Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

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.

Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.

In search of inorganic nonlinear optical materials for second harmonic generation

In a search for inorganic oxide materials showing second-order nonlinear optical (NLO) susceptibility, we investigated several berates, silicates, and a phosphate containing trans-connected MO6, octahedral chains or MO5 square pyramids, where, M = d(0): Ti(IV), Nb(V), or Ta(V), Our investigations identified two new NLO structures: batisite, Na2Ba(TiO)(2)Si4O12, containing trans-connected TiO5 octahedral chains, and fresnoite, Ba2TiOSi2O7, containing square-pyramidal TiO5. Investigation of two other materials containing square-pyramidal TiO5 viz,, Cs2TiOP2O7 and Na4Ti2Si8O22. 4H(2)O, revealed that isolated TiO5, square pyramids alone do not cause a second harmonic generation (SHG) response; rather, the orientation of TiO5 units to produce -Ti-O-Ti-O- chains with alternating long and short Ti-O distances in the fresnoite structure is most likely the origin of a strong SHG response in fresnoite,

Spin-state equilibria in the LCoO3 system from 59Co NMR

Spin-state equilibria in the whole set of LCoO3 (where L stands for a rare-earth metal or Y) have been investigated with the use of 59Co NMR as a probe for the polycrystalline samples (except Ce) in the temperature interval 110-550 K and frequency range 3- 11.6 MHz. Besides confirming the coexistence of the high-spin—low-spin state in this temperature range, a quadrupolar interaction of ∼0.1 -0.5 MHz has been detected for the first time from 59Co NMR. The NMR line shape is found to depend strongly on the relative magnitude of the magnetic and quadrupolar interactions present. Analysis of the powder pattern reveals two basically different types of transferred hyperfine interaction between the lighter and heavier members of the rare-earth series. The first three members of the lighter rare-earth metals La, Pr (rhombohedral), and Nd (tetragonal), exhibit second-order quadrupolar interaction with a zero-asymmetry parameter at lower temperatures. Above a critical temperature TS (dependent on the size of the rare-earth ion), the quadrupolar interaction becomes temperature dependent and eventually gives rise to a first-order interaction thus indicating a possible second-order phase change. Sm and Eu (orthorhombic) exhibit also a second-order quadrupolar interaction with a nonzero asymmetry parameter ((η∼0.47)) at 300 K, while the orthorhombic second-half members (Dy,..., Lu and Y) exhibit first-order quadrupolar interaction at all temperatures. Normal paramagnetic behavior, i.e., a linear variation of Kiso with T-1, has been observed in the heavier rare-earth cobaltites (Er,..., Lu and Y), whereas an anomalous variation has been observed in (La,..., Nd)CoO3. Thus, Kiso increases with increasing temperature in PrCoO3 and NdCoO3. These observations corroborate the model of the spin-state equilibria in LCoO3 originally proposed by Raccah and Goodenough. A high-spin—low-spin ratio, r=1, can be stabilized in the perovskite structure by a cooperative displacement of the oxygen atoms from the high-spin towards the low-spin cation. Where this ordering into high- and low-spin sublattices occurs at r=1, one can anticipate equivalent displacement of all near-neighbor oxygen atoms towards a low-spin cobalt ion. Thus the heavier LCoO3 exhibits a small temperature-independent first-order quadrupolar interaction. Where r<1, the high- and low-spin states are disordered, giving rise to a temperature-dependent second-order quadrupolar interaction with an anomalous Kiso for the lighter LCoO3.

Optical Properties of Nanocrystalline Potassium Lithium Niobate in the Glass System (100-x) TeO2-x(1.5K(2)O-Li2O-2.5Nb(2)O(5))

Optically clear glasses of various compositions in the system (100-x) TeO2-x(1.5K(2)O-Li2O-2.5Nb(2)O(5)) (2 <= x <= 12, in molar ratio) were prepared by the melt-quenching technique. The glassy nature of the as-quenched samples was established via differential scanning calorimetry (DSC). The amorphous and the crystalline nature of the as-quenched and heat-treated samples were confirmed by the X-ray powder diffraction and transmission electron microscopic (TEM) studies. Transparent glasses comprising potassium lithium niobate (K3Li2Nb5O15) microcrystallites on the surface and nanocrystallites within the glass were obtained by controlled heat-treatment of the as-quenched glasses just above the glass transition temperature (T-g). The optical transmission spectra of these glasses and glass-crystal composites of various compositions were recorded in the 200-2500 nm wavelength range. Various optical parameters such as optical band gap, Urbach energy, refractive index were determined. Second order optical non-linearity was established in the heat-treated samples by employing the Maker-Fringe method.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

The homologous recombination system of phage lambda. Pairing activities of beta protein

The red genes of phage lambda specify two proteins, exonuclease and beta protein, which are essential for its general genetic recombination in recA- cells. These proteins seem to occur in vivo as an equimolar complex. In addition, beta protein forms a complex with another polypeptide, probably of phage origin, of Mr 70,000. The 70-kDa protein appears to be neither a precursor nor an aggregated form of either exonuclease or beta protein, since antibodies directed against the latter two proteins failed to react with 70-kDa protein on Ouchterlony double diffusion analysis. beta protein promotes Mg2+-dependent renaturation of complementary strands (Kmiec, E., and Holloman, W. K. (1981) J. Biol. Chem. 256, 12636-12639). To look for other pairing activities of beta protein, we developed methods of purification to free it of associated exonuclease. Exonuclease-free beta protein appeared unable to cause the pairing of a single strand with duplex DNA; however, like Escherichia coli single strand binding protein (SSB), beta protein stimulated formation of joint molecules by recA protein from linear duplex DNA and homologous circular single strands. Like recA protein, but unlike SSB, beta protein promoted the joining of the complementary single-stranded ends of phage lambda DNA. beta protein specifically protected single-stranded DNA from digestion by pancreatic DNase. The half-time for renaturation catalyzed by beta protein was independent of DNA concentration, unlike renaturation promoted by SSB and spontaneous renaturation, which are second order reactions. Thus, beta protein resembles recA protein in its ability to bring single-stranded DNA molecules together and resembles SSB in its ability to reduce secondary structure in single-stranded DNA.

Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

Influence of poling methods on the orientational dynamics of 2-methyl-4-nitro-aniline in poly(methyl methacrylate) studied by second harmonic generation

The magnitude and stability of the induced dipolar orientation of 2-methyl-4-nitroaniline (MNA)/poly(methyl methacrylate) (PMMA) guest/host system is investigated. The chromophores are aligned using both the corona discharge and contact electrode poling techniques. The magnitude of order parameter (also an indicator for the second order nonlinear susceptibility) is measured by recording absorbances of the poled (by the two different techniques) and unpoled PMMA films at different concentrations of MNA. Under the same conditions the corona poling technique creates a higher alignment of molecules along the field direction. The time dependence of the second harmonic intensity of the MNA/PMMA film prepared by the two techniques can be described by a Kohlrausch-Williams-Watts stretched exponential. The temperature dependence of the decay time constant is found to generally follow a modified Williams-Landel-Ferry (WLF) or Vogel-Tamann-Fulcher (VTF) equation. The glass transition temperature seems to be the single most important parameter for determining the relaxation time tau(T).

System Dy-Fe-O: thermodynamic properties of ternary oxides using Calvet calorimetry and solid-state electrochemical cell

The enthalpy increments and the standard molar Gibbs energies of formation-of DyFeO3(s) and Dy3Fe5O12(s) have been measured using a Calvet micro-calorimeter and a solid oxide galvanic cell, respectively. A co-operative phase transition, related to anti-ferromagnetic to paramagnetic transformation, is apparent. from the heat capacity data for DyFeO3 at similar to 648 K. A similar type of phase transition has been observed for Dy3Fe5O12 at similar to 560 K which is related to ferrimagnetic to paramagnetic transformation. Enthalpy increment data for DyFeO3(s) and Dy3Fe5O12(s), except in the vicinity of the second-order transition, can be represented by the following polynomial expressions:{H(0)m(T) - H(0)m(298.15 K)) (Jmol(-1)) (+/-1.1%) = -52754 + 142.9 x (T (K)) + 2.48 x 10(-3) x (T (K))(2) + 2.951 x 10(6) x (T (K))(-1); (298.15 less than or equal to T (K) less than or equal to 1000) for DyFeO3(s), and {H(0)m(T) - H(0)m(298.15 K)} (Jmol(-1)) (+/-1.2%) = -191048 + 545.0 x (T - (K)) + 2.0 x 10(-5) x (T (K))(2) + 8.513 x 10(6) x (T (K))(-1); (208.15 less than or equal to T (K) less than or equal to 1000)for Dy3Fe5O12(s). The reversible emfs of the solid-state electrochemical cells: (-)Pt/{DyFeO3(s) + Dy2O3(s) + Fe(s)}/YDT/CSZ//{Fe(s) + Fe0.95O(s)}/Pt(+) and (-)Pt/{Fe(s) + Fe0.95O(s)}//CSZ//{DyFeO3(s) + Dy3Fe5O12(s) + Fe3O4(s)}/Pt(+), were measured in the temperature range from 1021 to 1250 K and 1035 to 1250 K, respectively. The standard Gibbs energies of formation of solid DyFeO3 and Dy3Fe5O12 calculated by the least squares regression analysis of the data obtained in the present study, and data for Fe0.95O and Dy2O3 from the literature, are given by Delta(f)G(0)m(DyFeO3,s)(kJmol(-1))(+/-3.2)= -1339.9 + 0.2473 x (T(K)); (1021 less than or equal to T (K) less than or equal to 1548)and D(f)G(0)m(Dy3Fe5O12,s) (kJmol(-1)) (+/-3.5) = -4850.4 + 0.9846 x (T (K)); (1035 less than or equal to T (K) less than or equal to 1250) The uncertainty estimates for Delta(f)G(0)m include the standard deviation in the emf and uncertainty in the data taken from the literature. Based on the thermodynamic information, oxygen potential diagram and chemical potential diagrams for the system Dy-Fe-O were developed at 1250 K. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Penetrative phototactic bioconvection in an isotropic scattering suspension

Phototaxis is a directed swimming response dependent upon the light intensity sensed by micro-organisms. Positive (negative) phototaxis denotes the motion directed towards (away from) the source of light. Using the phototaxis model of Ghorai, Panda, and Hill ''Bioconvection in a suspension of isotropically scattering phototactic algae,'' Phys. Fluids 22, 071901 (2010)], we investigate two-dimensional phototactic bioconvection in an absorbing and isotropic scattering suspension in the nonlinear regime. The suspension is confined by a rigid bottom boundary, and stress-free top and lateral boundaries. The governing equations for phototactic bioconvection consist of Navier-Stokes equations for an incompressible fluid coupled with a conservation equation for micro-organisms and the radiative transfer equation for light transport. The governing system is solved efficiently using a semi-implicit second-order accurate conservative finite-difference method. The radiative transfer equation is solved by the finite volume method using a suitable step scheme. The resulting bioconvective patterns differ qualitatively from those found by Ghorai and Hill ''Penetrative phototactic bioconvection,'' Phys. Fluids 17, 074101 (2005)] at a higher critical wavelength due to the effects of scattering. The solutions show transition from steady state to periodic oscillations as the governing parameters are varied. Also, we notice the accumulation of micro-organisms in two horizontal layers at two different depths via their mean swimming orientation profile for some governing parameters at a higher scattering albedo. (C) 2013 AIP Publishing LLC.

System Reliability Analysis of Flexible Pavements

The uncertainty in material properties and traffic characterization in the design of flexible pavements has led to significant efforts in recent years to incorporate reliability methods and probabilistic design procedures for the design, rehabilitation, and maintenance of pavements. In the mechanistic-empirical (ME) design of pavements, despite the fact that there are multiple failure modes, the design criteria applied in the majority of analytical pavement design methods guard only against fatigue cracking and subgrade rutting, which are usually considered as independent failure events. This study carries out the reliability analysis for a flexible pavement section for these failure criteria based on the first-order reliability method (FORM) and the second-order reliability method (SORM) techniques and the crude Monte Carlo simulation. Through a sensitivity analysis, the most critical parameter affecting the design reliability for both fatigue and rutting failure criteria was identified as the surface layer thickness. However, reliability analysis in pavement design is most useful if it can be efficiently and accurately applied to components of pavement design and the combination of these components in an overall system analysis. The study shows that for the pavement section considered, there is a high degree of dependence between the two failure modes, and demonstrates that the probability of simultaneous occurrence of failures can be almost as high as the probability of component failures. Thus, the need to consider the system reliability in the pavement analysis is highlighted, and the study indicates that the improvement of pavement performance should be tackled in the light of reducing this undesirable event of simultaneous failure and not merely the consideration of the more critical failure mode. Furthermore, this probability of simultaneous occurrence of failures is seen to increase considerably with small increments in the mean traffic loads, which also results in wider system reliability bounds. The study also advocates the use of narrow bounds to the probability of failure, which provides a better estimate of the probability of failure, as validated from the results obtained from Monte Carlo simulation (MCS).

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.