The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

On Averaging Multiview Relations for 3D Scan Registration

In this paper, we present an extension of the iterative closest point (ICP) algorithm that simultaneously registers multiple 3D scans. While ICP fails to utilize the multiview constraints available, our method exploits the information redundancy in a set of 3D scans by using the averaging of relative motions. This averaging method utilizes the Lie group structure of motions, resulting in a 3D registration method that is both efficient and accurate. In addition, we present two variants of our approach, i.e., a method that solves for multiview 3D registration while obeying causality and a transitive correspondence variant that efficiently solves the correspondence problem across multiple scans. We present experimental results to characterize our method and explain its behavior as well as those of some other multiview registration methods in the literature. We establish the superior accuracy of our method in comparison to these multiview methods with registration results on a set of well-known real datasets of 3D scans.

Energy-dependent orbital modulation of X-rays and constraints on emission of the jet in Cyg X-3

We study the orbital modulation of X-rays from Cyg X-3, using data from Swift, INTEGRAL and RXTE. Using the wealth of data presently available and an improved averaging method, we obtain energy-dependent folded and averaged light curves with unprecedented accuracy. We find that above similar to 5?keV the modulation depth decreases with increasing energy, which is consistent with the modulation being caused by both boundfree absorption and Compton scattering in the stellar wind of the donor, with minima corresponding to the highest optical depth, which occurs around the superior conjunction. We find a decrease of the depth below similar to 3?keV, which appears to be due to re-emission of the absorbed continuum by the wind in soft X-ray lines. Based on the shape of the folded light curves, any X-ray contribution from the jet in Cyg X-3, which emits ?-rays detected at energies >0.1?GeV in the soft spectral states, is found to be minor up to similar to 100?keV. This implies the presence of a rather sharp low-energy break in the jet MeV-range spectrum. We also calculate phase-resolved RXTE X-ray spectra and show that the difference between the spectra corresponding to phases around superior and inferior conjunctions can indeed be accounted for by the combined effect of boundfree absorption in an ionized medium and Compton scattering.

On an asymptotic method of Krylov-Bogoliubov for overdamped nonlinear systems

A general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems. A second-order system with both roots real is treated first and the method is then extended to higher-order systems. Two illustrative examples show good agreement with results obtained by numerical integration.

Approximate analysis of coupled non-linear non-conservative systems subjected to step-function excitation

The paper deals with the approximate analysis of non-linear non-conservative systems oftwo degrees of freedom subjected to step-function excitation. The method of averaging of Krylov and Bogoliubov is used to arrive at the approximate equations for amplitude and phase. An example of a spring-mass-damper system is presented to illustrate the method and a comparison with numerical results brings out the validity of the approach.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Block coherence: a method for measuring the interdependence between two blocks of neurobiological time series

Multisensor recordings are becoming commonplace. When studying functional connectivity between different brain areas using such recordings, one defines regions of interest, and each region of interest is often characterized by a set (block) of time series. Presently, for two such regions, the interdependence is typically computed by estimating the ordinary coherence for each pair of individual time series and then summing or averaging the results over all such pairs of channels (one from block 1 and other from block 2). The aim of this paper is to generalize the concept of coherence so that it can be computed for two blocks of non-overlapping time series. This quantity, called block coherence, is first shown mathematically to have properties similar to that of ordinary coherence, and then applied to analyze local field potential recordings from a monkey performing a visuomotor task. It is found that an increase in block coherence between the channels from V4 region and the channels from prefrontal region in beta band leads to a decrease in response time.

The variation of N-gamma with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing-soil interface friction angle (delta) on the bearing capacity factor N-gamma was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B-t from the footing edge. For a given footing width (B), the value of B-t increases continuously with a decrease in delta. For delta = 0, no trapped wedge exists below the footing base, that is, B-t/B = 0.5. On the contrary, with delta = phi, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in phi. The magnitude of N-gamma increases substantially with an increase in delta/phi. The maximum depth of the plastic zone becomes higher for greater values of delta/phi. The results from the present analysis were found to compare well with those reported in the literature.

A new two point method of obtaining Cv from a consolidation test: Discussion

Careful study of various aspects presented in the note reveals basic fallacies in the concept and final conclusions.The Authors claim to have presented a new method of determining C-v. However, the note does not contain a new method. In fact, the method proposed is an attempt to generate settlement vs. time data using only two values of (t,8). The Authors have used a rectangular hyperbola method to determine C-v from the predicated 8- t data. In this context, the title of the paper itself is misleading and questionable. The Authors have compared C-v values predicated with measured values, both of them being the results of the rectangular hyperbola method.

A New Method For The Generation Of 5,6-Quinolinedione 5-Methide .5. Synthesis Of Polycyclic Heteroaromatics

Reaction of 6-acetoxy-5-bromomethylquinoline (1c) and 2-bromomethyl-4-(2'-pyridyl)phenyl acetate (2b) with tetrachlorocatechol in acetone in the presence of anhydrous potassium carbonate resulted in the formation of diastereomeric products 3c, 3d, 4e and 4f.

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

Improved root t method to evaluate consolidation test results - Discussion

Taylor (1948) suggested the method for determination of the settlement, d, corresponding to 90% consolidation utilizing the characteristics of the degree of consolidation, U, versus the square root of the time factor, square root of T, plot. Based on the properties of the slope of U versus square root of T curve, a new method is proposed to determine d corresponding to any U above 70% consolidation for evaluation of the coefficient of consolidation, Cn. The effects of the secondary consolidation on the Cn value at different percentages of consolidation can be studied. Cn, closer to the field values, can be determined in less time as compared to Taylor's method. At any U in between 75 and 95% consolidation, Cn(U) due to the new method lies in between Taylor's Cn and Casagrande's Cn.

Enhanced sensitivity in detection of Kerr rotation by double modulation and time averaging based on Allan variance

Experiments in spintronics necessarily involve the detection of spin polarization. The sensitivity of this detection becomes an important factor to consider when extending the low temperature studies on semiconductor spintronic devices to room temperature, where the spin signal is weaker. In pump-probe experiments, which optically inject and detect spins, the sensitivity is often improved by using a photoelastic modulator (PEM) for lock-in detection. However, spurious signals can arise if diode lasers are used as optical sources in such experiments, along with a PEM. In this work, we eliminated the spurious electromagnetic coupling of the PEM onto the probe diode laser, by the double modulation technique. We also developed a test for spurious modulated interference in the pump-probe signal, due to the PEM. Besides, an order of magnitude enhancement in the sensitivity of detection of spin polarization by Kerr rotation, to 3x10(-8) rad was obtained by using the concept of Allan variance to optimally average the time series data over a period of 416 s. With these improvements, we are able to experimentally demonstrate at room temperature, photoinduced steady-state spin polarization in bulk GaAs. Thus, the advances reported here facilitate the use of diode lasers with a PEM for sensitive pump-probe experiments. They also constitute a step toward detection of spin-injection in Si at room temperature.

A rapid and highly selective method for the estimation of pyro-,tri- and orthophosphates

A rapid, highly selective and simple method has been developed for the quantitative determination of pyro-, tri- and orthophosphates. The method is based on the formation of a solid complex of bis(ethylenediamine)cobalt(III) species with pyrophosphate at pH 4.2-4.3, with triphosphate at pH 2.0-2.1 and with orthophosphate at pH 8.2-8.6. The proposed method for pyro- and triphosphates differs from the available method, which is based on the formation of an adduct with tris(ethylenediamine)cobalt(III) species. The complexes have the composition [Co(en)(2)HP2O7]4H(2)O and [Co(en)(2)H2P3O10]2H(2)O, respectively. The precipitation is instantaneous and quantitative under the recommended optimum conditions giving 99.5% gravimetric yield in both cases. There is no interferences from orthophosphate, trimetaphosphate and pyrophosphate species in the triphosphate estimation up to 5% of each component. The efficacy of the method has been established by determining pyrophosphate and triphosphate contents in various matrices. In the case of orthophosphate, the proposed method differs from the available methods such as ammonium phosphomolybdate, vanadophosphomolybdate and quinoline phosphomolybdate, which are based on the formation of a precipitate, followed by either titrimetry or gravimetry. The precipitation is instantaneous and the method is simple. Under the recommended pH and other reaction conditions, gravimetric yields of 99.6-100% are obtainable. The method is applicable to orthophosphoric acid and a variety of phosphate salts.