201 research outputs found
Nematic Films and Radially Anisotropic Delaunay Surfaces
We develop a theory of axisymmetric surfaces minimizing a combination of
surface tension and nematic elastic energies which may be suitable for
describing simple film and bubble shapes. As a function of the elastic constant
and the applied tension on the bubbles, we find the analogues of the unduloid,
sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure
On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
We study transformations of coordinates on a Lorentzian Einstein manifold
with a parallel distribution of null lines and show that the general Walker
coordinates can be simplified. In these coordinates, the full Lorentzian
Einstein equation is reduced to equations on a family of Einstein Riemannian
metrics.Comment: Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthda
Stability of complex hyperbolic space under curvature-normalized Ricci flow
Using the maximal regularity theory for quasilinear parabolic systems, we
prove two stability results of complex hyperbolic space under the
curvature-normalized Ricci flow in complex dimensions two and higher. The first
result is on a closed manifold. The second result is on a complete noncompact
manifold. To prove both results, we fully analyze the structure of the
Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result,
we also define suitably weighted little H\"{o}lder spaces on a complete
noncompact manifold and establish their interpolation properties.Comment: Some typos in version 2 are correcte
Bounding λ2 for KaÌhlerâEinstein metrics with large symmetry groups
We calculate an upper bound for the second non-zero eigenvalue of the scalar Laplacian, λ2, for toric-KaÌhlerâEinstein metrics in terms of the polytope data. We also give a similar upper bound for KoisoâSakane type KaÌhlerâEinstein metrics. We provide some detailed examples in complex dimensions 1, 2 and 3
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
Evidence of the Purely Leptonic Decay B- --> tau- nu_tau-bar
We present the first evidence of the decay B- --> tau- nu_tau-bar using 414
fb^-1 of data collected at the Upsilon(4S) resonance with the Belle detector at
the KEKB asymmetric-energy e+e- collider. Events are tagged by fully
reconstructing one of the B mesons in hadronic modes. We detect the signal with
a significance of 3.5 standard deviations including systematics, and measure
the branching fraction to be Br(B- --> tau- nu_tau-bar) = (1.79
+0.56-0.49(stat) +0.46-0.51(syst))*10^-4. This implies that f_B = 0.229
+0.036-0.031(stat) +0.034-0.037(syst) GeV and is the first direct measurement
of this quantity.Comment: 6 pages, 3 figures, to appear in Physical Review Letter
Space-Time Diffusion of Ground and Its Fractal Nature
We present evidences of the diffusive motion of the ground and tunnels and
show that if systematic movements are excluded then the remaining uncorrelated
component of the motion obeys a characteristic fractal law with the
displacement variance dY^2 scaling with time- and spatial intervals T and L as
dY^2 \propto T^(Alpha)L^(Gamma) with both exponents close to 1. We briefly
describe experimental methods of the mesa- and microscopic ground motion
detection used in the measurements at the physics research facilities sensitive
to the motion, particularly, large high energy elementary particle
accelerators. A simple mathematical model of the fractal motion demonstrating
the observed scaling law is also presented and discussed.Comment: 83 pages, 46 fig
Very Singular Diffusion Equations-Second and Fourth Order Problems
This paper studies singular diffusion equations whose diffusion effect is so strong that the speed of evolution becomes a nonlocal quantity. Typical examples include the total variation flow as well as crystalline flow which are formally of second order. This paper includes fourth order models which are less studied compared with second order models. A typical example of this model is an Hâ1 gradient flow of total variation. It turns out that such a flow is quite different from the second order total variation flow. For example, we prove that the solution may instantaneously develop jump discontinuity for the fourth order total variation flow by giving an explicit example
Observation of B0->pi0pi0
We report the first observation of the decay B0->pi0pi0, using a 253/fb data
sample collected at the Upsilon(4S) resonance with the Belle detector at the
KEKB e+e- collider. The measured branching fraction is BF(B0->pi0pi0) = {2.32
+0.4-0.5(stat) +0.2-0.3(syst)} x 10^-6, with a significance of 5.8 standard
deviations including systematic uncertainties. We also make the first
measurement of the direct CP violating asymmetry in this mode.Comment: 6 pages, 2 figures, submitted to ICHEP04, Beijing and Physical Review
Letters. v2: a possible pile-up background is checked and a systematic error
for it is include
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