The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Two-level k-means clustering algorithm for k-tau relationship establishment and linear-time classification

Partitional clustering algorithms, which partition the dataset into a pre-defined number of clusters, can be broadly classified into two types: algorithms which explicitly take the number of clusters as input and algorithms that take the expected size of a cluster as input. In this paper, we propose a variant of the k-means algorithm and prove that it is more efficient than standard k-means algorithms. An important contribution of this paper is the establishment of a relation between the number of clusters and the size of the clusters in a dataset through the analysis of our algorithm. We also demonstrate that the integration of this algorithm as a pre-processing step in classification algorithms reduces their running-time complexity.

A one-step technique to prepare aligned arrays of carbon nanotubes

A simple effective pyrolysis technique has been developed to synthesize aligned arrays of multi-walled carbon nanotubes (MWCNTs) without using any carrier gas in a single-stage furnace at 700 °C. This technique eliminates nearly the entire complex and expensive machinery associated with other extensively used methods for preparation of CNTs such as chemical vapour deposition (CVD) and pyrolysis. Carbon source materials such as xylene, cyclohexane, camphor, hexane, toluene, pyridine and benzene have been pyrolyzed separately with the catalyst source material ferrocene to obtain aligned arrays of MWCNTs. The synthesized CNTs have been characterized by scanning electron microscopy (SEM), x-ray diffraction (XRD), transmission electron microscopy (TEM), thermogravimetric analysis (TGA) and Raman spectroscopy. In this technique, the need for the tedious and time-consuming preparation of metal catalysts and continuously fed carbon source material containing carrier gas can be avoided. This method is a single-step process where not many parameters are required to be monitored in order to prepare aligned MWCNTs. For the production of CNTs, the technique has great advantages such as low cost and easy operation.

Two-Step Folding of Donor-Acceptor Foldamers

In a series of polymers containing alternately placed electron-rich dialkoxyilaphthalene (DAN) donors and electron-deficient pyromellitic diimide (PDI) acceptors linked by hexa(oxyethylene) (OE-6) segments, the ability to form a folded D-A stack was intentionally disrupted by random inclusion of varying amounts of a comonomer that is devoid of DAN donor units. NMR spectroscopic studies of folding in these copolymers, induced by NH4SCN that coordinates with the OE-6 segments and facilitates the charge-transfer (C-T) induced D-A stacking, clearly reveals the presence of PDI units that are isolated and those that are located at the ends of (D-A),, stacks. Similar conclusions regarding the presence of stacked and unstacked regions along the polymer chain were also inferred from UV-vis spectroscopic studies that probe the evolution of charge-transfer band. One fascinating aspect of these copolymers wits their ability to undergo it two-step folding: first, short (D-A),, stacks are formed by the interaction of the NH4+ ion with some specific regions of the polymer chain, and subsequently these Stacks are further stacked via a two-point interaction with it suitably designed external folding agent that carries a DAN unit and all ammonium group. In the second step, the interaction first occurs by the coordination of the ammonium group of the folding agent with the OE-6 segment, which in turn facilitates the C-T interaction of the DAN unit with the adjacent uncomplexed PDI units along the polymer chain, leading to an increase ill the slacking. Variations of several spectral features, during both UV-vis and NMR spectroscopic titrations, clearly reveal this novel two-step folding process.

Generalized survival in step fluctuations

The properties of the generalized survival probability, that is, the probability of not crossing an arbitrary location R during relaxation, have been investigated experimentally (via scanning tunneling microscope observations) and numerically. The results confirm that the generalized survival probability decays exponentially with a time constant tau(s)(R). The distance dependence of the time constant is shown to be tau(s)(R)=tau(s0)exp[-R/w(T)], where w(2)(T) is the material-dependent mean-squared width of the step fluctuations. The result reveals the dependence on the physical parameters of the system inherent in the prior prediction of the time constant scaling with R/L-alpha, with L the system size and alpha the roughness exponent. The survival behavior is also analyzed using a contrasting concept, the generalized inside survival S-in(t,R), which involves fluctuations to an arbitrary location R further from the average. Numerical simulations of the inside survival probability also show an exponential time dependence, and the extracted time constant empirically shows (R/w)(lambda) behavior, with lambda varying over 0.6 to 0.8 as the sampling conditions are changed. The experimental data show similar behavior, and can be well fit with lambda=1.0 for T=300 K, and 0.5

Deploy and search strategy for multi-agent systems using Voronoi partitions

In this paper we analyze a deploy and search strategy for multi-agent systems. Mobile agents equipped with sensors carry out search operation in the search space. The lack of information about the search space is modeled as an uncertainty density distribution over the space, and is assumed to be known to the agents a priori. In each step, the agents deploy themselves in an optimal way so as to maximize per step reduction in the uncertainty density. We analyze the proposed strategy for convergence and spatial distributedness. The control law moving the agents has been analyzed for stability and convergence using LaSalle's invariance principle, and for spatial distributedness under a few realistic constraints on the control input such as constant speed, limit on maximum speed, and also sensor range limits. The simulation experiments show that the strategy successfully reduces the average uncertainty density below the required level.

Hydrocarbon oxidation and three-way catalytic activity on a single step directly coated cordierite monolith: High catalytic activity of Ce0.98Pd0.02O2−δ

Catalytic activity of cordierite honeycomb by a completely new coating method for the oxidation of major hydrocarbons in exhaust gas is reported here. The new coating process consists of (a) dipping and growing γ-Al2O3 on cordierite by combustion of monolith dipped in the aqueous solution of Al(NO3)3 and oxalyldihydrazide (ODH) (or glycine) at 600 °C and active catalyst phase Ce0.98Pd0.02O2−δ on γ-Al2O3-coated cordierite again by combustion of monolith dipped in the aqueous solution of ceric ammonium nitrate, ODH and 1.2 × 10−3 M PdCl2 solution at 500 °C. Weight of active catalyst can be varied from 0.02 wt% to 2 wt% which is sufficient but can be loaded even up to 12 wt% by repeating dip dry combustion. Adhesion of catalyst to cordierite surface is via oxide growth, which is very strong. ‘HC’ oxidation over the monolith catalyst is carried out with a mixture having the composition, 470 ppm of both propene and propane and 870 ppm of both ethylene and acetylene with the varying amount of O2. Three-way catalytic test is done by putting hydrocarbon mixture along with CO (10 000 ppm), NO (2000 ppm) and O2 (15 000 ppm). Below 350 °C full conversion is achieved. In this method, handling of nano-material powder is avoided.

Paired electromagnetically induced transparency with dual mode laser: A step towards EIT-Comb

Coupled electromagnetically induced transparency (EIT) has been observed with a dual mode control laser. The technique can be used for generating EIT-comb from optical frequency comb.

Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map

We describe a noniterative method for recovering optical absorption coefficient distribution from the absorbed energy map reconstructed using simulated and noisy boundary pressure measurements. The source reconstruction problem is first solved for the absorbed energy map corresponding to single- and multiple-source illuminations from the side of the imaging plane. It is shown that the absorbed energy map and the absorption coefficient distribution, recovered from the single-source illumination with a large variation in photon flux distribution, have signal-to-noise ratios comparable to those of the reconstructed parameters from a more uniform photon density distribution corresponding to multiple-source illuminations. The absorbed energy map is input as absorption coefficient times photon flux in the time-independent diffusion equation (DE) governing photon transport to recover the photon flux in a single step. The recovered photon flux is used to compute the optical absorption coefficient distribution from the absorbed energy map. In the absence of experimental data, we obtain the boundary measurements through Monte Carlo simulations, and we attempt to address the possible limitations of the DE model in the overall reconstruction procedure.

Single and multi-step phase transformation in CuZr nanowire under compressive/tensile loading

A novel stress induced martenistic phase transformation is reported in an initial B2-CuZr nanowire of cross-sectional dimensions in the range of 19.44 x 19.44-38.88 x 38.88 angstrom(2) and temperature in the range of 10-400 K under both tensile and compressive loading. Extensive Molecular Dynamic simulations are performed using an inter-atomic potential of type Finnis and Sinclair. The nanowire shows a phase transformation from an initial B2 phase to BCT (body-centered-tetragonal) phase with failure strain of similar to 40% in tension, whereas in compression, comparatively a small B2 -> BCT phase transformation is observed with failure strain of similar to 25%. Size and temperature dependent deformation mechanisms which control ultimately the B2 -> BCT phase transformation are found to be completely different for tensile and compressive loadings. Under tensile loading, small cross-sectional nanowire shows a single step phase transformation, i.e. B2 -> BCT via twinning along {100} plane, whereas nanowires with larger cross-sectional area show a two step phase transformation, i.e. B2 -> R phase -> BCT along with intermediate hardening. In the first step, nanowire shows phase transformation from B2 -> R phase via twinning along {100} plane, afterwards the nanowire deforms via twinning along {110} plane which cause further transformation from R phase -> BCT phase. Under compressive loading, the nanowire shows crushing along {100} plane after a single step phase transformation from B2 -> BCT. Proper tailoring of such size and temperature dependent phase transformation can be useful in designing nanowire for high strength applications with corrosion and fatigue resistance. (C) 2009 Elsevier Ltd. All rights reserved.

A voltage-sensorless control method to balance the input currents of a three-wire boost rectifier under unbalanced input voltages condition

This paper proposes a control method that can balance the input currents of the three-phase three-wire boost rectifier under unbalanced input voltage condition. The control objective is to operate the rectifier in the high-power-factor mode under balanced input voltage condition but to give overriding priority to the current balance function in case of unbalance in the input voltage. The control structure has been divided into two major functional blocks. The inner loop current-mode controller implements resistor emulation to achieve high-power-factor operation on each of the two orthogonal axes of the stationary reference frame. The outer control loop performs magnitude scaling and phase-shifting operations on current of one of the axes to make it balanced with the current on the other axis. The coefficients of scaling and shifting functions are determined by two closed-loop prportional-integral (PI) controllers that impose the conditions of input current balance as PI references. The control algorithm is simple and high performing. It does not require input voltage sensing and transformation of the control variables into a rotating reference frame. The simulation results on a MATLAB-SIMULINK platform validate the proposed control strategy. In implementation Texas Instrument's digital signal processor TMS320F24OF is used as the digital controller. The control algorithm for high-power-factor operation is tested on a prototype boost rectifier under nominal and unbalanced input voltage conditions.

Response spectrum of non-linear spring mass system subjected to transient disturbances

The transient response spectrum of a cubic spring mass system subjected to a step function input is obtained. An approximate method is adopted where non-linear restoring force characteristic is replaced by two linear segments, so that the mean square error between them is a minimum. The effect of viscous damping on the peak response is also discussed for various values of the damping constant and the non-linearity restoring force parameter.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.