1,998 research outputs found
Instability of the solitary waves for the generalized Boussinesq equations
In this work, we consider the following generalized Boussinesq equation
\begin{align*}
\partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad
(t,x)\in\mathbb R\times \mathbb R, \end{align*} with . This
equation has the traveling wave solutions , with the
frequency and satisfying \begin{align*}
-\partial_{xx}{\phi}_{\omega}+(1-{\omega^2}){\phi}_{\omega}-{\phi}_{\omega}^{p+1}=0.
\end{align*} Bona and Sachs (1988) proved that the traveling wave
is orbitally stable when . Liu (1993) proved the orbital instability under the conditions
or . In this paper, we prove
the orbital instability in the degenerate case .Comment: 29 page
Effects of density-dependent quark mass on phase diagram of three-flavor quark matter
Considering the density dependence of quark mass, we investigate the phase
transition between the (unpaired) strange quark matter and the
color-flavor-locked matter, which are supposed to be two candidates for the
ground state of strongly interacting matter. We find that if the current mass
of strange quark is small, the strange quark matter remains stable unless
the baryon density is very high. If is large, the phase transition from
the strange quark matter to the color-flavor-locked matter in particular to its
gapless phase is found to be different from the results predicted by previous
works. A complicated phase diagram of three-flavor quark matter is presented,
in which the color-flavor-locked phase region is suppressed for moderate
densities.Comment: 4 figure
Comment on " a unified scheme for flavored mesons and baryons"
We would comment on the results of the paper "a unified scheme for flavored
mesons and baryons" (P.C.Vinodkumar, J.N.Panandya, V.M.Bannur, and
S.B.Khadkikar Eur. Phys. J. A4(1999)83), and point out some inconsistencies and
mistakes in the work for solving the Dirac equation. In terms of an example for
a single particle we investigate the reliability of the perturbative method for
computing the Coulomb energy and discuss the contribution to the wavefunction
at origin from the Coulomb potential. We conclude that the accuracy of their
numerical results needs to be reconsidered.Comment: Latex file, 11page
Detectable MeV neutrinos from black hole neutrino-dominated accretion flows
Neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black
holes (BHs) have been theorized as the central engine of relativistic jets
launched in massive star core collapse events or compact star mergers. In this
work, we calculate the electron neutrino/anti-neutrino spectra of NDAFs by
fully taking into account the general relativistic effects, and investigate the
effects of viewing angle, BH spin, and mass accretion rate on the results. We
show that even though a typical NDAF has a neutrino luminosity lower than that
of a typical supernova (SN), it can reach
peaking at MeV, making them potentially detectable with the upcoming
sensitive MeV neutrino detectors if they are close enough to Earth. Based on
the observed GRB event rate in the local universe and requiring that at least 3
neutrinos are detected to claim a detection, we estimate a detection rate up to
(0.10-0.25) per century for GRB-related NDAFs by the Hyper-Kamiokande
(Hyper-K) detector if one neglects neutrino oscillation. If one assumes that
all Type Ib/c SNe have an engine-driven NDAF, the Hyper-K detection rate would
be (1-3) per century. By considering neutrino oscillations, the
detection rate may decrease by a factor of 2-3. Detecting one such event would
establish the observational evidence of NDAFs in the universe.Comment: 7 pages, 2 figures, 2 tables, accepted for publication in PR
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