Inducing chaos by resonant perturbations: theory and experiment

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.     

Solitary waves in an isotropic ferromagnetic chain

It is shown that due to high-order terms in the Holstein-Primakoff boson-like spin operator transformation we can have a solitary wave solution even in an isotropic ferromagnetic chain.     

A nonlinear problem in dynamic visco-elasticity with friction

This paper presents a study of the dynamics of a pile driven into the ground under the action of a pile hammer. Due to the effects of friction one is led to a model consisting of a variational inequality. Results about existence, uniqueness and stability of solutions of an initial value problem for this variational inequality are obtained.     

Antimicrobial screening and quantitative determination of benzoic acid derivative of Gomphrena celosioides by TLC-densitometry

The antimicrobial activity of ethanolic extract and pure compounds of Gomphrena celosioides have been screened by Kirby-Bauer method. Quantitative determination of 4-hydroxy-3-methoxy-benzoic acid in stems, leaves, flowers and roots was established by TLC-densitometry. Results showed significant activity against Staphylococcus aureus and Salmonella typhi. There were no significant differences in the determined benzoic acid derivative.     

M?ssbauer characterization of the iron-sulfur clusters in Desulfovibrio vulgaris hydrogenase.

The periplasmic hydrogenase of Desulfovibrio vulgaris (Hildenbourough) is an all Fe-containing hydrogenase. It contains two ferredoxin type [4Fe-4S] clusters, termed the F clusters, and a catalytic H cluster. Recent X-ray crystallographic studies on two Fe hydrogenases revealed that the H cluster is composed of two sub-clusters, a [4Fe-4S] cluster ([4Fe-4S](H)) and a binuclear Fe cluster ([2Fe](H)), bridged by a cysteine sulfur. The aerobically purified D. vulgaris hydrogenase is stable in air. It is inactive and requires reductive activation. Upon reduction, the enzyme becomes sensitive to O(2), indicating that the reductive activation process is irreversible. Previous EPR investigations showed that upon reoxidation (under argon) the H cluster exhibits a rhombic EPR signal that is not seen in the as-purified enzyme, suggesting a conformational change in association with the reductive activation. For the purpose of gaining more information on the electronic properties of this unique H cluster and to understand further the reductive activation process, variable-temperature and variable-field M?ssbauer spectroscopy has been used to characterize the Fe-S clusters in D. vulgaris hydrogenase poised at different redox states generated during a reductive titration, and in the CO-reacted enzyme. The data were successfully decomposed into spectral components corresponding to the F and H clusters, and characteristic parameters describing the electronic and magnetic properties of the F and H clusters were obtained. Consistent with the X-ray crystallographic results, the spectra of the H cluster can be understood as originating from an exchange coupled [4Fe-4S]-[2Fe] system. In particular, detailed analysis of the data reveals that the reductive activation begins with reduction of the [4Fe-4S](H) cluster from the 2+ to the 1+ state, followed by transfer of the reducing equivalent from the [4Fe-4S](H) subcluster to the binuclear [2Fe](H) subcluster. The results also reveal that binding of exogenous CO to the H cluster affects significantly the exchange coupling between the [4Fe-4S](H) and the [2Fe](H) subclusters. Implication of such a CO binding effect is discussed.     

Coupling 3D and 1D fluid-structure interaction models for blood flow simulations

Three-dimensional (3D) simulations of blood flow in medium to large vessels are now a common practice. These models consist of the 3D Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall structure. However, it is still computationally unaffordable to simulate very large sections, let alone the whole, of the human circulatory system with fully 3D fluid-structure interaction models. Thus truncated 3D regions have to be considered. Reduced models, one-dimensional (1D) or zero-dimensional (0D), can be used to approximate the remaining parts of the cardiovascular system at a low computational cost. These models have a lower level of accuracy, since they describe the evolution of averaged quantities, nevertheless they provide useful information which can be fed to the more complex model. More precisely, the 1D models describe the wave propagation nature of blood flow and coupled with the 3D models can act also as absorbing boundary conditions. We consider in this work the coupling of a 3D fluid-structure interaction model with a 1D hyperbolic model. We study the stability of the coupling and present some numerical results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A strategy for parallel implementation of finite difference numerical schemes associated to evolution differential equations

Within the framework of parallel numerical treatment, there are many more results on stationary (or time-frozen) PDE's than on their evolution (or time-dependent) counterparts. This is justified as computer simulation of time flow – an intrinsically sequential phenomenum – leads naturally to a sequential algorithm, thus inhibiting any search for concurrent ones. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Counterion Nature and Alkylammonium Halide Adsorption Thermodynamics

Two surfactants were synthesized by reacting hydrogen halides (hydrogen chloride and hydrogen bromide) with 1-dodecylamine. The resultant cationic surfactants, 1-dodecylammonium chloride (DDAC) and 1-dodecylammonium bromide (DDAB), were characterized by NMR spectrometry and FTIR spectroscopy and data related to their adsorption at the fluid liquid/gas interface were obtained employing bubble surface tensiometry, in pure water and in HCl 0.1 M. Data did not fit well to Langmuir isotherm but Frumkin isotherm did adequately describe to process of adsorption. Adsorption isotherms, as well as data related to critical micelle concentration, CMC, indicated that in HCl 0.1 M, the presence of electrolytes and a common ion to DDAC decreased chloride solvation, changing surface packing and adsorption profile for this surfactant.     

Anderson localization in a disordered chain with a finite nonlinear response time

In this work, we investigate the competition of disorder, nonlinearity and non-adiabatic process on the wave packet dynamics in 1D. We follow the time evolution of the second moment of the wave packet distribution to characterize its spreading behavior. In order to describe the dynamical behavior of one-electron wave packets, we solve a discrete nonlinear Schr?dinger equation which effectively takes into account a diagonal disorder and a nonlinear contribution. Going beyond the adiabatic regime, we consider that the nonlinearity relaxes in time according to a Debye-like law. In the adiabatic regime, it has been recently demonstrated that the interplay of disorder and nonlinearity leads to a sub-diffusive spread of the wave packet. Here, we numerically demonstrate that no sub-diffusive spreading of the second moment of the wave packet distribution takes place when the finite response time of the nonlinearity is taken into account.