Experimental investigation of high-quality synchronization of coupled oscillators

We describe two experiments in which we investigate the synchronization of coupled periodic oscillators. Each experimental system consists of two identical coupled electronic periodic oscillators that display bursts of desynchronization events similar to those observed previously in coupled chaotic systems. We measure the degree of synchronization as a function of coupling strength. In the first experiment, high-quality synchronization is achieved for all coupling strengths above a critical value. In the second experiment, no high-quality synchronization is observed. We compare our results to the predictions of the several proposed criteria for synchronization. We find that none of the criteria accurately predict the range of coupling strengths over which high-quality synchronization is observed. (c) 2000 American Institute of Physics.     

Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

A two-dimensional steady-sate analysis of semi-infinite brittlecrack growth at a constant subcritical rate in an unboundedfully-coupled thermoelastic solid under mixed-mode thermomechanicalloading is made. The loading consists of normal and shear tractionsand heat fluxes applied as point sources (line loads in theout-of-plane direction). A related problem is solved exactly in an integral transformspace, and robust asymptotic forms used to reduce the originalproblem to a set of integral equations. The equations are partiallycoupled and exhibit operators of both Cauchy and Abel types,yet can be solved analytically. The temperature change field at a distance from the moving crackedge is then constructed, and its dominant term is found tobe controlled by the imposed heat fluxes. The role of this termis, indeed, enhanced if the heat fluxes serve to render thecrack as a net heat source/sink for the solid, as opposed tobeing a transmitter of heat across its plane. More generally,the influence of the thermoelastic coupling on this field, aswell as other functions, is found to increase with crack speed.     

Problem-Solving Methodology Design on the Run

This paper discusses a risk analysis study which considered the best way to cross a river with a large diameter gas pipeline, one possibility being a bridge carrying a large diameter oil line. About 30 ‘riskateers’ were involved, over a 3-month period, most of whom were engineers or economists with no risk analysis, O.R. or systems experience. A large number of interested parties were involved, with different perspectives. The paper stresses methodology design as an organizational vehicle, and the implications of designing problem-solving methodology in the midst of a problem-solving process.     

Infrared and Raman studies of rotational correlation functions in liquids

Raman and infrared band shapes of some symmetric top molecules in the neat liquid and in solution were measured and used to obtain vibrational and rotational correlation functions and relaxation times. The results are compared with the predictions of the Debye rotational diffusion theory, the Gordon J diffusion model and the Ivanov rotational-jump model. Except for the latter theory none of these theories are consistent with both the infrared and Raman results for CD₃I and CH₃I.     

Fundamentals of synchronization in chaotic systems,concepts, and applications

The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and "cottage industries" have emerged that have taken on bona fide lives of their own. Our purpose in this paper is to collect results from these various areas in a review article format with a tutorial emphasis. Fundamentals of chaotic synchronization are reviewed first with emphases on the geometry of synchronization and stability criteria. Several widely used coupling configurations are examined and, when available, experimental demonstrations of their success (generally with chaotic circuit systems) are described. Particular focus is given to the recent notion of synchronous substitution-a method to synchronize chaotic systems using a larger class of scalar chaotic coupling signals than previously thought possible. Connections between this technique and well-known control theory results are also outlined. Extensions of the technique are presented that allow so-called hyperchaotic systems (systems with more than one positive Lyapunov exponent) to be synchronized. Several proposals for "secure" communication schemes have been advanced; major ones are reviewed and their strengths and weaknesses are touched upon. Arrays of coupled chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuitive phenomena including bursting above synchronization thresholds, destabilizing transitions as coupling increases (short-wavelength bifurcations), and riddled basins. In addition, a general mathematical framework for analyzing the stability of arrays with arbitrary coupling configurations is outlined. Finally, the topic of generalized synchronization is discussed, along with data analysis techniques that can be used to decide whether two systems satisfy the mathematical requirements of generalized synchronization. (c) 1997 American Institute of Physics.     

Dynamics of Biological Polyelectrolytes

Summary: Biological polymers and structures, including proteins and DNAs, can be made in essentially monodisperse form. Proteins usually have well-defined shapes. Duplex oligonucleotides are rigid and rodlike, and longer DNAs are semiflexible coils. The DNAs also constitute a homologous series. The dynamics of both proteins and DNAs can be studied by readily available techniques such as dynamic light scattering (DLS) and fluorescence correlation spectroscopy (FCS). These systems can thus be used as model systems to elucidate elusive charge effects on the dynamics of macromolecules in solution (polyelectrolyte effects) for both rigid and semiflexible polymers. We present here as examples the results of measurements of mutual and self-diffusion coefficients dynamics of a rodlike oligonucleotide as functions of polymer concentration and the concentration of added salt (which screens the charges).     

Self-diffusion in solutions of a 20 base pair oligonucleotide: effects of concentration and ionic strength

The long-time self-diffusion coefficients of a 20 base pair duplex oligonucleotide are measured as functions of 20-mer and added NaCl salt concentrations. The self-diffusion coefficients decrease monotonically with increasing 20-mer concentrations for the high-added salt sample and display non-monotonically decreasing 20-mer concentration dependences at lower added salt concentrations. The non-monotonic behavior is attributed to the opposing effects of the tendency to increase the interactions between 20-mers as the concentration is increased and to a decrease in the extent of the Coulomb forces as counterions from the 20-mer increasingly screen them. Attempts to account for the effect of the Coulomb forces on the self-diffusion coefficients by using effective dimensions in the hard rod theory give good agreement with experiment at the highest salt concentration studied. For the lower salt concentrations there appear to be two scaling regimes--one at low polyion concentration in which the high salt scaling of the rod dimensions by adding the Debye screening to the length and diameter of the rod is appropriate and one at high polyion concentrations where the scaling of the dimensions is the addition of 1/2 the Debye screening length. Estimates of the "overlap" concentration C*=1/L(eff) indicate that the non-monotonic decrease occurs at concentrations lower than C*. Finally, the fluorescence correlation spectroscopy self-diffusion coefficients measured here are compared with the mutual diffusion coefficients measured by dynamic light scattering.     

Synthetic magnetic opals

We present studies of novel nanocomposites of BiNi impregnated into the structure of opals as well as inverse opals. Atomic force microscopy and high resolution elemental analyses show a highly ordered structure and uniform distribution of the BiNi filler in the matrix. These BiNi-based nanocomposites are found to exhibit distinct ferromagnetic-like ordering with transition temperature of about 675 K. As far as we know there exists no report in literature on any BiNi compound which is magnetic.