23,348 research outputs found
Oscillatory and nonoscillatory properties of solutions of functional differential equations and difference equations
Oscillation and nonoscillation of solutions of functional differential equations and difference equations are analyzed qualitatively. A qualitative approach is usually concerned with the behavior of solutions of a given equation and does not seek explicit solutions. The dissertation is divided into five chapters. The first chapter is essentially introductory in nature. Its main purpose is to introduce certain well-known basic concepts and to present some result that are not as well-known. In chapter 2 and chapter 3 we present sufficient conditions for oscillation of solutions of neutral differential equations of the form [a(t)[x(t) + p(t)x([tau](t))] [superscript](n-1)] [superscript]\u27 + q(t)f(x([sigma](t))) = 0and [x(t) + p(t)x([tau](t))] [superscript](n) + q[subscript]1(t)f(x([sigma][subscript]1(t))) + q[subscript]2(t)f(x([sigma][subscript]2(t))) = h(t)respectively. Chapter 4 discusses the oscillation, nonoscillation, and the asymptotic behavior of solutions of higher order functional differential equations of the form (r[subscript]2(r[subscript]1 x[superscript]\u27(t))[superscript]\u27)[superscript]\u27 + q(t)f(x([sigma](t))) = h(t)and x[superscript](n)(t) + F(t,x([sigma][subscript]1(t)),...,x([sigma][subscript]m(t))) = h(t).Chapter 5 is devoted the study of oscillatory solutions of neutral type difference equations of the form [delta][a[subscript]n[delta][superscript]m-1(x[subscript]n + p[subscript]nx[subscript][tau][subscript]n)] + q[subscript]nf(x[subscript][sigma][subscript]n) = 0and that of asymptotic behavior for n → [infinity] of solutions of equations of the form [delta][superscript]mx[subscript]n + F(n, x[subscript][sigma][subscript]n) = h[subscript]n.The results obtained here are the discrete analogs of several of those in chapter 1 and chapter 4;A function x(t) : [a,[infinity]) → R is said to be oscillatory if it has a zero on [T,[infinity]) for every T ≥ a; otherwise it is called nonoscillatory. Similarly a sequence \x[subscript]n of real numbers is oscillatory if it is not eventually positive or eventually negative; otherwise it is nonoscillatory
A delay differential model of ENSO variability: Parametric instability and the distribution of extremes
We consider a delay differential equation (DDE) model for El-Nino Southern
Oscillation (ENSO) variability. The model combines two key mechanisms that
participate in ENSO dynamics: delayed negative feedback and seasonal forcing.
We perform stability analyses of the model in the three-dimensional space of
its physically relevant parameters. Our results illustrate the role of these
three parameters: strength of seasonal forcing , atmosphere-ocean coupling
, and propagation period of oceanic waves across the Tropical
Pacific. Two regimes of variability, stable and unstable, are separated by a
sharp neutral curve in the plane at constant . The detailed
structure of the neutral curve becomes very irregular and possibly fractal,
while individual trajectories within the unstable region become highly complex
and possibly chaotic, as the atmosphere-ocean coupling increases. In
the unstable regime, spontaneous transitions occur in the mean ``temperature''
({\it i.e.}, thermocline depth), period, and extreme annual values, for purely
periodic, seasonal forcing. The model reproduces the Devil's bleachers
characterizing other ENSO models, such as nonlinear, coupled systems of partial
differential equations; some of the features of this behavior have been
documented in general circulation models, as well as in observations. We
expect, therefore, similar behavior in much more detailed and realistic models,
where it is harder to describe its causes as completely.Comment: 22 pages, 9 figure
On Nonoscillation of Mixed Advanced-Delay Differential Equations with Positive and Negative Coefficients
For a mixed (advanced--delay) differential equation with variable delays and
coefficients
where explicit
nonoscillation conditions are obtained.Comment: 17 pages; 2 figures; to appear in Computers & Mathematics with
Application
Speed-up of neutrino transformations in a supernova environment
When the neutral current neutrino-neutrino interaction is treated completely,
rather than as an interaction among angle-averaged distributions, or as a set
of flavor-diagonal effective potentials, the result can be flavor mixing at a
speed orders of magnitude faster than that one would anticipate from the
measured neutrino oscillation parameters. It is possible that the energy
spectra of the three active species of neutrinos emerging from a supernova are
nearly identical.Comment: 8 pages, 4 figure
Asymptotically polynomial solutions of difference equations of neutral type
Asymptotic properties of solutions of difference equation of the form are studied. We give
sufficient conditions under which all solutions, or all solutions with
polynomial growth, or all nonoscillatory solutions are asymptotically
polynomial. We use a new technique which allows us to control the degree of
approximation
Tau Neutrinos Underground: Signals of Oscillations with Extragalactic Neutrinos
The appearance of high energy tau neutrinos due to
oscillations of extragalactic neutrinos can be observed by measuring the
neutrino induced upward hadronic and electromagnetic showers and upward muons.
We evaluate quantitatively the tau neutrino regeneration in the Earth for a
variety of extragalactic neutrino fluxes. Charged-current interactions of the
upward tau neutrinos below and in the detector, and the subsequent tau decay
create muons or hadronic and electromagnetic showers. The background for these
events are muon neutrino and electron neutrino charged-current and
neutral-current interactions, where in addition to extragalactic neutrinos, we
consider atmospheric neutrinos. We find significant signal to background ratios
for the hadronic/electromagnetic showers with energies above 10 TeV to 100 TeV
initiated by the extragalactic neutrinos. We show that the tau neutrinos from
point sources also have the potential for discovery above a 1 TeV threshold. A
kilometer-size neutrino telescope has a very good chance of detecting the
appearance of tau neutrinos when both muon and hadronic/electromagnetic showers
are detected.Comment: section added and two new figs; accepted for publication in Physical
Review
Bulk viscosity in kaon-condensed color-flavor locked quark matter
Color-flavor locked (CFL) quark matter at high densities is a color
superconductor, which spontaneously breaks baryon number and chiral symmetry.
Its low-energy thermodynamic and transport properties are therefore dominated
by the H (superfluid) boson, and the octet of pseudoscalar pseudo-Goldstone
bosons of which the neutral kaon is the lightest. We study the CFL-K^0 phase,
in which the stress induced by the strange quark mass causes the kaons to
condense, and there is an additional ultra-light "K^0" Goldstone boson arising
from the spontaneous breaking of isospin. We compute the bulk viscosity of
matter in the CFL-K^0 phase, which arises from the beta-equilibration processes
K^0H+H and K^0+HH. We find that the bulk viscosity varies as T^7, unlike
the CFL phase where it is exponentially Boltzmann-suppressed by the kaon's
energy gap. However, in the temperature range of relevance for r-mode damping
in compact stars, the bulk viscosity in the CFL-K^0 phase turns out to be even
smaller than in the uncondensed CFL phase, which already has a bulk viscosity
much smaller than all other known color-superconducting quark phases.Comment: 23 pages, 8 figures, v2: references added; minor rephrasings in the
conclusions; version to appear in J. Phys.
On the stability of the -rheology for granular flow
This article deals with the Hadamard instability of the so-called
model of dense rapidly-sheared granular flow, as reported recently by Barker et
al. (2015,this journal, , 794-818). The present paper presents a
more comprehensive study of the linear stability of planar simple shearing and
pure shearing flows, with account taken of convective Kelvin wave-vector
stretching by the base flow. We provide a closed form solution for the linear
stability problem and show that wave-vector stretching leads to asymptotic
stabilization of the non-convective instability found by Barker et al. We also
explore the stabilizing effects of higher velocity gradients achieved by an
enhanced-continuum model based on a dissipative analog of the van der
Waals-Cahn-Hilliard equation of equilibrium thermodynamics. This model involves
a dissipative hyper-stress, as the analog of a special Korteweg stress, with
surface viscosity representing the counterpart of elastic surface tension.
Based on the enhanced continuum model, we also present a model of steady shear
bands and their non-linear stability against parallel shearing. Finally, we
propose a theoretical connection between the non-convective instability of
Barker et al. and the loss of generalized ellipticity in the quasi-static field
equations. Apart from the theoretical interest, the present work may suggest
stratagems for the numerical simulation of continuum field equations involving
the rheology and variants thereof.Comment: 30 pages, 13 figure
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