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 $P$ neighbors (where $P$ 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 $P$-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

Bayesian Economists...Bayesian Agents II: Evolution of Beliefs in the Single Sector Growth Model

In "Bayesian Economists ... Bayesian Agents I" (BBI), we generalized the results on Bayesian learning based on the martingale convergence theorem from the repeated to the sequential framework. In BBI, we showed that the variability introduced by the sequential framework is sufficient under very mild identifiability conditions to circumvent the incomplete learning results that characterize the literature. In this paper, we demonstrate that result in the neo-classical single sector growth model under even weaker identifiability conditions. We study the evolution of agent-beliefs in that model and show that, under reasonable conditions, the dependence of the current capital stock on the previous capital stock induces enough variability for our complete learning results to become relevant. Not only does complete learning take place from the subjective point of view of the agents' priors, but it also takes place from the point of view of an objective observer (modeling economist) who knows the true structure

Bayesian Economist ... Bayesian Agents I: An Alternative Approach to Optimal Learning

We study the framework of optimal decision making under uncertainty where the agents do not know the full structure of the model and try to learn it optimally. We generalize the results on Bayesian learning based on the martingale convergence theorem to the sequential framework instead of the repeated framework for which results are currently available. We also show that the variability introduced by the sequential framework is sufficient under very mild identifiability conditions to circumvent the incomplete learning results that characterize the literature. We then question the type of convergence so achieved, and give an alternative Bayesian approach whereby we let the economist himself be a Bayesian with a prior on the priors that his agents may have. We prove that such an economist cannot justify endowing all his agents with the same (much less the true) prior on the basis that the model has been running long enough that we can almost surely approximate any agent's beliefs by any other's. We then examine a possibly weaker justification based on the convergence of the economist's measure on beliefs, and fully characterize it by the Harris ergodicity of the relevant Markov kernel. By means of very simple examples, we then show that learning, partial learning, and non-learning may all occur under the weak conditions that we impose. For complicated models where the Harris ergodicity of the Markov kernel in question can neither be proved nor disproved, the mathematical/statistical test of Domowitz and El-Gamal (1989) can be utilized