9,077 research outputs found
Multiple boundary peak solutions for some singularly perturbed Neumann problems
We consider the problem \left \{
\begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega,
\end{array} \right. where \Omega is a bounded smooth domain in R^N, \varepsilon>KK-peakH(P)K-peak$ solutions.
We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions.
Then we use a maximizing procedure to obtain multiple boundary spikes
Generalised CP and Family Symmetry
We perform a comprehensive study of family symmetry models based on
combined with the generalised CP symmetry . We investigate the
lepton mixing parameters which can be obtained from the original symmetry
breaking to different remnant symmetries in the
neutrino and charged lepton sectors. We find that only one case is
phenomenologically viable, namely in the neutrino sector and in the charged lepton sector, leading to the
prediction of no CP violation, namely and the Majorana phases
and are all equal to either zero or . We then
propose an effective supersymmetric model based on the symmetry in which trimaximal lepton mixing is predicted together with
either zero CP violation or with non-trivial
Majorana phases. An ultraviolet completion of the effective model yields a
neutrino mass matrix which depends on only three real parameters. As a result
of this, all three CP phases and the absolute neutrino mass scale are
determined, the atmospheric mixing angle is maximal, and the Dirac CP can
either be preserved with or maximally broken with
and sharp predictions for the Majorana phases and
neutrinoless double beta decay.Comment: 38 pages, 3 figure
Generalized reflection symmetry and leptonic CP violation
We propose a generalized reflection symmetry to constrain the
lepton flavor mixing parameters. We obtain a new correlation between the
atmospheric mixing angle and the "Dirac" CP violation phase
. Only in a specific limit our proposed CP transformation
reduces to standard reflection, for which and
are both maximal. The "Majorana" phases are predicted to lie at
their CP-conserving values with important implications for the neutrinoless
double beta decay rates. We also study the phenomenological implications of our
scheme for present and future neutrino oscillation experiments including T2K,
NOA and DUNE.Comment: 14 pages, 9 figures, latex, Final version to appear in Physics
Letters
Electron-positron pair creation in a vacuum by an electromagnetic field in 3+1 and lower dimensions
We calculate the probability of electron-positron pair creation in vacuum in
3+1 dimensions by an external electromagnetic field composed of a constant
uniform electric field and a constant uniform magnetic field, both of arbitrary
magnitudes and directions. The same problem is also studied in 2+1 and 1+1
dimensions in appropriate external fields and similar results are obtained.Comment: REVTeX, 10 pages, no figure, a brief note and some more references
added in the proo
Scattering by a contact potential in three and lower dimensions
We consider the scattering of nonrelativistic particles in three dimensions
by a contact potential which is defined
as the limit of . It is
surprising that it gives a nonvanishing cross section when and
. When the contact potential is approached by a spherical square
well potential instead of the above spherical shell one, one obtains basically
the same result except that the parameter that gives a nonvanishing
cross section is different. Similar problems in two and one dimensions are
studied and results of the same nature are obtained.Comment: REVTeX, 9 pages, no figur
Phase-field-crystal modeling of the (2x1)-(1x1) phase-transitions of Si(001) and Ge(001) surfaces
We propose a two-dimensional phase-field-crystal model for the
(21)-(11) phase transitions of Si(001) and Ge(001) surfaces.
The dimerization in the 21 phase is described with a
phase-field-crystal variable which is determined by solving an evolution
equation derived from the free energy. Simulated periodic arrays of
dimerization variable is consistent with scanning-tunnelling-microscopy images
of the two dimerized surfaces. Calculated temperature dependence of the
dimerization parameter indicates that normal dimers and broken ones coexist
between the temperatures describing the charactristic temperature width of the
phase-transition, and , and a first-order phase transition takes
place at a temperature between them. The dimerization over the whole
temperature is determined. These results are in agreement with experiment. This
phase-field-crystal approach is applicable to phase-transitions of other
reconstructed surface phases, especially semiconductor 1 reconstructed
surface phases.Comment: 10 pages with 4 figures include
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