Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique

In this paper, we have analyzed the mathematical model of various nonlinear oscillators arising in different fields of engineering. Further, approximate solutions for different variations in oscillators are studied by using feedforward neural networks (NNs) based on the backpropagated Levenberg–Marquardt algorithm (BLMA). A data set for different problem scenarios for the supervised learning of BLMA has been generated by the Runge–Kutta method of order 4 (RK-4) with the “NDSolve” package in Mathematica. The worth of the approximate solution by NN-BLMA is attained by employing the processing of testing, training, and validation of the reference data set. For each model, convergence analysis, error histograms, regression analysis, and curve fitting are considered to study the robustness and accuracy of the design scheme.     

NMR Analysis of a Complex Spin System from a Siruo-Chamigrene

The compound 2,10-dibromo-3-chloro-8-hydroxy-β-chamigrene was analysed in detail by NMR Spectroscopy. the complete assignment of the signals in the ¹H and ¹³C NMR spectra and the determination of the relative configurations were achieved by 2D NMR techniques, AM1 data and ¹H spectrum simulation. Comparisons of the results with related spiro chamigrene systems are also presented.     

Crystal plasticity modeling of irradiation growth in Zircaloy-2

Abstract

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.     

Morera and mean-value type theorems in the hyperbolic disk

Some Morera and mean-value type theorems are proved in the hyperbolic disk. Partially supported by NSF grants DMS-9000619 and CDR-8803012. Partially supported by NSF grants DMS-8703072 and DMS-9000619, and DGI-CYT grant PB 89-0311.     

Generative Art with Swarm Landscapes

We present a generative swarm art project that creates 3D animations by running a Particle Swarm Optimization algorithm over synthetic landscapes produced by an objective function. Different kinds of functions are explored, including mathematical expressions, Perlin noise-based terrain, and several image-based procedures. A method for displaying the particle swarm exploring the search space in aesthetically pleasing ways is described. Several experiments are detailed and analyzed and a number of interesting visual artifacts are highlighted.     

Dynamical structure of linearizedGL(4) gravities

The physical content of the three more natural models ofGL(4) gravity is analyzed, for the case of weak fields. The first model we deal with is the linearized version of Yang's onetensor-field gravity. It is shown that this is a scalar-tensor theory, with its scalar part contained in the symmetric tensorh , instead of appearing explicitly, externally to the symmetric tensorh , as happens in Brans-Dicke type of scalar-tensor theories. The second and the third linearized models, which can both be derived from the fourth-order action postulated by Yang, turn out to be two-tensor decoupled systems. In both cases one of the tensors is the symmetric weak metric gravity tensor field. The second tensor appearing in these two models, representing theGL(4)-gauge field, is either a linearized symmetric affinity (in the second model) or a linearized but nonsymmetric affinity (for the third model). It is shown that in these last two cases the affinity contains a helicity-3 propagating field. The connection is also given between the fourth-order system which determines the dynamical structure (for the last two models) of the metric tensor and the third-order Yang model of gravity. Owing to the presence of helicity-3 fields we show that it is better to regard Yang's action as an action for a two-tensor system instead of trying to recover from it a pure gravity (one-tensor-field) action. Finally, it is shown what is the dynamical structure of the second and third linearized two-tensor models which can be derived from Yang's action.On leave of absence from the Universidad Simón Bolívar.     

Laurdan in Fluid Bilayers: Position and Structural Sensitivity

Laurdan (2-dimethylamino-6-lauroylnaphthalene) is a hydrophobic fluorescent probe widely used in lipid systems. This probe was shown to be highly sensitive to lipid phases, and this sensitivity related to the probe microenvironment polarity and viscosity. In the present study, Laurdan was incorporated in 1,2-dipalmitoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DPPG), which has a phase transition around 41°C, and DLPC (1,2-dilauroyl-sn-glycero-3-phosphocholine), which is in the fluid phase at all temperatures studied. The temperature dependence of Laurdan fluorescent emission was analyzed via the decomposition into two gaussian bands, a short- and a long-wavelength band, corresponding to a non-relaxed and a water-relaxed excited state, respectively. As expected, Laurdan fluorescence is highly sensitive to DPPG gel–fluid transition. However, it is shown that Laurdan fluorescence, in DLPC, is also dependent on the temperature, though the bilayer phase does not change. This is in contrast to the rather similar fluorescent emission obtained for the analogous hydrophilic probe, Prodan (2-dimethylamino-6-propionylnaphthalene), when free in aqueous solution, over the same range of temperature. Therefore, Laurdan fluorescence seems to be highly dependent on the lipid bilayer packing, even for fluid membranes. This is supported by Laurdan fluorescence anisotropy and spin labels incorporated at different positions in the fluid lipid bilayer of DLPC. The latter were used both as structural probes for bilayer packing, and as Laurdan fluorescence quenchers. The results confirm the high sensitivity of Laurdan fluorescence emission to membrane packing, and indicate a rather shallow position for Laurdan in the membrane.     

Investigating directed influences between activated brain areas in a motor-response task using fMRI

Localization of cognitive processes is a strength of functional neuroimaging. However, information about functional interactions between brain areas is crucial for a deeper understanding of brain function. We applied vector autoregressive modeling in the context of Granger causality as a method to analyze directed connectivity in a standard event-related fMRI study using a simple auditory-motor paradigm. The basic idea is to use temporal information in stochastic time series of a brain region in order to predict signal time courses in other brain regions. Thus, we predicted that the method should demonstrate causal influence of the auditory cortex and the supplementary motor area (SMA) on primary motor cortex. Eleven right-handed healthy female subjects were instructed to press a ball with either their left or their right hand when hearing the command "left" or "right" in the scanner. Influence to the left motor cortex was found from bilateral auditory cortex as well as from the SMA in 9 of 11 subjects. Granger causality to the right motor cortex existed from bilateral auditory cortex in 5 and from SMA in 6 subjects. Granger causality to the SMA existed from right auditory cortex in 7 subjects and from left auditory cortex in 8 subjects. Our findings in a simple task show that even under suboptimal circumstances (a relatively long TR of 2440 ms), Granger causality can be a useful tool to explore effective connectivity. Temporally optimized scanning should increase that potential.     

An electrothermal instability: the influence of albedo boundary conditions on the stationary states of an exactly solvable model

In order to study the effect of partially reflective (albedo) boundary conditions on pattern formation and stability in reaction-diffusion systems, we have analyzed an exactly soluble model of an electrothermal instability: the Ballast resistor. The present results allow a continuous interpolation between the results corresponding to Neumann and Dirichlet boundary conditions, and they allow qualitative changes in the patterns to be followed.