Failure of classical elasticity in auxetic foams

A recent derivation [P.H. Mott and C.M. Roland, Phys. Rev. B 80, 132104 (2009).] of the bounds on Poisson's ratio, v, for linearly elastic materials showed that the conventional lower limit, -1, is wrong, and that v cannot be less than 0.2 for classical elasticity to be valid. This is a significant result, since it is precisely for materials having small values of v that direct measurements are not feasible, so that v must be calculated from other elastic constants. Herein we measure directly Poisson's ratio for four materials, two for which the more restrictive bounds on v apply, and two having values below this limit of 0.2. We find that while the measured v for the former are equivalent to values calculated from the shear and tensile moduli, for two auxetic materials (v < 0), the equations of classical elasticity give inaccurate values of v. This is experimental corroboration that the correct lower limit on Poisson's ratio is 0.2 in order for classical elasticity to apply.Comment: 9 pages, 2 figure

Quasi-Local Energy Flux of Spacetime Perturbation

A general expression for quasi-local energy flux for spacetime perturbation is derived from covariant Hamiltonian formulation using functional differentiability and symplectic structure invariance, which is independent of the choice of the canonical variables and the possible boundary terms one initially puts into the Lagrangian in the diffeomorphism invariant theories. The energy flux expression depends on a displacement vector field and the 2-surface under consideration. We apply and test the expression in Vaidya spacetime. At null infinity the expression leads to the Bondi type energy flux obtained by Lindquist, Schwartz and Misner. On dynamical horizons with a particular choice of the displacement vector, it gives the area balance law obtained by Ashtekar and Krishnan.Comment: 8 pages, added appendix, version to appear in Phys. Rev.

Some Spinor-Curvature Identities

We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential. Certain special cases in 3 and 4 dimensions which have been or could be used in applications to General Relativity are noted.Comment: 5 pages Plain TeX, NCU-GR-93-SSC

Interface behavior of a multi-layer fluid configuration subject to acceleration in a microgravity environment, supplement 1

With the increasing opportunities for research in a microgravity environment, there arises a need for understanding fluid mechanics under such conditions. In particular, a number of material processing configurations involve fluid-fluid interfaces which may experience instabilities in the presence of external forcing. In a microgravity environment, these accelerations may be periodic or impulse-type in nature. This research investigates the behavior of a multi-layer idealized fluid configuration which is infinite in extent. The analysis is linear, and each fluid region is considered inviscid, incompressible, and immiscible. An initial parametric study of confiquration stability in the presence of a constant acceleration field is performed. The zero mean gravity limit case serves as the base state for the subsequent time-dependent forcing cases. A stability analysis of the multi-layer fluid system in the presence of periodic forcing is investigated. Floquet theory is utilized. A parameter study is performed, and regions of stability are identified. For the impulse-type forcing case, asymptotic stability is established for the configuration. Using numerical integration, the time response of the interfaces is determined

A Quadratic Spinor Lagrangian for General Relativity

We present a new finite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof is fully four-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity Research Foundation Essay.)Comment: 5 pages (Plain TeX), NCU-GR-94-QSL

Stationary untrapped boundary conditions in general relativity

A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density is enough to have a functionally differentiable Hamiltonian, thus providing definition of conserved quantities for the quasi-local regions. If on the boundary the evolution vector normal to the 2-surface is chosen to be proportional to the dual expansion vector, we obtain a generalization of the Hawking energy associated with a generalized Kodama vector. This vector plays the role for the stationary untrapped boundary conditions which the stationary Killing vector plays for stationary black holes. When the dual expansion vector is null, the boundary conditions reduce to the ones given by the non-expanding horizons and the null trapping horizons.Comment: 11 pages, improved discussion section, a reference added, accepted for publication in Classical and Quantum Gravit

Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions

We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying ``energy-momentum'' vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the resulting Dirichlet and Neumann vectors for topologically spherical 2-surfaces in Minkowski spacetime, spherically symmetric spacetimes, and stationary axisymmetric spacetimes. Moreover, we show the relation between these vectors and the ADM energy-momentum vector for a 2-surface taken in a limit to be spatial infinity in asymptotically flat spacetimes. We also discuss the geometrical properties of the Dirichlet and Neumann vectors and obtain several striking results relating these vectors to the mean curvature and normal curvature connection of the 2-surface. Most significantly, the part of the Dirichlet vector normal to the 2-surface depends only the spacetime metric at this surface and thereby defines a geometrical normal vector field on the 2-surface. Properties and examples of this normal vector are discussed.Comment: 46 pages; minor errata corrected in Eqs. (3.15), (3.24), (4.37) and in discussion of examples in sections IV B,

Electronic Structure of Electron-doped Sm1.86Ce0.14CuO4: Strong `Pseudo-Gap' Effects, Nodeless Gap and Signatures of Short Range Order

Angle resolved photoemission (ARPES) data from the electron doped cuprate superconductor Sm$_{1.86}$Ce$_{0.14}$CuO$_4$ shows a much stronger pseudo-gap or "hot-spot" effect than that observed in other optimally doped $n$-type cuprates. Importantly, these effects are strong enough to drive the zone-diagonal states below the chemical potential, implying that d-wave superconductivity in this compound would be of a novel "nodeless" gap variety. The gross features of the Fermi surface topology and low energy electronic structure are found to be well described by reconstruction of bands by a $\sqrt{2}\times\sqrt{2}$ order. Comparison of the ARPES and optical data from the $same$ sample shows that the pseudo-gap energy observed in optical data is consistent with the inter-band transition energy of the model, allowing us to have a unified picture of pseudo-gap effects. However, the high energy electronic structure is found to be inconsistent with such a scenario. We show that a number of these model inconsistencies can be resolved by considering a short range ordering or inhomogeneous state.Comment: 5 pages, 4 figure

Analogue-to-digital interface technique for digital controllers in DC-DC converters

A digital controller for a DC-DC converter is implemented with an efficient analogue-to-digital interface scheme. Conventional digital controllers require flash-type ADCs, which need large analogue circuits and thus significantly diminish the advantage of digital implementation. The presented delta-sigma modulated single-bit interface effectively reduces the analogue circuit area, while it achieves good voltage regulations. A silicon chip is implemented and measured to prove the successful operation of the controller