Anomalous thermodynamics of Coulomb-interacting massless Dirac fermions in two spatial dimensions

It is argued that the specific heat of N massless Dirac fermions in two spatial dimensions interacting with 1/r Coulomb interactions is suppressed logarithmically relative to its noninteracting counterpart. The (dimensionless) coefficient of the logarithm is calculated in a closed form in the leading order in large N expansion, but to all orders in the effective fine structure constant, alpha(F), a procedure which takes into account finite temperature screening. This effect is expected to occur in a single-layer graphene embedded in a dielectric medium. Its dependence on the dielectric constant is calculated analytically.     

Novel polycarbonate-based polyurethane elastomers: Composition–property relationship

Novel all-aliphatic polycarbonate-based polyurethane (PC-PU) elastomers, as well as PC-PU nanocomposites filled with organic-modified clays were synthesized, characterized and studied. It was found that they have very attractive mechanical properties (e.g., elongation at break between 600% and 800%). The prepared PC-PUs possess a distinctly segmented structure, which is the key prerequisite for their behavior as strong physical rubbery networks. All synthesized materials melt at elevated temperatures (between 110 and 200 °C) and hence can be processed like normal thermoplastics. The dispersion of the clay nanofiller was achieved by its one day swelling in the alcohol and a brief successive stirring. This procedure is very successful and leads to a partial exfoliation of the clay (documented by X-ray diffraction and TEM). The best nanocomposites with very good tensile properties, particularly with significantly increased moduli were obtained using the bentonite nanofiller. The study shows that the nanofiller interacts strongly with the hard domains and influences their melting temperature (DMTA and DSC), but it does not affect the glass transition temperature of soft domains. While Cloisite 15A was found to interact preferentially with the hard domains, the organic modified bentonite shows a strong interaction with both soft and hard segments, behaving as a blending agent. Hard domains in neat matrices, formed by hydrogen bonding of hard segments, were practically invisible by X-ray or TEM, but were successfully detected by AFM. Besides excellent mechanical properties, the prepared elastomers and their nanocomposites showed an interesting phase behavior (which was studied by combining DMTA and modulated DSC).     

Black hole uniqueness from a hidden symmetry of Einstein's gravity

A theorem is proven that the only possible exterior solution for a pseudostationary, rotating, electrovacuum black hole with nondegenerate event horizon is the Kerr-Newman solution withM ²-J²/M²-Q²>0. A special role played in the proof of this theorem by the hidden symmetry groupSU(1, 2) of Einstein's equations is established.This essay received the third award from the Gravity Research Foundation for the year 1983 [Ed.].     

Über Ähnlichkeit,Dehnung und Schrumpfung in der hyperbolischen Geometrie

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Seiten und Diagonalen eines Kreisvierecks in der hyperbolischen Geometrie

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