7,607 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
Intercomparison of cloud properties in DYAMOND simulations over the Atlantic Ocean
We intercompared the cloud properties of the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND) simulation output over the Atlantic Ocean. The domain averaged outgoing longwave radiation (OLR) is relatively similar across the models, but the net shortwave radiation at the top of the atmosphere (NSR) shows large differences among the models. The models capture the triple modes of cloud systems corresponding to shallow, congestus, and high clouds, although their partition in these three categories is strongly model dependent. The simulated height of the shallow and congestus peaks is more robust than the peak of high clouds, whereas cloud water content exhibits larger intermodel differences than does cloud ice content. Furthermore, we investigated the resolution dependency of the vertical profiles of clouds for NICAM (Nonhydrostatic ICosahedral Atmospheric Model), ICON (Icosahedral Nonhydrostatic), and IFS (Integrated Forecasting System). We found that the averaged mixing ratio of ice clouds consistently increased with finer grid spacing. Such a consistent signal is not apparent for the mixing ratio of liquid clouds for shallow and congestus clouds. The impact of the grid spacing on OLR is smaller than on NSR and also much smaller than the intermodel differences
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.
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
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,
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