2,139 research outputs found
Critical Lattice Size Limit for Synchronized Chaotic State in 1-D and 2-D Diffusively Coupled Map Lattices
We consider diffusively coupled map lattices with neighbors (where is
arbitrary) and study the stability of synchronized state. We show that there
exists a critical lattice size beyond which the synchronized state is unstable.
This generalizes earlier results for nearest neighbor coupling. We confirm the
analytical results by performing numerical simulations on coupled map lattices
with logistic map at each node. The above analysis is also extended to
2-dimensional -neighbor diffusively coupled map lattices.Comment: 4 pages, 2 figure
Remarks on non-gaussian fluctuations of the inflaton and constancy of \zeta outside the horizon
We point out that the non-gaussianity arising from cubic self interactions of
the inflaton field is proportional to \xi N_e where \xi ~ V"' and N_e is the
number of e-foldings from horizon exit till the end of inflation. For scales of
interest N_e = 60, and for models of inflation such as new inflation, natural
inflation and running mass inflation \xi is large compared to the slow roll
parameter \epsilon ~ V'^{2}. Therefore the contribution from self interactions
should not be outrightly ignored while retaining other terms in the
non-gaussianity parameter f_{NL}. But the N_e dependent term seems to imply the
growth of non-gaussianities outside the horizon. Therefore we briefly discuss
the issue of the constancy of correlations of the curvature perturbation \zeta
outside the horizon. We then calculate the 3-point function of the inflaton
fluctuations using the canonical formalism and further obtain the 3-point
function of \zeta_k. We find that the N_e dependent contribution to f_{NL} from
self interactions of the inflaton field is cancelled by contributions from
other terms associated with non-linearities in cosmological perturbation
theory.Comment: 16 pages, Minor changes, matches the published version. v3: Minor
typo correcte
Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach
Networks of coupled neural systems represent an important class of models in
computational neuroscience. In some applications it is required that
equilibrium points in these networks remain stable under parameter variations.
Here we present a general methodology to yield explicit constraints on the
coupling strengths to ensure the stability of the equilibrium point. Two models
of coupled excitatory-inhibitory oscillators are used to illustrate the
approach.Comment: 20 pages, 4 figure
A new method for the determination of atmospheric turbidity
Atmospheric turbidity is usually measured using either a pyrheliometer fitted with a red RG630 filter or a Volz sun photometer, the turbidity coefficients so determined being designated as β and B, respectively. Both techniques are subject to error, the former in underestimating high turbidities and the latter in giving rise to errors at low turbidities. The present paper describes a new, simpler and less expensive method of evaluating β from measurements of direct and diffuse solar radiation, made as a routine at principal radiation stations. Using a theoretical model for determining the attenuation of solar radiation due to absorption and scattering by water vapour and other gases, dust and aerosols in the atmosphere, an expression for the ratio of diffuse to direct solar radiation D/IH is derived as a function of β. Then, from the hourly mean values of global and diffuse solar radiation routinely recorded at principal radiation stations, D/IH is calculated. β can now be readily evaluated using a special nomogram based on the formula relating β to D/IH. The values of β derived for Indian stations using the above technique show remarkable internal consistency and stability, proving its utility and reliabilit
Numerical Investigation of In-Cylinder Fuel Atomization and Mixing For a GDI Engine
Gasoline Direct Injection (GDI) engines have been shown to have better fuel economy, transient response and cold-start hydrocarbon emissions. Additionally they have lower NOx emissions when operated under lean conditions. However, controlling charge stratification under various load conditions is a major challenge in GDI engines. In the present study a numerical simulations have been performed to understand factors affecting air/fuel mixture preparation under various engine operating conditions. Fuel spray atomization was studied using the two-way coupled Eulerian-Lagrangian approach. Momentum, energy and species equations were solved for the continuous gas phase. The droplet life history was tracked using the Lagrangian approach. Parameters like fuel injection time, fuel mass flow rate and engine speed was varied to determine their effect on air/fuel mixture preparation inside the cylinder. NOMENCLATURE A Area (m 2) B Spalding number Cd Coefficient of discharge Cp Constant pressure specific heat (kJ/kgK) do Injector inner diameter (m) Dp Droplet diameter (m) Fs Surface force (N) Fb Body force (N) g Acceleration due to gravity (m/s 2) he Heat transfer coefficient (WK/m
Solvable Map Representation Of A Nonlinear Symplectic Map
The evolution of a particle under the action of a beam transport system can be represented by a nonlinear symplectic map M. This map can be factorized into a product of Lie transformations. The evaluation of any given lie transformation in general requires the summation of an infinite number of terms. There are several ways of dealing with this difficulty: The summation can be truncated, thus producing a map that is nonsymplectic, but still useful for short term tracking. Alternatively, for long term tracking, the Lie transformation can be replaced by some symplectic map that agrees with it to some order and can be evaluated exactly. This paper shows how this may be done using solvable symplectic maps. A solvable map gives rise to a power series that either terminates or can be summed explicitly. This method appears to work quite well in the various examples that we have considered
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