1,917 research outputs found
The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
We extend the Jang equation proof of the positive energy theorem due to R.
Schoen and S.-T. Yau from dimension to dimensions . This
requires us to address several technical difficulties that are not present when
. The regularity and decay assumptions for the initial data sets to which
our argument applies are weaker than those of R. Schoen and S.-T. Yau. In
recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a
different proof of the full positive mass theorem in dimensions .
We pointed out that this theorem can alternatively be derived from our density
argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy
Foliations and Chern-Heinz inequalities
We extend the Chern-Heinz inequalities about mean curvature and scalar
curvature of graphs of -functions to leaves of transversally oriented
codimension one -foliations of Riemannian manifolds. That extends
partially Salavessa's work on mean curvature of graphs and generalize results
of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and
Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of
3-dimensional Riemannian manifolds by constant mean curvature surfaces. These
Chern-Heinz inequalities for foliations can be applied to prove
Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of
bounded open subsets in terms of its inradius)
for embedded tubular neighborhoods of simple curves of .Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz
Inequalities. 8 Pages, Late
Results of special mechanical analyses of Luna 16 material
The studies carried out on the Luna 16 regolith have confirmed the data that were already published internationally. By means of activation analysis under irradiation in the reactor, activation analysis with a 14 MeV U-generator, and mass spectroscopy on samples of 10 or 20 mg, six main and 63 trace elements were quantitatively determined and compared with known data
Deformations of the hemisphere that increase scalar curvature
Consider a compact Riemannian manifold M of dimension n whose boundary
\partial M is totally geodesic and is isometric to the standard sphere S^{n-1}.
A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at
least n(n-1), then M is isometric to the hemisphere S_+^n equipped with its
standard metric. This conjecture is inspired by the positive mass theorem in
general relativity, and has been verified in many special cases. In this paper,
we construct counterexamples to Min-Oo's conjecture in dimension n \geq 3.Comment: Revised version, to appear in Invent. Mat
A compactness theorem for scalar-flat metrics on manifolds with boundary
Let (M,g) be a compact Riemannian manifold with boundary. This paper is
concerned with the set of scalar-flat metrics which are in the conformal class
of g and have the boundary as a constant mean curvature hypersurface. We prove
that this set is compact for dimensions greater than or equal to 7 under the
generic condition that the trace-free 2nd fundamental form of the boundary is
nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential
Equation
Boundary lubrication with a glassy interface
Recently introduced constitutive equations for the rheology of dense,
disordered materials are investigated in the context of stick-slip experiments
in boundary lubrication. The model is based on a generalization of the shear
transformation zone (STZ) theory, in which plastic deformation is represented
by a population of mesoscopic regions which may undergo non affine deformations
in response to stress. The generalization we study phenomenologically
incorporates the effects of aging and glassy relaxation. Under experimental
conditions associated with typical transitions from stick-slip to steady
sliding and stop start tests, these effects can be dominant, although the full
STZ description is necessary to account for more complex, chaotic transitions
Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei
The Asakura-Oosawa model for colloid-polymer mixtures is studied by Monte
Carlo simulations at densities inside the two-phase coexistence region of fluid
and solid. Choosing a geometry where the system is confined between two flat
walls, and a wall-colloid potential that leads to incomplete wetting of the
crystal at the wall, conditions can be created where a single nanoscopic
wall-attached crystalline cluster coexists with fluid in the remainder of the
simulation box. Following related ideas that have been useful to study
heterogeneous nucleation of liquid droplets at the vapor-liquid coexistence, we
estimate the contact angles from observations of the crystalline clusters in
thermal equilibrium. We find fair agreement with a prediction based on Young's
equation, using estimates of interface and wall tension from the study of flat
surfaces. It is shown that the pressure versus density curve of the finite
system exhibits a loop, but the pressure maximum signifies the "droplet
evaporation-condensation" transition and thus has nothing in common with a van
der Waals-like loop. Preparing systems where the packing fraction is deep
inside the two-phase coexistence region, the system spontaneously forms a "slab
state", with two wall-attached crystalline domains separated by (flat)
interfaces from liquid in full equilibrium with the crystal in between;
analysis of such states allows a precise estimation of the bulk equilibrium
properties at phase coexistence
Does Young's equation hold on the nanoscale? A Monte Carlo test for the binary Lennard-Jones fluid
When a phase-separated binary () mixture is exposed to a wall, that
preferentially attracts one of the components, interfaces between A-rich and
B-rich domains in general meet the wall making a contact angle .
Young's equation describes this angle in terms of a balance between the
interfacial tension and the surface tensions ,
between, respectively, the - and -rich phases and the wall,
. By Monte Carlo simulations
of bridges, formed by one of the components in a binary Lennard-Jones liquid,
connecting the two walls of a nanoscopic slit pore, is estimated from
the inclination of the interfaces, as a function of the wall-fluid interaction
strength. The information on the surface tensions ,
are obtained independently from a new thermodynamic integration method, while
is found from the finite-size scaling analysis of the
concentration distribution function. We show that Young's equation describes
the contact angles of the actual nanoscale interfaces for this model rather
accurately and location of the (first order) wetting transition is estimated.Comment: 6 pages, 6 figure
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