7,823 research outputs found
A Nagumo-like uniqueness result for a second order ODE
In this note, we present an extension to second order nonlinear ordinary
differential equations (ODEs) of the Nagumo-like uniqueness criterion for first
order ODEs established in [A. Constantin, On Nagumo's theorem, Proc. Japan
Acad. 86(A) (2010), pp. 41--44]
On the uniqueness of flow in a recent tsunami model
We give an elementary proof of uniqueness for the integral curve starting
from the vertical axis in the phase-plane analysis of the recent model [A.
Constantin, R.S. Johnson, Propagation of very long water waves, with vorticity,
over variable depth, with applications to tsunamis, Fluid Dynam. Res. 40
(2008), 175--211]. Our technique can be applied easily in circumstances where
the reparametrization device from [A. Constantin, A dynamical systems approach
towards isolated vorticity regions for tsunami background states, Arch.
Rational Mech. Anal. doi: 10.1007/s00205-010-0347-1] might lead to some serious
difficulties
On isolated vorticity regions beneath the water surface
We present a class of vorticity functions that will allow for isolated,
circular vorticity regions in the background of still water preceding the
arrival of a tsunami wave at the shoreline
Oscillatory solutions of some perturbed second order differential equations
We discuss the occurrence of oscillatory solutions which decay to 0 as
for a class of perturbed second order ordinary differential
equations. As opposed to other results in the recent literature, the
perturbation is as small as desired in terms of its improper integrals and it
is independent of the coefficients of the non-oscillatory unperturbed equation.
This class of equations reveals thus a new pathology in the theory of perturbed
oscillations
Anisotropic Strange Quintessence Stars in Gravity
In this paper, we have formulated the new exact model of quintessence
anisotropic star in theory of gravity. The dynamical equations in
theory with the anisotropic fluid and quintessence field have been solved by
using Krori-Barua solution. In this case, we have used the Starobinsky model of
gravity. We have determined that all the obtained solutions are free
from central singularity and potentially stable. The observed values of mass
and radius of the different strange stars PSR J 1614-2230,
SAXJ1808.4-3658(SS1), 4U1820- 30, PSR J 1614-2230 have been used to calculate
the values of unknown constants in Krori and Barua metric. The physical
parameters like anisotropy, stability and redshift of the stars have been
investigated in detail.Comment: 20 Pages, 12 figures, Accepted for publication in Astrophys. Space
Sci. arXiv admin note: substantial text overlap with arXiv:1412.212
A Modified Hard Thermal Loop Perturbation Theory
Based on the external perturbation that disturbs the system only slightly
from its equilibrium position we make the Taylor expansion of the pressure of a
quark gas. It turns out that the first term was used in the literature to
construct a Hard Thermal Loop perturbation theory (HTLpt) within the variation
principle of the lowest order of the thermal mass parameter. Various
thermodynamic quantities within the 1-loop HTLpt encountered overcounting of
the leading order (LO) contribution and also required a separation scale for
soft and hard momenta. Using same variational principle we reconstruct the
HTLpt at the first derivative level of the pressure that takes into account the
effect of the variation of the external source through the conserved density
fluctuation. This modification markedly improves those quantities in 1-loop
HTLpt in a simple way instead of pushing the calculation to a considerably more
complicated 2-loop HTLpt. Moreover, the results also agree with those obtained
in the 2-loop approximately self-consistent \Phi-derivable Hard Thermal Loop
resummation. We also discuss how this formalism can be extended for the higher
order contributionsComment: Paper revised; a sec. deleted and title change
On the asymptotic integration of a class of sublinear fractional differential equations
We estimate the growth in time of the solutions to a class of nonlinear
fractional differential equations which
includes with for
the case of slowly-decaying coefficients . The proof is based on the triple
interpolation inequality on the real line and the growth estimate reads as
when for . Our
result can be thought of as a non--integer counterpart of the classical Bihari
asymptotic integration result for nonlinear ordinary differential equations. By
a carefully designed example we show that in some circumstances such an
estimate is optimal
On the critical exponent of \eta/s and a new exponent-less measure of fluidity
We discuss on the critical exponent of for a fluid, and propose a
new exponent-less measure of fluidity based on a mode-mode coupling theory.
This exhibits a remarkable universality for fluids obeying a liquid-gas phase
transition both in hydrodynamic as well as in nonhydrodynamic region. We show
that this result is independent of the choice of the fluid dynamics, {\em
viz.}, relativistic or nonrelativistic. Quark-Gluon Plasma, being a hot
relativistic and a nearly perfect fluid produced in relativistic heavy-ion
collisions, is expected to obey the same universality constrained by both the
viscous and the thermal flow modes in it. We also show that if the elliptic
flow data in RHIC puts a constraint on then the new fluidity measure
for Quark-Gluon Plasma in turn also restricts the other transport coefficient,
{\it viz.}, the thermal conductivity.Comment: 4 pages and 2 figures; Title and abstract changed; discussion adde
On the Nagumo uniqueness theorem
By a convenient reparametrisation of the integral curves of a nonlinear
ordinary differential equation (ODE), we are able to improve the conclusions of
the recent contribution [A. Constantin, Proc. Japan Acad. {\bf 86(A)} (2010),
41--44]. In this way, we establish a flexible uniqueness criterion for ODEs
without Lipschitz-like nonlinearities
Temperature dependent Nucleon Mass and entropy bound inequality
Mass of a baryon as a function of temperature is calculated using
colour-singlet partition function for massless quarks (with two flavours) and
abelian gluons confined in a bag with a temperature dependent bag pressure
constant . The non-perturbative aspect of QCD interaction is included
through colour-singlet restriction on quark-gluon partition function in a
phenomenological way. The entropy bound inequality , where and are entropy, energy and radius, respectively of
the enclosed system with MeVfm, is found to be
consistent with the equilibrium solutions of the baryon mass upto a temperature
. There is a region of temperature ( is critical
temperature for quark-gluon plasma formation) in which no admissible
equilibrium states exist for the bag. We say that the system expriences a phase
jump from hadron to quark-gluon plasma through thermodynamic non-equlibrium
processes.Comment: Latex file(3 figures obtainable from first author
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