318 research outputs found
On free general relativistic initial data on the light cone
We provide a simple explicit parameterization of free general relativistic
data on the light cone
Nonlinear interaction of seismic waves in the lab: A potential tool for characterizing pore structure and fluids
As more and more resources are extracted from unconventional reservoirs, an understanding of the microstructure of reservoir rocks is of increasing importance. Many conventional techniques struggle to sense variations in the micro-structure and pore-fluids of rock samples. The nonlinear coupling of two elastic waves is known to be sensitive to these parameters, however, and so is a natural candidate to improve our understanding of these structures. Here, we develop an experimental technique to sense the nonlinear interaction of two propagating waves: a strong S-wave pump that changes (minutely) the elastic properties of the sample and a weaker P-wave probe that senses those changes. By measuring the delay in the P-wave probe traveltime induced by the S-wave pump, we show that this signal is significant in a Berea sandstone sample and absent in Aluminum and Plexiglass samples. The polarization of the S-wave (particle motion aligned or perpendicular to the P-wave probe) has a large impact on the measured response; this is evidence that the signal we measure is sensitive to the micro-structure of the rock. We show that the method is sensitive to fluids by imaging the variations in two specific nonlinear parameters, caused by the introduction of fluid into a Berea sandstone sample
On the Weyl Curvature Hypothesis
The Weyl curvature hypothesis of Penrose attempts to explain the high
homogeneity and isotropy, and the very low entropy of the early universe, by
conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity.
In previous papers it has been proposed an equivalent form of Einstein's
equation, which extends it and remains valid at an important class of
singularities (including in particular the Schwarzschild, FLRW, and isotropic
singularities). Here it is shown that if the Big-Bang singularity is from this
class, it also satisfies the Weyl curvature hypothesis.
As an application, we study a very general example of cosmological models,
which generalizes the FLRW model by dropping the isotropy and homogeneity
constraints. This model also generalizes isotropic singularities, and a class
of singularities occurring in Bianchi cosmologies. We show that the Big-Bang
singularity of this model is of the type under consideration, and satisfies
therefore the Weyl curvature hypothesis.Comment: 10 pages, slides at
http://www.sciencedirect.com/science/article/pii/S000349161300171
Parallel spinors and holonomy groups
In this paper we complete the classification of spin manifolds admitting
parallel spinors, in terms of the Riemannian holonomy groups. More precisely,
we show that on a given n-dimensional Riemannian manifold, spin structures with
parallel spinors are in one to one correspondence with lifts to Spin_n of the
Riemannian holonomy group, with fixed points on the spin representation space.
In particular, we obtain the first examples of compact manifolds with two
different spin structures carrying parallel spinors.Comment: 10 pages, LaTeX2
Manifolds with small Dirac eigenvalues are nilmanifolds
Consider the class of n-dimensional Riemannian spin manifolds with bounded
sectional curvatures and diameter, and almost non-negative scalar curvature.
Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of
the Dirac operator on such a manifold has small eigenvalues, then the
manifold is diffeomorphic to a nilmanifold and has trivial spin structure.
Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a
non-trivial spin structure, then there exists a uniform lower bound on the r-th
eigenvalue of the square of the Dirac operator. If a manifold with almost
nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume
is not too small, then we show that the metric is close to a Ricci-flat metric
on M with a parallel spinor. In dimension 4 this implies that M is either a
torus or a K3-surface
Wideband THz time domain spectroscopy based on optical rectification and electro-optic sampling
We present an analytical model describing the full electromagnetic propagation in a THz time-domain spectroscopy (THz-TDS) system, from the THz pulses via Optical Rectification to the detection via Electro Optic-Sampling. While several investigations deal singularly with the many elements that constitute a THz-TDS, in our work we pay particular attention to the modelling of the time-frequency behaviour of all the stages which compose the experimental set-up. Therefore, our model considers the following main aspects: (i) pump beam focusing into the generation crystal; (ii) phase-matching inside both the generation and detection crystals; (iii) chromatic dispersion and absorption inside the crystals; (iv) Fabry-Perot effect; (v) diffraction outside, i.e. along the propagation, (vi) focalization and overlapping between THz and probe beams, (vii) electro-optic sampling. In order to validate our model, we report on the comparison between the simulations and the experimental data obtained from the same set-up, showing their good agreement
A natural Finsler--Laplace operator
We give a new definition of a Laplace operator for Finsler metric as an
average with regard to an angle measure of the second directional derivatives.
This definition uses a dynamical approach due to Foulon that does not require
the use of connections nor local coordinates. We show using 1-parameter
families of Katok--Ziller metrics that this Finsler--Laplace operator admits
explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio
The exact 8d chiral ring from 4d recursion relations
We consider the local F-theory set-up corresponding to four D7 branes in type
I' theory, in which the exact axio-dilaton background tau(z) is identified with
the low-energy effective coupling of the four-dimensional N=2 super Yang-Mills
theory with gauge group SU(2) and Nf=4 flavours living on a probe D3 brane
placed at position z. Recently, an intriguing relation has been found between
the correlators forming the chiral ring of the eight-dimensional theory on the
D7 branes and the large-z expansion of the tau profile. Here we apply to the
SU(2), Nf=4 theory some recursion techniques that allow to derive the
coefficients of the large-z expansion of tau in terms of modular functions of
the UV coupling. In this way we obtain exact expressions for the elements of
the eight-dimensional chiral ring that resum their instanton expansions,
previously known only up to the first few orders by means of localization
techniques.Comment: 23 pages, Latex2
Towards a unified theory of Sobolev inequalities
We discuss our work on pointwise inequalities for the gradient which are
connected with the isoperimetric profile associated to a given geometry. We
show how they can be used to unify certain aspects of the theory of Sobolev
inequalities. In particular, we discuss our recent papers on fractional order
inequalities, Coulhon type inequalities, transference and dimensionless
inequalities and our forthcoming work on sharp higher order Sobolev
inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1
- …