2,155 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
Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology
A key symmetry of classical -branes is invariance under worldvolume
diffeomorphisms. Under the assumption that the worldvolume, at fixed values of
the time, is a compact, quantisable K\"ahler manifold, we prove that the Lie
algebra of volume-preserving diffeomorphisms of the worldvolume can be
approximated by , for . We also prove, under the same
assumptions regarding the worldvolume at fixed time, that classical Nambu
brackets on the worldvolume are quantised by the multibrackets corresponding to
cocycles in the cohomology of the Lie algebra .Comment: This is a contribution to the Special Issue on Deformation
Quantization, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
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
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
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
Pinwheel patterns and powder diffraction
Pinwheel patterns and their higher dimensional generalisations display
continuous circular or spherical symmetries in spite of being perfectly
ordered. The same symmetries show up in the corresponding diffraction images.
Interestingly, they also arise from amorphous systems, and also from regular
crystals when investigated by powder diffraction. We present first steps and
results towards a general frame to investigate such systems, with emphasis on
statistical properties that are helpful to understand and compare the
diffraction images. We concentrate on properties that are accessible via an
alternative substitution rule for the pinwheel tiling, based on two different
prototiles. Due to striking similarities, we compare our results with the toy
model for the powder diffraction of the square lattice.Comment: 7 pages, 4 figure
Some comments on the inverse problem of pure point diffraction
In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for
constructing families of real solutions to the inverse problem for a given pure
point diffraction measure. Applying their technique and discussing some
possible extensions, we present, in a non-technical manner, some examples of
homometric structures.Comment: 6 pages, contribution to Aperiodic 201
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