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

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

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

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

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

Inverse Statistics in the Foreign Exchange Market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) $\rho$ in the price of an investment. The analysis is performed for the Deutsch mark (DM) against the $US for the full year of 1998, but similar results are obtained for the Japanese Yen against the$US. With high statistical significance, the presence of "resonance peaks" in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the markets participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new {\em stylized fact}, is observed for the waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale dependent features of the market activity.Comment: 8 pages. Accepted Physica

High Efficiency Nuclear Power Plants Using Liquid Fluoride Thorium Reactor Technology

An overall system analysis approach is used to propose potential conceptual designs of advanced terrestrial nuclear power plants based on Oak Ridge National Laboratory (ORNL) Molten Salt Reactor (MSR) experience and utilizing Closed Cycle Gas Turbine (CCGT) thermal-to-electric energy conversion technology. In particular conceptual designs for an advanced 1 GWe power plant with turbine reheat and compressor intercooling at a 950 K turbine inlet temperature (TIT), as well as near term 100 MWe demonstration plants with TITs of 950 and 1200 K are presented. Power plant performance data were obtained for TITs ranging from 650 to 1300 K by use of a Closed Brayton Cycle (CBC) systems code which considered the interaction between major sub-systems, including the Liquid Fluoride Thorium Reactor (LFTR), heat source and heat sink heat exchangers, turbo-generator machinery, and an electric power generation and transmission system. Optional off-shore submarine installation of the power plant is a major consideration