1,178 research outputs found
Absence of squirt singularities for the multi-phase Muskat problem
In this paper we study the evolution of multiple fluids with different
constant densities in porous media. This physical scenario is known as the
Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that
the fluids do not develop squirt singularities.Comment: 16 page
Breakdown of smoothness for the Muskat problem
In this paper we show that there exist analytic initial data in the stable
regime for the Muskat problem such that the solution turns to the unstable
regime and later breaks down i.e. no longer belongs to .Comment: 93 pages, 10 figures (6 added
On the noncommutative eikonal
We study the eikonal approximation to quantum mechanics on the Moyal plane.
Instead of using a star product, the analysis is carried out in terms of
operator-valued wavefunctions depending on noncommuting, operator-valued
coordinates.Comment: 18 page
Ricci flow, quantum mechanics and gravity
It has been argued that, underlying any given quantum-mechanical model, there
exists at least one deterministic system that reproduces, after
prequantisation, the given quantum dynamics. For a quantum mechanics with a
complex d-dimensional Hilbert space, the Lie group SU(d) represents classical
canonical transformations on the projective space CP^{d-1} of quantum states.
Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and
let P denote the projection from the Hopf bundle onto its base CP^{d-1}. Then
the underlying deterministic model we propose here is the Lie group SU(d),
acted on by the operation PR. Finally we comment on some possible consequences
that our model may have on a quantum theory of gravity.Comment: 8 page
Neutrino mixing and masses in a left-right model with mirror fermions
In the framework of a left-right model containing mirror fermions with gauge
group SU(3),
we estimate the neutrino masses, which are found to be consistent with their
experimental bounds and hierarchy. We evaluate the decay rates of the Lepton
Flavor Violation (LFV) processes , and . We obtain upper limits for the
flavor-changing branching ratios in agreement with their present experimental
bounds. We also estimate the decay rates of heavy Majorana neutrinos in the
channels , and , which are roughly equal for large values of the heavy
neutrino mass. Starting from the most general Majorana neutrino mass matrix,
the smallness of active neutrino masses turns out from the interplay of the
hierarchy of the involved scales and the double application of seesaw
mechanism. An appropriate parameterization on the structure of the neutrino
mass matrix imposing a symmetric mixing of electron neutrino with muon and tau
neutrinos leads to Tri-bimaximal mixing matrix for light neutrinos.Comment: Accepted by European Physical Journal
Neutrino masses and mixing parameters in a left-right model with mirror fermions
In this work we consider a left-right model containing mirror fermions with
gauge group SU(3). The model has several free parameters which here we have
calculated by using the recent values for the squared-neutrino mass
differences. Lower bound for the mirror vacuum expectation value helped us to
obtain crude estimations for some of these parameters. Also we estimate the
order of magnitude of the masses of the standard and mirror neutrinos.Comment: 13 pages, version submitted to European Physical Journal
Rank one discrete valuations of power series fields
In this paper we study the rank one discrete valuations of the field
whose center in k\lcor\X\rcor is the maximal ideal. In
sections 2 to 6 we give a construction of a system of parametric equations
describing such valuations. This amounts to finding a parameter and a field of
coefficients. We devote section 2 to finding an element of value 1, that is, a
parameter. The field of coefficients is the residue field of the valuation, and
it is given in section 5.
The constructions given in these sections are not effective in the general
case, because we need either to use the Zorn's lemma or to know explicitly a
section of the natural homomorphism R_v\to\d between the ring and
the residue field of the valuation .
However, as a consequence of this construction, in section 7, we prove that
k((\X)) can be embedded into a field L((\Y)), where is an algebraic
extension of and the {\em ``extended valuation'' is as close as possible to
the usual order function}
A maximum principle for the Muskat problem for fluids with different densities
We consider the fluid interface problem given by two incompressible fluids
with different densities evolving by Darcy's law. This scenario is known as the
Muskat problem for fluids with the same viscosities, being in two dimensions
mathematically analogous to the two-phase Hele-Shaw cell. We prove in the
stable case (the denser fluid is below) a maximum principle for the
norm of the free boundary.Comment: 16 page
Superconducting density of states at the border of an amorphous thin film grown by focused-ion-beam
We present very low temperature Scanning Tunneling Microscopy and
Spectroscopy (STM/S) measurements of a W based amorphous thin film grown with
focused-ion-beam. In particular, we address the superconducting properties
close to the border, where the thickness of the superconducting film decreases,
and the Au substrate emerges. When approaching the Au substrate, the
superconducting tunneling conductance strongly increases around the Fermi
level, and the quasiparticle peaks do not significantly change its position.
Under magnetic fields, the vortex lattice is observed, with vortices positioned
very close to the Au substrate.Comment: To appear in Journal of Physics: Conference serie
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