Slipping friction of an optically and magnetically manipulated microsphere rolling at a glass-water interface

The motion of submerged magnetic microspheres rolling at a glass-water interface has been studied using magnetic rotation and optical tweezers combined with bright-field microscopy particle tracking techniques. Individual microspheres of varying surface roughness were magnetically rotated both in and out of an optical trap to induce rolling, along either plain glass cover slides or glass cover slides functionalized with polyethylene glycol. It has been observed that the manipulated microspheres exhibited nonlinear dynamic rolling-while-slipping motion characterized by two motional regimes: At low rotational frequencies, the speed of microspheres free-rolling along the surface increased proportionately with magnetic rotation rate; however, a further increase in the rotation frequency beyond a certain threshold revealed a sharp transition to a motion in which the microspheres slipped with respect to the external magnetic field resulting in decreased rolling speeds. The effects of surface-microsphere interactions on the position of this threshold frequency are posed and investigated. Similar experiments with microspheres rolling while slipping in an optical trap showed congruent results.Comment: submitted to Journal of Applied Physics, 11 figure

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Виділення щільних областей у метричних просторах на основі кристалізації

Application of artificial intelligence methods and fuzzy sets theory to the clusterization problem is considered. Data on dense accumulations in finite metric spaces is an object of the research. Calculations based on the fuzzy sets theory and “optical” approach to the metric space analysis are used. The result of the research is realization of “Crystal” algorithms in searching for dense areas in multidimensional data arrays.Рассмотрено применение методов искусственного интеллекта и теории нечетких множеств к задаче кластеризации. Объект исследования — данные о плотных скоплениях в конечных метрических пространствах. В работе использован математический аппарат на базе теории нечетких множеств и “оптический” подход к анализу метрических пространств. Результат исследования — реализация серии алгоритмов “Кристалл” поиска плотных скоплений в многомерных массивах данных.Розглянуто застосування методів штучного інтелекту і теорії нечітких множин до задачі кластеризації. Об’єкт дослідження — дані про щільні скупчення у кінцевих метричних просторах. У роботі використано математичний апарат на базі теорії нечітких множин та “оптичний” підхід до аналізу метричних просторів. Результат дослідження — реалізація серії алгоритмів “Кристал” пошуку щільних скупчень у багатовимірних масивах даних