259,666 research outputs found
A refined invariant subspace method and applications to evolution equations
The invariant subspace method is refined to present more unity and more
diversity of exact solutions to evolution equations. The key idea is to take
subspaces of solutions to linear ordinary differential equations as invariant
subspaces that evolution equations admit. A two-component nonlinear system of
dissipative equations was analyzed to shed light on the resulting theory, and
two concrete examples are given to find invariant subspaces associated with
2nd-order and 3rd-order linear ordinary differential equations and their
corresponding exact solutions with generalized separated variables.Comment: 16 page
Nearly Mass-Degenerate Majorana Neutrinos: Double Beta Decay and Neutrino Oscillations
Assuming equal tree-level Majorana masses for the standard-model neutrinos,
either from the canonical seesaw mechanism or from a heavy scalar triplet, I
discuss how their radiative splitting may be relevant to neutrinoless double
beta decay and neutrino oscillations.Comment: 12 pages, including 4 figures, talk at NANP9
Solutions of the Polchinski ERG equation in the O(N) scalar model
Solutions of the Polchinski exact renormalization group equation in the
scalar O(N) theory are studied. Families of regular solutions are found and
their relation with fixed points of the theory is established. Special
attention is devoted to the limit , where many properties can be
analyzed analytically.Comment: 34 pages, 10 figures. References added. Version accepted for
publication in the International Journal of Modern Physics
Lensed Arcs and Inner Structure of Abell 697
We present new optical observations of the z=0.282 cluster Abell 697 from the
Keck II telescope. Images show an unusual disturbed structure in the cD halo
and a previously unknown faint gravitational lens arc. A spectrum of the arc
did not yield a redshift, but its spectrum and colors suggest it lies at z>1.3.
We construct models to reproduce the arc that show the potential is likely to
be highly elliptical. We suggest that this cluster may have undergone a recent
merger and is in the process of forming its cD galaxy. Analysis of X-ray data
from ROSAT and ASCA suggests that the merging process is sufficiently advanced
that the gas in the cluster has relaxed, and A697 lies near the L_x-T_x
relation for normal clusters.Comment: LaTeX; 12 pages, 3 figures, submitted to ApJ Letter
Neutrino Mass from Triplet and Doublet Scalars at the TeV Scale
If the minimal standard model of particle interactions is extended to include
a scalar triplet with lepton number and a scalar doublet with ,
neutrino masses eV is possible,
where GeV is the electroweak symmetry breaking scale,
TeV is the typical mass of the new scalars, and GeV is a soft
lepton-number-violating parameter.Comment: 6 pages, no figur
Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
The leptonic Higgs doublet model of neutrino masses is implemented with an
A_4 discrete symmetry (the even permutation of 4 objects or equivalently the
symmetry of the tetrahedron) which has 4 irreducible representations: 1, 1',
1'', and 3. The resulting spontaneous and soft breaking of A_4 provides a
realistic model of charged-lepton masses as well as a nearly degenerate
neutrino mass matrix. Phenomenological consequences at and below the TeV scale
are discussed.Comment: 11 pages, no figur
Lagrangian Based Methods for Coherent Structure Detection
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic
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