24,074 research outputs found
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
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
A New Nonlinear Liquid Drop Model. Clusters as Solitons on The Nuclear Surface
By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations
and the corresponding boundary conditions, the higher order terms in the
deviation of the shape, we obtain in the second order the Korteweg de Vries
equation (KdV). The same equation is obtained by introducing in the liquid drop
model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms
in the second order. The KdV equation has the cnoidal waves as steady-state
solutions. These waves could describe the small anharmonic vibrations of
spherical nuclei up to the solitary waves. The solitons could describe the
preformation of clusters on the nuclear surface. We apply this nonlinear liquid
drop model to the alpha formation in heavy nuclei. We find an additional
minimum in the total energy of such systems, corresponding to the solitons as
clusters on the nuclear surface. By introducing the shell effects we choose
this minimum to be degenerated with the ground state. The spectroscopic factor
is given by the ratio of the square amplitudes in the two minima.Comment: 27 pages, LateX, 8 figures, Submitted J. Phys. G: Nucl. Part. Phys.,
PACS: 23.60.+e, 21.60.Gx, 24.30.-v, 25.70.e
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