Structure and fragmentation in colloidal artificial molecules and nuclei

Motivated by recent experiments on colloidal systems with competing attractive and repulsive interactions, we simulate a two-dimensional system of colloids with competing interactions that can undergo fragmentation. In the absence of any other confining potential, the colloids can form stable clusters depending on the strength of the short range attractive term. By suddenly changing the strength of one of the interaction terms we find a rich variety of fragmentation behavior which is affected by the existence of “magic” cluster numbers. Such soft matter systems can be used to construct artificial nuclei.     

Piecewise analysis of oblique vibro-impacting systems

A great number of studies have shown the complex nonlinear dynamics of mechanical systems with repeated normal impacts. An oblique frictional impact introduces even more complicated dynamics such as stick-slip motions to those systems. Hence, the dynamics of oblique vibro-impacting systems with possible sliding motion is an open problem. Based on a hybrid analysis of vibro-impact dynamics, kinematics and complementary conditions, a piecewise analysis method is developed in the paper to describe the sliding motion during an oblique impact. Thereby, a parametrically excited planar pendulum between two parallel rigid walls is studied as an illustrative example. The example, together with the corresponding numerical results, shows that the sliding impacts occur in such a system with a set of properly selected parameters. The project supported by the National Natural Science Foundation of China (59905010) and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education, China     

Topological methods for transients of driven systems

We consider the application of topological methods (such as knot, braid and Nielsen-Thurston theory) to transient, rather than periodic, orbits of periodically-forced nonlinear oscillators. The methods are restricted to systems with a three-dimensional phase space.

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Sommario Si considera l'applicazione di metodi topologici (basati sulle teorie dei nodi, delle trecce e di Nielsen-Thurston) allo studio delle orbite transitorie, piuttosto che stazionarie, di oscillatori nonlineari forzati periodicamente. Tali applicazioni sono ristrette a sistemi aventi spazio delle fasi tridimensionale.

     

Three-dimensional effects on line-of-sight visualization measurements of supersonic and hypersonic flow over cylinders

Flow visualization experiments were performed for supersonic and hypersonic nitrogen test gas flows over a cylinder. The results were used to quantify the influence of three-dimensional effects on optical line-of-sight visualization measurements. Images of cylindrical models of varying aspect ratios (length to diameter) were taken. Shock stand-off distance measurements for the models were compared with a two-dimensional approximation and numerical simulations. For aspect ratios of two and above, the two-dimensional approximation was acceptable within experimental uncertainty. The measured shock stand-off decreased by less than 5% from an asymptotic value for an infinite length cylinder. For smaller aspect ratios, a correction factor for the shock stand-off needs to be applied if comparisons between the two-dimensional approximation and experimental measurements are to be drawn. An estimate of this correction factor has been derived from an empirical fit to the available data.      

A self-assembling hexameric spheroid with variable degrees of hydration

The V-shaped racemic compound 4,12-dinitro-6,7,14,15-tetrahydro-6,14-methanocycloocta[1,2-b:5,6-b??]diquinoline 2 crystallises from solvents of differing water content as a centrosymmetric spheroidal hexamer in the form of a series of isostructural clusters (2)₆·(water) _x X-ray structures of these crystals in space group $ R\bar{3} $ show that they can exhibit an extent of hydration anywhere throughout the composition range x = 0 to 1.     

Bubbles navigating through networks of microchannels

This paper describes the behavior of bubbles suspended in a carrier liquid and moving within microfluidic networks of different connectivities. A single-phase continuum fluid, when flowing in a network of channels, partitions itself among all possible paths connecting the inlet and outlet. The flow rates along different paths are determined by the interaction between the fluid and the global structure of the network. That is, the distribution of flows depends on the fluidic resistances of all channels of the network. The movement of bubbles of gas, or droplets of liquid, suspended in a liquid can be quite different from the movement of a single-phase liquid, especially when they have sizes slightly larger than the channels, so that the bubbles (or droplets) contribute to the fluidic resistance of a channel when they are transiting it. This paper examines bubbles in this size range; in the size range examined, the bubbles are discrete and do not divide at junctions. As a consequence, a single bubble traverses only one of the possible paths through the network, and makes a sequence of binary choices ("left" or "right") at each branching intersection it encounters. We designed networks so that, at each junction, a bubble enters the channel into which the volumetric flow rate of the carrier liquid is highest. When there is only a single bubble inside a network at a time, the path taken by the bubble is, counter-intuitively, not necessarily the shortest or the fastest connecting the inlet and outlet. When a small number of bubbles move simultaneously through a network, they interact with one another by modifying fluidic resistances and flows in a time dependent manner; such groups of bubbles show very complex behaviors. When a large number of bubbles (sufficiently large that the volume of the bubbles occupies a significant fraction of the volume of the network) flow simultaneously through a network, however, the collective behavior of bubbles-the fluxes of bubbles through different paths of the network-can resemble the distribution of flows of a single-phase fluid.     

The Cavity Method for the Rigidity Transition

In order to motivate an analogy between the rigidity theory and combinatorial optimization, we have used the cavity method to study the floppy to rigid transition in a 2-dimensional (2D) random graph as well as in a 3D small world chain. Our analytic results are in excellent agreement with numerical studies using the pebble game algorithm. We also illustrate that a transfer matrix method is equivalent to the cavity method at the replica symmetric level     

Nonlinear heave-roll coupling and ship rolling

A nonlinear model for simulating the heave-roll motions of ships in following waves is presented. The parametric excitation is modeled by a Hill's type equation, instead of the conventional Mathieu's equation. The model includes not only the linear but also the quadratic coupling term. Instability conditions for parametrically excited rolling motions are derived using the harmonic balance method. The results are verified by numerical analyses. The effects of including the quadratic coupling term on the instability conditions and nonlinear responses are studied. The complex dynamic behaviour of the coupled system in the various instability regions is also investigated. Bifurcations of the flip, fold and pitchfork types are observed in the Poincaré mapping of the numerically simulated responses. Chaotic motions leading to boundary crises and inevitable capsize are also reported.     

Warped products of Hadamard spaces

In the Riemannian case, our approach to warped products illuminates curvature formulas that previously seemed formal and somewhat mysterious. Moreover, the geometric approach allows us to study warped products in a much more general class of spaces. For complete metric spaces, it is known that nonpositive curvature in the Alexandrov sense is preserved by gluing on isometric closed convex subsets and by Gromov–Hausdorff limits with strictly positive convexity radius; we show it is also preserved by warped products with convex warping functions. Received: 9 January 1998/ Revised version: 12 March 1998     

Supersonic velocimetry in a shock tube using laser enhanced ionisation and planar laser induced fluorescence

 A novel flow-tagging technique is presented which was employed to measure gas velocities in the free stream of a shock tube. This method is based on the laser spectroscopic techniques of Laser-Enhanced Ionisation (LEI) and Laser-Induced Fluorescence (LIF). The flow in the shock tube is seeded with small amounts of sodium, and LEI is used to produce a substantial depletion of neutral sodium atom concentration in a well-defined region of the flow, by using two wavelength-resonance excitation and subsequent collisional ionisation. At a specific time delay, single-laser-pulse planar LIF is utilised to produce a two-dimensional (2-D) inverse image of the depleted tagged region downstream of the flow. By measuring the displacement of the tagged region, free stream velocities in a shock tube were determined. Large variations in the concentration of sodium seeded into the flow were observed and even in the presence of these large variations accurate free-stream velocity measurements were obtained. The experimentally determined value for velocity compares very well with the predicted velocity. Received: 25 March 1996/Revised version: 8 July 1996