A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao-Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao-Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito-Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-a-vis results from a form of sequential importance sampling filter.

Field Emission Properties of Carbon Nanotube Arrays with Defects and Impurities

It has been found experimentally that the results related to the collective field emission performance of carbon nanotube (CNT) arrays show variability. The emission performance depends on the electronic structure of CNTs (especially their tips). Due to limitations in the synthesis process, production of highly pure and defect free CNTs is very difficult. The presence of defects and impurities affects the electronic structure of CNTs. Therefore, it is essential to analyze the effect of defects on the electronic structure, and hence, the field emission current. In this paper, we develop a modeling approach for evaluating the effect of defects and impurities on the overall field emission performance of a CNT array. We employ a concept of effective stiffness degradation for segments of CNTs, which is due to structural defects. Then, we incorporate the vacancy defects and charge impurity effects in our Green's function based approach. Simulation results indicate decrease in average current due to the presence of such defects and impurities.

Cellular and molecular regulation of mammalian blastocyst hatching

In mammals including humans, failure in blastocyst hatching and implantation leads to early embryonic loss and infertility. Prior to implantation, the blastocyst must hatch out of its acellular glycoprotein coat, the zona pellucida (ZP). The phenomenon of blastocyst hatching is believed to be regulated by (i) dynamic cellular components such as actin-based trophectodermal projections (TEPs), and (ii) a variety of autocrine and paracrine molecules such as growth factors, cytokines and proteases. The spatio-temporal regulation of zona lysis by blastocyst-derived cellular and molecular signaling factors is being keenly investigated. Our studies show that hamster blastocyst hatching is acelerated by growth factors such as heparin binding-epidermal growth factor and leukemia inhibitory factor and that embryo-derived, cysteine proteases including cathepsins are responsible for blastocyst hatching. Additionally, we believe that cyclooxygenase-generated prostaglandins, estradiol-17 beta mediated estrogen receptor-alpha signaling and possibly NF kappa B could be involved in peri-hatching development. Moreover, we show that TEPs are intimately involved with lysing ZP and that the TEPs potentially enrich and harbor hatching-enabling factors. These observations provide new insights into our understanding of the key cellular and molecular regulators involved in the phenomenon of mammalian blastocyst hatching, which is essential for the establishment of early pregnancy.

Are Metallocene-Acetylene (M = Ti, Zr, Hf) Complexes Aromatic Metallacyclopropenes?

The bonding nature of metallocene acetylene complexes Cp2M(eta(2)-H3SiC2SiH3) 1M and CP2M (eta(2)- HC2H) 1M' (M = Ti, Zr, Hf) wits studied by density functional theory method. It is found that this acetylene complex has indeed it metallacyclopropene moiety with two in-plane M-C sigma-bonds and one out-of-plane pi-bond interacting with the metal center, resulting in the formation of it delocalized three-center and two-electron (3c-2e) system. Along with its delocalized out-of-plane bonding, this complex has been characterized its aromatic on the basis of the computed stabilizing energy and negative nucleus-independent chemical shifts (NICS). The aromatic stabilization increases from Ti to Zr and Hf, and this is because of the increased charge separation between the CP2M fragment and the H3SiC2SiH3 (also HC2H) unit. The decrease of the M-C bond length from Zr to Hf is ttributed to the increased s character of both M and C hybridization of the M-C a-bonds.

Temperature and Stress Controlled Surface Manipulation in Ni-Al Nano-Layers

In the present paper the effects of temperature and high strain rate loading on the formation of various surface patterns in Ni-Al nano-layers are discussed. Effects of boundary conditions on the B2 -> BCT phase transformation in the nano-layer are also discussed. This study is aimed at developing several interesting patterned surface structures in Ni-Al nanolayer by controlling the phase transformation temperature and mechanical loading.

High Resolution Surface Imaging Using a Carbon Nanotube Array with Pointed Height distribution

In this paper we discuss a new technique to image the surfaces of metallic substrates using field emission from a pointed array of carbon nanotubes (CNTs). We consider a pointed height distribution of the CNT array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The CNT array on a metallic substrate is considered as the cathode and the test substrate as the anode. Scanning the test Substrate with the cathode reveals that the field emission current is highly sensitive to the surface features with nanometer resolution. Surface features of semi-circular, triangular and rectangular geometries (projections and grooves) are considered for simulation. This surface scanning/mapping technique can be applied for surface roughness measurements with nanoscale accuracy. micro/nano damage detection, high precision displacement sensors, vibrometers and accelerometers. among other applications.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Anaerobic DNA cleavage activity in red light and photocytotoxicity of (pyridine-2-thiol)cobalt(III) complexes of phenanthroline bases

Cobalt(III) complexes [Co(pnt)(B)(2)](NO3)(2) (1-3) of pyridine-2-thiol (pnt) and phenanthroline bases (B), viz. 1,10-phenanthroline (phen in 1), dipyrido[3,2-d: 2',3'-f]quinoxaline (dpq in 2) and dipyrido[3,2-a:2',3'-c] phenazine (dppz in 3), have been prepared, characterized and their photo-induced anaerobic DNA cleavage activity studied. The crystal structure of 1a as mixed ClO4- and PF6- salt of 1 shows a (CoN5S)-N-III coordination geometry in which the pnt and phen showed N,S- and N,N-donor binding modes, respectively. The complexes exhibit Co(III)/Co(II) redox couple near -0.3 V (vs. SCE) in 20% DMF-Tris-HCl buffer having 0.1 M TBAP. The complexes show binding propensity to calf thymus DNA giving K-b values within 2.2 x 10(4)-7.3 x 10(5) M-1. Thermal melting and viscosity data suggest DNA surface and/or groove binding of the complexes. The complexes show significant anaerobic DNA cleavage activity in red light under argon atmosphere possibly involving sulfide anion radical or thiyl radical species. The DNA cleavage reaction under aerobic medium in red light is found to involve both singlet oxygen and hydroxyl radical pathways. The dppz complex 3 shows non-specific BSA and lysozyme protein cleavage activity in UV-A light of 365 nm via both hydroxyl and singlet oxygen pathways. The dppz complex 3 exhibits photocytotoxicity in HeLa cervical cancer cells giving IC50 values of 767 nM and 19.38 mu M in UV-A light of 365 nm and in the dark, respectively. A significant reduction of the dark toxicity of the dppz base (IC50 = 8.34 mu M in dark) is observed on binding to the cobalt(III) center.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

Design Optimization of Field Emission From A Stacked Carbon Nanotube Array

Fluctuation of field emission in carbon nanotubes (CNTs) is riot desirable in many applications and the design of biomedical x-ray devices is one of them. In these applications, it is of great importance to have precise control of electron beams over multiple spatio-temporal scales. In this paper, a new design is proposed in order to optimize the field emission performance of CNT arrays. A diode configuration is used for analysis, where arrays of CNTs act as cathode. The results indicate that the linear height distribution of CNTs, as proposed in this study, shows more stable performance than the conventionally used unifrom distribution.