2,633 research outputs found
Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations
We consider the focusing nonlinear Schr\"odinger equations in dimension and for slightly
supercritical nonlinearities p_c
with and 0<\e\ll 1. We prove the existence and stability in the energy space of a self similar finite time blow up dynamics and provide a qualitative description of the singularity formation near the blow up tim
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension
We consider the semilinear wave equation with power nonlinearity in one space
dimension. We consider an arbitrary blow-up solution , the graph
of its blow-up points and the set
of all characteristic points. We show that {\ca S} is locally finite.Comment: 57 page
Blow-up behavior outside the origin for a semilinear wave equation in the radial case
We consider the semilinear wave equation in the radial case with conformal
subcritical power nonlinearity. If we consider a blow-up point different from
the origin, then we exhibit a new Lyapunov functional which is a perturbation
of the one dimensional case and extend all our previous results known in the
one-dimensional case. In particular, we show that the blow-up set near non-zero
non-characteristic points is of class , and that the set of characteristic
points is made of concentric spheres in finite number in for any .Comment: 21 page
Effective theory of a doubly charged singlet scalar: complementarity of neutrino physics and the LHC
We consider a rather minimal extension of the Standard Model involving just
one extra particle, namely a single singlet scalar and its
antiparticle . We propose a model independent effective operator, which
yields an effective coupling of to pairs of same sign weak gauge
bosons, . We also allow tree-level couplings of
to pairs of same sign right-handed charged leptons of the
same or different flavour. We calculate explicitly the resulting two-loop
diagrams in the effective theory responsible for neutrino mass and mixing. We
propose sets of benchmark points for various masses and couplings
which can yield successful neutrino masses and mixing, consistent with limits
on charged lepton flavour violation (LFV) and neutrinoless double beta decay.
We discuss the prospects for discovery at the LHC, for these
benchmark points, including single and pair production and decay into same sign
leptons plus jets and missing energy. The model represents a minimal example of
the complementarity between neutrino physics (including LFV) and the LHC,
involving just one new particle, the .Comment: 57 pages, 14 figures, 10 tables, version accepted for publication in
JHE
Dark Radiation or Warm Dark Matter from long lived particle decays in the light of Planck
Although Planck data supports the standard \Lambda CDM model, it still allows
for the presence of Dark Radiation corresponding up to about half an extra
standard neutrino species. We propose a scenario for obtaining a fractional
"effective neutrino species" from a thermally produced particle which decays
into a much lighter stable relic plus standard fermions. At lifetimes much
longer than 1 sec, both the relic particles and the non-thermal neutrino
component contribute to Dark Radiation. By increasing the stable-to-unstable
particle mass ratio, the relic particle no longer acts as Dark Radiation but
instead becomes a candidate for Warm Dark Matter with mass O(1keV - 100GeV). In
both cases it is possible to address the lithium problem.Comment: 18 pages, 2 figures; v3 matches version to be published in PL
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