A hybrid-parallel framework for the nonlinear seismic analysis of very tall buildings

FRAME3D, a program for the nonlinear seismic analysis of steel structures, has previously been used to study the collapse mechanisms of steel buildings up to 20 stories tall. The present thesis is inspired by the need to conduct similar analysis for much taller structures. It improves FRAME3D in two primary ways.

First, FRAME3D is revised to address specific nonlinear situations involving large displacement/rotation increments, the backup-subdivide algorithm, element failure, and extremely narrow joint hysteresis. The revisions result in superior convergence capabilities when modeling earthquake-induced collapse. The material model of a steel fiber is also modified to allow for post-rupture compressive strength.

Second, a parallel FRAME3D (PFRAME3D) is developed. The serial code is optimized and then parallelized. A distributed-memory divide-and-conquer approach is used for both the global direct solver and element-state updates. The result is an implicit finite-element hybrid-parallel program that takes advantage of the narrow-band nature of very tall buildings and uses nearest-neighbor-only communication patterns.

Using three structures of varied sized, PFRAME3D is shown to compute reproducible results that agree with that of the optimized 1-core version (displacement time-history response root-mean-squared errors are ~〖10〗^(-5) m) with much less wall time (e.g., a dynamic time-history collapse simulation of a 60-story building is computed in 5.69 hrs with 128 cores—a speedup of 14.7 vs. the optimized 1-core version). The maximum speedups attained are shown to increase with building height (as the total number of cores used also increases), and the parallel framework can be expected to be suitable for buildings taller than the ones presented here.

PFRAME3D is used to analyze a hypothetical 60-story steel moment-frame tube building (fundamental period of 6.16 sec) designed according to the 1994 Uniform Building Code. Dynamic pushover and time-history analyses are conducted. Multi-story shear-band collapse mechanisms are observed around mid-height of the building. The use of closely-spaced columns and deep beams is found to contribute to the building's “somewhat brittle” behavior (ductility ratio ~2.0). Overall building strength is observed to be sensitive to whether a model is fracture-capable.

Nonlinear response and optical limiting in SrBi2Ta2O9 thin films

SrBi2Ta2O9 (SBT) thin films on quartz substrates were prepared by use of the pulsed-laser deposition technique. The nonlinear refractive indices, n(2), Of the SBT films were measured by use of z-scan techniques with picosecond pulses. Large negative nonlinear refractive indices of 3.84 and 3.58 cm(2)/GW were obtained for the wavelengths 532 nm and 1.064 mum, respectively. The two-photon absorption coefficient was determined to be 7.3 cm/GW for 532 nm. The limiting behavior of SBT thin film on a quartz substrate was investigated in an f/5 defocusing geometry by use of 38-ps-duration, 532-nm, 1.064-mum. laser excitation. (C) 2001 Optical Society of America.

Nanosecond nonlinear absorption in Au and Ag nanoparticles precipitated glasses induced by a femtosecond laser

We obtain Au and Ag nanoparticles precipitated in glasses by irradiation of focused femtosecond pulses, and investigate the nonlinear absorptions of the glasses by using Z-scan technique with ns pulses at 532 nm. We observe the saturable absorption behavior for An nanoparticles precipitated glasses and the reverse saturable ones for Ag ones. We also obtain, by fitting to the experimental results in the light of the local field effect near and away from the surface plasmon resonance, chi(m)((3)) = 4.5 x 10(-7) and 5.9 x 10(-8) esu for m the imaginary parts of the third-order susceptibilities for Au and Ag nanoparticles, respectively. The nonlinear response of Au nanoparticles in the glass samples arises mainly from the hot-electron contribution and the saturation of the interband transitions near the surface plasmon resonance, whereas that of Ag nanoparticles in the glass samples from the interband transitions. These show that the obtained glasses can be used as optoelectronic devices suiting for different demands. (c) 2005 Elsevier B.V. All rights reserved.

A model for nonlinear viscoelastic mechanical responses of collagenous soft tissues

Experimental observations of the time-dependent mechanical responses of collagenous tissues have demonstrated behavior that deviates from standard treatments of linear or quasi-linear viscoelasticity. In particular, time-dependent deformation can be strongly coupled to strain level, and strain-rate independence can be observed under monotonic loading, even for a tissue with dramatic stress relaxation. It was postulated that this nonlinearity is fundamentally associated with gradual recruitment of individual collagen fibrils during applied mechanical loading. Based on previously observed experimental results for the time-dependent response of collagenous soft tissues, a model is developed to describe the mechanical behavior of these tissues under uniaxial loading. Tissue stresses, under applied strain-controlled loading, are assumed to be a sum of elastic and viscoelastic stress contributions. The relative contributions of elastic and viscoelastic stresses is assumed to vary with strain level, leading to strain- and time-dependent mechanical behavior. The model formulation is examined under conditions of monotonic loading at varying constant strain rates and stress-relaxation at different applied strain levels. The model is compared with experimental data for a membranous biological soft tissue, the amniotic sac, and is found to agree well with experimental results. The limiting behavior of the novel model, at large strains relative to the collagen recruitment, is consistent with the quasi-linear viscoelastic approach. © 2006 Materials Research Society.

The nonlinear heat release response of stratified lean-premixed flames to acoustic velocity oscillations

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to high-amplitude acoustic forcing in a laboratory-scale stratified burner operated with CH4 and air at atmospheric pressure. The double-swirler, double-channel annular burner was specially designed to generate high-amplitude acoustic velocity oscillations and a radial equivalence ratio gradient at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the response are not considered in the present investigation. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a constant temperature anemometer and photomultiplier tubes with narrow-band OH*/CH* interference filters. Time-averaged and phase-synchronized CH* chemiluminescence intensities were measured using an intensified CCD camera. The measurements show that flame stabilization mechanisms vary depending on equivalence ratio gradients for a constant global equivalence ratio (φg=0.60). Under uniformly premixed conditions, an enveloped M-shaped flame is observed. In contrast, under stratified conditions, a dihedral V-flame and a toroidal detached flame develop in the outer stream and inner stream fuel enrichment cases, respectively. The modification of the stabilization mechanism has a significant impact on the nonlinear response of stratified flames to high-amplitude acoustic forcing (u'/U∼0.45 and f=60, 160Hz). Outer stream enrichment tends to improve the flame's stiffness with respect to incident acoustic/vortical disturbances, whereas inner stream stratification tends to enhance the nonlinear flame dynamics, as manifested by the complex interaction between the swirl flame and large-scale coherent vortices with different length scales and shedding points. It was found that the behavior of the measured flame describing functions (FDF), which depend on radial fuel stratification, are well correlated with previous measurements of the intensity of self-excited combustion instabilities in the stratified swirl burner. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, its effect on flame location and the interaction with unsteady flow structures. © 2011 The Combustion Institute.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Chaotic behavior of pulsating heat pipes

Chaotic behavior of closed loop pulsating heat pipes (PHPs) was studied. The PHPs were fabricated by capillary tubes with outer and inner diameters of 2.0 and 1.20 mm. FC-72 and deionized water were used as the working fluids. Experiments cover the following data ranges: number of turns of 4, 6, and 9, inclination angles from 5 degrees (near horizontal) to 90, (vertical), charge ratios from 50% to 80%, heating powers from 7.5 to 60.0 W. The nonlinear analysis is based on the recorded time series of temperatures on the evaporation, adiabatic, and condensation sections. The present study confirms that PHPs are deterministic chaotic systems. Autocorrelation functions (ACF) are decreased versus time, indicating prediction ability of the system is finite. Three typical attractor patterns are identified. Hurst exponents are very high, i.e., from 0.85 to 0.95, indicating very strong persistent properties of PHPs. Curves of correlation integral versus radius of hypersphere indicate two linear sections for water PHPs, corresponding to both high frequency, low amplitude, and low frequency, large amplitude oscillations. At small inclination angles near horizontal, correlation dimensions are not uniform at different turns of PHPs. The non-uniformity of correlation dimensions is significantly improved with increases in inclination angles. Effect of inclination angles on the chaotic parameters is complex for FC-72 PHPs, but it is certain that correlation dimensions and Kolmogorov entropies are increased with increases in inclination angles. The optimal charge ratios are about 60-70%, at which correlation dimensions and Kolmogorov entropies are high. The higher the heating power, the larger the correlation dimensions and Kolmogorov entropies are. For most runs, large correlation dimensions and Kolmogorov entropies correspond to small thermal resistances, i.e., better thermal performance, except for FC-72 PHPs at small inclination angles of theta < 15 degrees.

Nonlinear optical properties of semiconductor quantum wells under intense terahertz radiation

The nonlinear optical properties of semiconductor quantum wells driven by intense in-plane terahertz electric fields are investigated theoretically by employing the extended semiconductor Bloch equations. The dynamical Franz-Keldysh effect of the optical absorption near the band edge is analyzed with Coulomb correlation among the carriers included. The in-plane terahertz field induces a variety of behavior in the absorption spectra, including terahertz replicas of the (dark) 2p exciton and terahertz sidebands of the 1s exciton. The dependence of these interesting features on the intensity, frequency, and phase of the terahertz field is explored in detail.

Adsorption Behavior of Exogenous Thorium on Soil Contaminated by Rare Earth Industries

The adsorption behavior of exogenous thorium on soil was studied to evaluate the contaminated risk on soil. The adsorption capacity, equilibrium time, distribution coefficient and desorption ability were investigated by the experiments of static adsorption. The strong adsorption ability of exogenous thorium on soil samples was observed by high adsorption ratio (> 92%) and low desorption ratio (< 5%) in equilibrium, and the biggest distribution coefficient was over 10(4). The adsorption capacity and equilibrium time were related to soil properties. According to the results of adsorption, Freundlich equation (r >= 0.916 7) and Elovich equation (R-2 >= 0. 898 0) were primely fit for describing the thermodynamics and kinetics of the adsorption of exogenous thorium on soil samples, respectively, which indicated that the adsorption was belonged to the nonlinear adsorption, and was affected by the diffusion of thorium on soil surface and in mineral interbed. Sequential extraction procedure was employed to evaluate the bound fractions of exogenous thorium adsorbed on soil samples.

Study of electrochemical behavior of ergosterol by in situ thin layer circular dichroic spectroelectrochemistry

The electroxidation of ergosterol was studied by in situ circular dichroic (CD) spectroelectrochemistry with a long optical path length thin layer cell. It was confirmed that the oxidation of ergosterol in ethanol solution is a two-electron irreversible electrochemical process with strong adsorption of an electroinactive product at the glassy carbon electrode, which blocks the electrochemical reaction. The CD spectroelectrochemical data were treated by the double logarithm method together with nonlinear regression, from which the formal potential, E-0 = 1.00 V, alpha n(alpha) = 0.302, the standard electrochemical rate constant, k(0) = 6.1(+/-0.4) x 10(-4) cm s(-1) and the adsorption constant, beta = 19 +/- 1, were obtained. The number of electrons transferred (n = 1.86) was estimated by cyclic voltammetry.

In situ UV-vis and CD thin-layer spectroelectrochemistry study of the electrochemical behavior of L-noradrenaline in alkaline solution

Electrochemical redox behavior of noradrenaline in alkaline solution on a glassy carbon electrode has been investigated by in situ UV-vis and CD spectroelectrochemistry by using a long optical path thin-layer cell. The experimental data were processed by using a double logarithmic method of analysis together with nonlinear regression which confirmed that the first step in both the oxidation of noradrenaline and reduction of noradrenochrome is a two-electron irreversible process governed by an EE mechanism. The kinetic parameters of the electrode reactions, i.e., charge transfer coefficient and the number of electrons transferred, alpha(1)n(1) = 0.11 and alpha(2)n(2) = 0.23, formal potentials modified with kinetics, E-1(0') = 0.65 (+/- 0.01) V and E-2(0') = 0.72V and standard rate cnstants, k(1)(0) = 7.0(+/-0.5)x10(-5) cm s(-1), for the first and second steps in the oxidation process of noradrenaline, and similarly, alpha(1)n(1) = 0.33, alpha(2)n(2) = 0.58, E-1(0') = 0.37(+/-0.01) V, E-0' = -0.25 (+/-0.01) V and k(1)(0) approximate to k(2)(0) = 1.06 (+/-0.05)x10(-4) cm s(-1) for the first and second steps in the reduction process of noradrenochrome were also determined.

Studies on the side chain liquid crystalline copolymer containing nonlinear optical groups

A new side chain liquid crystalline poly[4-(methacryloxy)hexanoloxy-4'-benzyloxy biphenyl] was synthesized. The phase behavior of the monomer and homopolymer was studied. The monomer shows a smectic B phase, while the homopolymer shows a nematic phase. The nonmesogenic nonlinear optical group was introduced to synthesize a series of side chain liquid crystalline copolymers which also show a nematic phase. Owing to the liquid crystallinity of the copolymer has been the orientational stability improved, down the relax of the orientation slowed and the nonlinear optical properties enhanced.

Summarizing Qualitative Behavior from Measurements of NonlinearsCircuits

This report describes a program which automatically characterizes the behavior of any driven, nonlinear, electrical circuit. To do this, the program autonomously selects interesting input parameters, drives the circuit, measures its response, performs a set of numeric computations on the measured data, interprets the results, and decomposes the circuit's parameter space into regions of qualitatively distinct behavior. The output is a two-dimensional portrait summarizing the high-level, qualitative behavior of the circuit for every point in the graph, an accompanying textual explanation describing any interesting patterns observed in the diagram, and a symbolic description of the circuit's behavior which can be passed on to other programs for further analysis.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Optical bistability in nonlinear surface-plasmon polaritonic crystals

Nonlinear optical transmission through periodically nanostructured metal films (surface-plasmon polaritonic crystals) has been studied. The surface polaritonic crystals have been coated with a nonlinear polymer. The optical transmission of such nanostructures has been shown to depend on the control-light illumination conditions. The resonant transmission exhibits bistable behavior with the control-light intensity. The bistability is different at different resonant signal wavelengths and for different wavelengths of the control light. The effect is explained by the strong sensitivity of the surface-plasmon mode resonances at the signal wavelength to the surrounding dielectric environment and the electromagnetic field enhancement due to plasmonic excitations at the controlled light wavelengths.