦ in the field-induced normal state, is due to the thermal decoupling of phonons and electrons in the sample. Upon lowering the temperature, the phonon-electron heat transfer rate decreases and, as a result, a heat current bottleneck develops between the phonons, which can in some cases be primarily responsible for heating the sample, and the electrons. The contribution that the electrons make to the total low-T heat current is thus limited by the phonon-electron heat transfer rate, and falls rapidly with decreasing temperature, resulting in the apparent low-T downturn of the thermal conductivity. We obtain the temperature and magnetic field dependence of the low-T thermal conductivity in the presence of phonon-electron thermal decoupling and find good agreement with the data in both the normal and superconducting states.

The craniofacial complex is anatomically the most sophisticated part of the body. It houses all the major sensory organ systems and its origins are synonymous with vertebrate evolution. Of fundamental importance to craniofacial development is a specialized population of stem and progenitor cells, known as the neural crest, which generate the majority of the bone, cartilage, connective and peripheral nerve tissue in the head. Approximately one third of all congenital abnormalities exhibit craniofacial malformations and consequently, most craniofacial anomalies are considered to arise through primary defects in neural crest cell development. Recent advances however, have challenged this classical dogma, underscoring the influence of tissues with which the neural crest cells interact as the primary origin of patterning defects in craniofacial morphogenesis. In this review we discuss these neural crest cell interactions with mesoderm, endoderm and ectoderm in the head in the context of a better understanding of craniofacial malformations such as in Treacher Collins and 22q11 deletion syndromes.

In this article a macroscopic invariance group describing the superconducting state of a twinned crystal is introduced and shown to provide a useful framework for the discussion of Josephson tunneling in twinned crystals. Josephson tunneling from time-reversal symmetry-breaking states is described and compared with that from time-reversal invariant states for both twinned and untwinned crystals and for both c-axis and basal-plane currents, in a model for orthorhombic Y-Ba-Cu-O. In addition, a ring geometry, which allows s-wave and d x 2 Ϫy 2-wave superconductivity in a tetragonal superconductor to be distinguished on the basis of symmetry arguments only, is proposed and analyzed. Finally, an appendix gives details of the experimental Josephson tunneling evidence for a superconducting state of orthorhombic ux 2 ϩvy 2 symmetry in Y-Ba-Cu-O.