2,660 research outputs found
Mathematical and computational studies of equilibrium capillary free surfaces
The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated
Lifting a Realistic SO(10) Grand Unified Model to Five Dimensions
It has been shown recently that the problem of rapid proton decay induced by
dimension five operators arising from the exchange of colored Higgsinos can be
simply avoided in grand unified models where a fifth spatial dimension is
compactified on an orbifold. Here we demonstrate that this idea can be used to
solve the Higgsino-mediated proton decay problem in any realistic SO(10) model
by lifting that model to five dimensions. A particular SO(10) model that has
been proposed to explain the pattern of quark and lepton masses and mixings is
used as an example. The idea is to break the SO(10) down to the Pati-Salam
symmetry by the orbifold boundary conditions. The entire four-dimensional
SO(10) model is placed on the physical SO(10) brane except for the gauge
fields, the 45 and a single 10 of Higgs fields, which are placed in the
five-dimensional bulk. The structure of the Higgs superpotential can be
somewhat simplified in doing so, while the Yukawa superpotential and mass
matrices derived from it remain essentially unaltered.Comment: 17 pages, version to be published in Phys. Rev. D with expanded
discussion of the suppression of dim-5 proton decay operator
Realization of the Large Mixing Angle Solar Neutrino Solution in an SO(10) Supersymmetric Grand Unified Model
An SO(10) supersymmetric grand unified model proposed earlier leading to the
solar solution involving ``just-so'' vacuum oscillations is reexamined to study
its ability to obtain the other possible solar solutions. It is found that all
four viable solar neutrino oscillation solutions can be achieved in the model
simply by modification of the right-handed Majorana neutrino mass matrix, M_R.
Whereas the small mixing and vacuum solutions are easily obtained with several
texture zeros in M_R, the currently-favored large mixing angle solution
requires a nearly geometric hierarchical form for M_R that leads by the seesaw
formula to a light neutrino mass matrix which has two or three texture zeros.
The form of the matrix which provides the ``fine-tuning'' necessary to achieve
the large mixing angle solution can be understood in terms of Froggatt-Nielsen
diagrams for the Dirac and right-handed Majorana neutrino mass matrices. The
solution fulfils several leptogenesis requirements which in turn can be
responsible for the baryon asymmetry in the universe.Comment: 14 pages including 2 figure
Horizontal symmetry in Higgs sector of GUT with U(1)_A symmetry
In a series of papers, we pointed out that an anomalous gauge
symmetry naturally solves various problems in grand unified theories (GUTs) and
that a horizontal gauge symmetry, or , not only realizes the
unification of three generation quarks and leptons in fewer multiplets but also
solves the supersymmetric flavor problem. In this paper, we examine the
possibility that the Higgs sectors of the GUT symmetry and of the horizontal
symmetry are unified, that is, there are some Higgs fields whose vacuum
expectation values (VEVs) break both the GUT gauge symmetry and the horizontal
symmetry at the same time. Although the scale of the VEVs become too large to
suppress the flavor changing neutral current processes sufficiently, the
unification is possible. In addition, for the models, the
gauge anomaly is cancelled in the unified models without introducing additional
fields in contrast with the previous models in which the Higgs sectors are not
unified.Comment: 35 page
`t Hooft Anomaly Matching for QCD
I present a set of theories which display non-trivial `t Hooft anomaly
matching for QCD with flavors. The matching theories are non-Abelian gauge
theories with "dual" quarks and baryons, rather than the purely confining
theories of baryons that `t Hooft originally searched for. The matching gauge
groups are required to have an dimensional representation. Such a
correspondence is reminiscent of Seiberg's duality for supersymmetric (SUSY)
QCD, and these theories are candidates for non-SUSY duality. However anomaly
matching by itself is not sufficiently restrictive, and duality for QCD cannot
be established at present. At the very least, the existence of multiple anomaly
matching solutions should provide a note of caution regarding conjectured
non-SUSY dualities.Comment: 8 pages, LaTeX, version to be published in PR
Lepton Flavor Violation in Supersymmetric SO(10) Grand Unified Models
The study for lepton flavor violation combined with the neutrino oscillation
may provide more information about the lepton flavor structure of the grand
unified theory. In this paper, we study two lepton flavor violation processes,
and , in the context of supersymmetric SO(10)
grand unified models. We find the two processes are both of phenomenological
interest. In particular the latter may be important in some supersymmetric
parameter space where the former is suppressed. Thus, Z-dacay may offer another
chance for looking for lepton flavor violation.Comment: 26 pages, 10 figure
Encephalocele – A Single Institution African Experience
Objective: This study seeks to find out the presentation, management and complications of encephaloceles in an African setting.Design: a retrospective study reviewing the age and sex of the patients, type and contents of encephaloceles, associated anomalies, preoperative evaluation and investigations, surgical approaches, intra- and post-operative complications as well as follow-up outcomes.Setting: Bethany Crippled Children’s centre and Bethanykids at Kijabe Hospital (BKKH), between January 1998 and August 2006.Patients: Of the 53 patients seen, 23 were males and 30 females. The median age at presentation was four months.Results: The follow-up period extended to eight years. Twenty nine patients had occipital encephaloceles, and 39 were operated using the direct external approach. Cererobrospinal fluid leak was the most common post-operative complication. Recurrence occurred in four patients and death in six.Conclusions: Most of the encephalocele patients managed at BKKH had good outcomes and proceeded to live normal or near-normal lives. Our study confirms that even in resource-constrained areas, children with encephaloceles can be successfully managed with acceptable outcomes
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