Invited paper Application of the least mean fourth (LMF) adaptive algorithm to signals associated with gaussian noise

This paper considers the applicability of the least mean fourth (LM F) power gradient adaptation criteria with 'advantage' for signals associated with gaussian noise, the associated noise power estimate not being known. The proposed method, as an adaptive spectral estimator, is found to provide superior performance than the least mean square (LMS) adaptation for the same (or even lower) speed of convergence for signals having sufficiently high signal-to-gaussian noise ratio. The results include comparison of the performance of the LMS-tapped delay line, LMF-tapped delay line, LMS-lattice and LMF-lattice algorithms, with the Burg's block data method as reference. The signals, like sinusoids with noise and stochastic signals like EEG, are considered in this study.

Analysis of randomly time varying systems by gaussian closure technique

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

How Good is the Assumption About Visible Surface Reflectance in MODIS Aerosol Retrieval Over Land? A Comparison With Aircraft Measurements Over an Urban Site in India

In this paper, we discuss the measurements of spectral surface reflectance (rho(s)(lambda)) in the wavelength range 350-2500 nm measured using a spectroradiometer onboard a low-flying aircraft over Bangalore (12.95 degrees N, 77.65 degrees E), an urban site in southern India. The large discrepancies in the retrieval of aerosol propertiesover land by the Moderate-Resolution Imaging Spectroradiometer (MODIS), which could be attributed to the inaccurate estimation of surface reflectance at many sites in India and elsewhere, provided motivation for this paper. The aim of this paper was to verify the surface reflectance relationships assumed by the MODIS aerosol algorithm for the estimation of surface reflectance in the visible channels (470 and 660 nm) from the surface reflectance at 2100 nm for aerosol retrieval over land. The variety of surfaces observed in this paper includes green and dry vegetations, bare land, and urban surfaces. The measuredreflectance data were first corrected for the radiative effects of atmosphere lying between the ground and aircraft using the Second Simulation of Satellite Signal in the Solar Spectrum (6S) radiative transfer code. The corrected surface reflectance in the MODIS's blue (rho(s)(470)), red (rho(s)(660)), and shortwave-infrared (SWIR) channel (rho(s)(2100)) was linearly correlated. We found that the slope of reflectance relationship between 660 and 2100 nm derived from the forward scattering data was 0.53 with an intercept of 0.07, whereas the slope for the relationship between the reflectance at 470 and 660 nm was 0.85. These values are much higher than the slope (similar to 0.49) for either wavelengths assumed by the MODIS aerosol algorithm over this region. The reflectance relationship for the backward scattering data has a slope of 0.39, with an intercept of 0.08 for 660 nm, and 0.65, with an intercept of 0.08 for 470 nm. The large values of the intercept (which is very small in the MODIS reflectance relationships) result in larger values of absolute surface reflectance in the visible channels. The discrepancy between the measured and assumed surface reflectances could lead to error in the aerosol retrieval. The reflectance ratio (rho(s)(660)/rho(s)(2100)) showed a clear dependence on the N D V I-SWIR where the ratio increased from 0.5 to 1 with an increase in N V I-SWIR from 0 to 0.5. The high correlation between the reflectance at SWIR wavelengths (2100, 1640, and 1240 nm) indicated an opportunity to derive the surface reflectance and, possibly, aerosol properties at these wavelengths. We need more experiments to characterize the surface reflectance and associated inhomogeneity of land surfaces, which play a critical role in the remote sensing of aerosols over land.

Brownian particles in stationary and moving traps: The mean and variance of the heat distribution function

A recent theoretical model developed by Imparato et al. Phys of the experimentally measured heat and work effects produced by the thermal fluctuations of single micron-sized polystyrene beads in stationary and moving optical traps has proved to be quite successful in rationalizing the observed experimental data. The model, based on the overdamped Brownian dynamics of a particle in a harmonic potential that moves at a constant speed under a time-dependent force, is used to obtain an approximate expression for the distribution of the heat dissipated by the particle at long times. In this paper, we generalize the above model to consider particle dynamics in the presence of colored noise, without passing to the overdamped limit, as a way of modeling experimental situations in which the fluctuations of the medium exhibit long-lived temporal correlations, of the kind characteristic of polymeric solutions, for instance, or of similar viscoelastic fluids. Although we have not been able to find an expression for the heat distribution itself, we do obtain exact expressions for its mean and variance, both for the static and for the moving trap cases. These moments are valid for arbitrary times and they also hold in the inertial regime, but they reduce exactly to the results of Imparato et al. in appropriate limits. DOI: 10.1103/PhysRevE.80.011118 PACS.

Multiaction learning automata possessing ergodicity of the mean

Multiaction learning automata which update their action probabilities on the basis of the responses they get from an environment are considered in this paper. The automata update the probabilities according to whether the environment responds with a reward or a penalty. Learning automata are said to possess ergodicity of the mean if the mean action probability is the state probability (or unconditional probability) of an ergodic Markov chain. In an earlier paper [11] we considered the problem of a two-action learning automaton being ergodic in the mean (EM). The family of such automata was characterized completely by proving the necessary and sufficient conditions for automata to be EM. In this paper, we generalize the results of [11] and obtain necessary and sufficient conditions for the multiaction learning automaton to be EM. These conditions involve two families of probability updating functions. It is shown that for the automaton to be EM the two families must be linearly dependent. The vector defining the linear dependence is the only vector parameter which controls the rate of convergence of the automaton. Further, the technique for reducing the variance of the limiting distribution is discussed. Just as in the two-action case, it is shown that the set of absolutely expedient schemes and the set of schemes which possess ergodicity of the mean are mutually disjoint.

R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.

Relaminarization in highly accelerated turbulent boundary layers

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

The mean geometry of the peptide unit from crystal structure data

The average dimensions of the peptide unit have been obtained from the data reported in recent crystal structure analyses of di- and tripeptides. The bond lengths and bond angles agree with those in common use, except for the bond angle C---N---H, which is about 4° less than the accepted value, and the angle C2α---N---H which is about 4° more. The angle τ (Cα) has a mean value of 114° for glycyl residues and 110° for non-glycyl residues. Attention is directed to these mean values as observed in crystal structures, as they are relevant for model building of peptide chain structures.

Crystal Physics, Diffraction, Theoretical and General Crystallography

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method. The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them. The theoretical values are in good agreement with those obtained by earlier workers from computer simulations. The present method makes it easier to optimize the number and the actual wavelengths to be employed in the multiwavelength method. The maximum benefits of this method are expected in experiments employing synchrotron radiation or neutrons.

Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

Error correction in nonbinary words

A simple error detecting and correcting procedure is described for nonbinary symbol words; here, the error position is located using the Hamming method and the correct symbol is substituted using a modulo-check procedure.

The sensitivity of the northern hemisphere summer mean meridional circulation to changes in the large scale eddy forcing

A zonally averaged version of the Goddard Laboratory for Atmospheric Sciences (GLAS) climate model is used to study the sensitivity of the northern hemisphere (NH) summer mean meridional circulation to changes in the large scale eddy forcing. A standard solution is obtained by prescribing the latent heating field and climatological horizontal transports of heat and momentum by the eddies. The radiative heating and surface fluxes are calculated by model parameterizations. This standard solution is compared with the results of several sensitivity studies. When the eddy forcing is reduced to 0.5 times or increased to 1.5 times the climatological values, the strength of the Ferrel cells decrease or increase proportionally. It is also seen that such changes in the eddy forcing can influence the strength of theNH Hadley cell significantly. Possible impact of such changes in the large scale eddy forcing on the monsoon circulation via changes in the Hadley circulation is discussed. Sensitivity experiments including only one component of eddy forcing at a time show that the eddy momentum fluxes seem to be more important in maintaining the Ferrel cells than the eddy heat fluxes. In the absence of the eddy heat fluxes, the observed eddy momentum fluxes alone produce subtropical westerly jets which are weaker than those in the standard solution. On the other hand, the observed eddy heat fluxes alone produce subtropical westerly jets which are stronger than those in the standard solution.

Absolute values of instantaneous corrosion rates by faradaic rectification

Doss and Agarwal 1 discovered the "redoxokinetic effect" which is now familiarly known as faradaic rectification. Subsequently, the theory and applications of faradaic rectification due to a single electrode reaction have been developed by several workers 2-5. The theory and application of faradaic rectification in the case of a corrosion cell sustaining mixed electrode reactions on a corroding metal was reported recently 6"7. This led to the development of a new electrochemical method of corrosion rate determination. It was shown that changes in the instantaneous corrosion rates of a metal are readily evaluated by faradaic rectification measurements at the corrosion potential of the metal in a given medium. The aim of the present work is to show that absolute values of instantaneous corrosion rates may also be obtained by the new method under certain conditions. The practical advantages that arise from this development are pointed out.