Unfolding the torus: Oscillator geometry from time delays

Summary We present a simple method of plotting the trajectories of systems of weakly coupled oscillators. Our algorithm uses the time delays between the “firings” of the oscillators. For any system ofn weakly coupled oscillators there is an attracting invariantn-dimensional torus, and the attractor is a subset of this invariant torus. The invariant torus intersects a suitable codimension-1 surface of section at an (n−1)-dimensional torus. The dynamics ofn coupled oscillators can thus be reduced,in principle, to the study of Poincaré maps of the (n−1)-dimensional torus. This paper gives apractical algorithm for measuring then−1 angles on the torus. Since visualization of 3 (or higher) dimensional data is difficult we concentrate onn=3 oscillators. For three oscillators, a standard projection of the Poincaré map onto the plane yields a projection of the 2-torus which is 4-to-1 over most of the torus, making it difficult to observe the structure of the attractor. Our algorithm allows a direct measurement of the 2 angles on the torus, so we can plot a 1-to-1 map from the invariant torus to the “unfolded torus” where opposite edges of a square are identified. In the cases where the attractor is a torus knot, the knot type of the attractor is obvious in our projection.     

Structural aspects of deformation of amorphous polymers

Experimental and theoretical data on the inelastic deformation of amorphous glassy polymers were analyzed. The decisive role of direct structural methods in determination of the deformation mechanism of glassy polymers was established. A new mechanism of deformation and thermally stimulated recovery of strained glassy polymers was considered on the basis of structural data analysis.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 1–6, January, 2005.     

A comparison of visualization of Stokes flow in a V-shaped and rectangular channel

A comparative study of visualization of Stokes flow induced by rotation of a circular cylinder in a V-shaped and rectangular channel was performed. The visualization was carried out using solid tracers of magnesium. Some quantitative data were deduced from visualization photographs and a comparison was made.     

Flow fields in a simulated axisymmetric terminal aneurysm with symmetric and asymmetric outflows

Laser-Doppler velocimetric measurements and flow visualization were performed in a glass axisymmetric aneurysm model with symmetric and asymmetric outflows through the branches. The bifurcation angle was fixed at 140°, and the Reynolds number based on the steady bulk average velocity and diameter of the affarent conduit was 500. The flow characteristics such as flow separation in the afferent conduit and flow activity inside the aneurysm for the symmetric and asymmetric outflow cases were compared in detail, and the case that is susceptible to thrombosis was identified. In addition, the onset of transition from laminar to turbulent flow inside the aneurysm was evidenced by the presence of vortex breakdown and the steep increase in the fluctuation level. Finally, the effect of pulsation on the flow pattern in the aneurysm was examined.     

微通道内红细胞流动与变形的可视化研究

微循环条件下,红细胞的尺寸与血管相近,血液不能视为均质流体,其流动表现出较强的颗粒性,红细胞流变特性对血液流动有较大影响。本文使用高倍显微镜对微流控芯片矩形截面微通道内红细胞的流动和变形特性进行可视化观察研究,并使用高速CCD相机拍摄和捕捉了红细胞在微通道内的流动和变形过程。通过观察不同浓度、粘度和速度下红细胞的聚集性、变形性以及常见的运动形态,发现红细胞在低粘度、低速流动条件下表现为两面凹圆盘形,沿流动方向运动过程总是伴随着翻转与旋转;在高粘度、高速运动条件下,红细胞表现为扁平椭圆形、呈坦克履带式(TTM)前进。     

Fast free-surface detection and level-set function definition in SPH solvers

The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.     

Optical design for enhanced prism type fingerprint scanner image contrast with asymmetrical aspheric lens

The design of optical prism fingerprint scanner with aspheric lens is researched. We propose a modified structure for optical prism fingerprint scanner, which has an asymmetrical aspheric lens on the output plane. It is numerically shown under elliptic valley similar fingerprint model that the optical image qualities of such a scanner are better than the scanner with symmetrical aspheric lens. When the fingerprint range is 15 mm, the results show that the minimum image contrast is 0.49 for an optical prism with asymmetrical aspheric lens, much better than a symmetrical aspheric lens with 0.20. The relative illumination variation is from 0.62 to 1.00 for optical prism with asymmetrical aspheric lens, and for the symmetrical aspheric lens it is 0.35 to 1.00. We conclude that an optical prism with asymmetrical aspheric lens is better than an optical prism with symmetrical aspheric lens.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers’ conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets – designed and used in an exploratory manner – promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.     

Measuring Lineup Difficulty By Matching Distance Metrics With Subject Choices in Crowd-Sourced Data

Graphics play a crucial role in statistical analysis and data mining. Being able to quantify structure in data that is visible in plots, and how people read the structure from plots is an ongoing challenge. The lineup protocol provides a formal framework for data plots, making inference possible. The data plot is treated like a test statistic, and lineup protocol acts like a comparison with the sampling distribution of the nulls. This article describes metrics for describing structure in data plots and evaluates them in relation to the choices that human readers made during several large Amazon Turk studies using lineups. The metrics that were more specific to the plot types tended to better match subject choices, than generic metrics. The process that we followed to evaluate metrics will be useful for general development of numerically measuring structure in plots, and also in future experiments on lineups for choosing blocks of pictures. Supplementary materials for this article are available online.