8,084 research outputs found
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.
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 SmCeCuO shows a much stronger pseudo-gap
or "hot-spot" effect than that observed in other optimally doped -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
order. Comparison of the ARPES and optical data from
the 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
The Hamiltonian boundary term and quasi-local energy flux
The Hamiltonian for a gravitating region includes a boundary term which
determines not only the quasi-local values but also, via the boundary variation
principle, the boundary conditions. Using our covariant Hamiltonian formalism,
we found four particular quasi-local energy-momentum boundary term expressions;
each corresponds to a physically distinct and geometrically clear boundary
condition. Here, from a consideration of the asymptotics, we show how a
fundamental Hamiltonian identity naturally leads to the associated quasi-local
energy flux expressions. For electromagnetism one of the four is distinguished:
the only one which is gauge invariant; it gives the familiar energy density and
Poynting flux. For Einstein's general relativity two different boundary
condition choices correspond to quasi-local expressions which asymptotically
give the ADM energy, the Trautman-Bondi energy and, moreover, an associated
energy flux (both outgoing and incoming). Again there is a distinguished
expression: the one which is covariant.Comment: 12 pages, no figures, revtex
Ashtekar's New Variables and Positive Energy
We discuss earlier unsuccessful attempts to formulate a positive
gravitational energy proof in terms of the New Variables of Ashtekar. We also
point out the difficulties of a Witten spinor type proof. We then use the
special orthonormal frame gauge conditions to obtain a locally positive
expression for the New Variables Hamiltonian and thereby a ``localization'' of
gravitational energy as well as a positive energy proof.Comment: 12 pages Plain Te
Making Operation-based CRDTs Operation-based
Conflict-free Replicated Datatypes can simplify the design of predictable eventual consistency. They can be classified into state-based or operation-based. Operation-based approaches have the potential for allowing compact designs in both the sent message and the object state size, but cur- rent approaches are still far from this objective. Here we explore the design space for operation-based solutions, and we leverage the interaction with the middleware by offering a technique that delivers very compact solutions, while only broadcasting operation names and arguments.(undefined)(undefined
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