Streamline topology and dilute particle dynamics in a Karman vortex street flow

Three types of streamline topology in a Karman vortex street flow are shown under the variation of spatial parameters. For the motion of dilute particles in the Karman vortex street flow, there exist a route of bifurcation to a chaotic orbit and more attractors in a bifurcation diagram for the proportion of particle density to fluid density. Along with the increase of spatial parameters in the flow field, the bifurcation process is suspended, as well as more and more attractors emerge. In the motion of dilute particles, a drag term and gravity term dominate and result in the bifurcation phenomenon.

Self-similarity limits of genomic signatures

It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display genomic signature in chaos game representation is obtained by eliminating effects of the finite sequence. The optimal string length is further shown as a self-similarity limit in computing information dimension. By using the method, self-similarity limits of bacteria complete genomic signatures are further determined.

Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude

Free surface waves in a cylinder of liquid under vertical excitation with slowly modulated amplitude are investigated in the current paper. It is shown by both theoretical analysis and numerical simulation that chaos may occur even for a single mode with modulation which can be used to explain Gollub and Meyer's experiment. The implied resonant mechanism accounting for this phenomenon is further elucidated.

Direct dynamical test for deterministic chaos

We present a direct and dynamical method to distinguish low-dimensional deterministic chaos from noise. We define a series of time-dependent curves which are closely related to the largest Lyapunov exponent. For a chaotic time series, there exists an envelope to the time-dependent curves, while for a white noise or a noise with the same power spectrum as that of a chaotic time series, the envelope cannot be defined. When a noise is added to a chaotic time series, the envelope is eventually destroyed with the increasing of the amplitude of the noise.

Molecular phylogenetics of the family Cyprinidae (Actinopterygii : Cypriniformes) as evidenced by sequence variation in the first intron of S7 ribosomal protein-coding gene: Further evidence from a nuclear gene of the systematic chaos in the family

The family Cyprinidae is the largest freshwater fish group in the world, including over 200 genera and 2100 species. The phylogenetic relationships of major clades within this family are simply poorly understood, largely because of the overwhelming diversity of the group; however, several investigators have advanced different hypotheses of relationships that pre- and post-date the use of shared-derived characters as advocated through phylogenetic systematics. As expected, most previous investigations used morphological characters. Recently, mitochondrial DNA (mtDNA) sequences and combined morphological and mtDNA investigations have been used to explore and advance our understanding of species relationships and test monophyletic groupings. Limitations of these studies include limited taxon sampling and a strict reliance upon maternally inherited mtDNA variation. The present study is the first endeavor to recover the phylogenetic relationships of the 12 previously recognized monophyletic subfamilies within the Cyprinidae using newly sequenced nuclear DNA (nDNA) for over 50 species representing members of the different previously hypothesized subfamily and family groupings within the Cyprinidae and from other cypriniform families as outgroup taxa. Hypothesized phylogenetic relationships are constructed using maximum parsimony and Basyesian analyses of 1042 sites, of which 971 sites were variable and 790 were phylogenetically informative. Using other appropriate cypriniform taxa of the families Catostomidae (Myxocyprinus asiaticus), Gyrinocheilidae (Gyrinocheilus aymonieri), and Balitoridae (Nemacheilus sp. and Beaufortia kweichotvensis) as outgroups, the Cyprinidae is resolved as a monophyletic group. Within the family the genera Raiamas, Barilius, Danio, and Rasbora, representing many of the tropical cyprinids, represent basal members of the family. All other species can be classified into variably supported and resolved monophyletic lineages, depending upon analysis, that are consistent with or correspond to Barbini and Leuciscini. The Barbini includes taxa traditionally aligned with the subfamily Cyprininae sensu previous morphological revisionary studies by Howes (Barbinae, Labeoninae, Cyprininae and Schizothoracinae). The Leuciscini includes six other subfamilies that are mainly divided into three separate lineages. The relationships among genera and subfamilies are discussed as well as the possible origins of major lineages. (c) 2008 Published by Elsevier Inc.

Fractals in fracture of bulk metallic glass

We investigate the nanoscale periodic corrugation (NPC) structures on the dynamic fracture surface of a typical tough bulk metallic glass, submitted to high-velocity plate impact and scanned by atomic force microscopy (AFM). The detrended fluctuation analysis (DFA) of the recorded AFM profiles reveals that the valley landscapes of the NPC are nearly memoryless, characterized by Hurst parameter of 0.52 and exhibiting a self-similar fractal character with the dimension of about 1.48. Our findings confirm the existence of the “quasi-cleavage” fracture underpinned by tension transformation zones (TTZs) in metallic glasses.

Evolution of spiral wave and pattern formation in a vortical polarized electric field

In this paper, the evolution of the pattern transition induced by the vortical electric field (VEF) is investigated. Firstly, a scheme is suggested to generate the VEF by changing the spatial magnetic field. Secondly, the VEF is imposed on the whole medium, and the evolutions of the spiral wave and the spatiotemporal chaos are investigated by using the numerical simulation. The result confirms that the drift and the breakup of the spiral wave and the new net-like pattern are observed when different polarized fields are imposed on the whole medium respectively. Finally, the pattern transition induced by the polarized field is discussed theoretically.

SAXS measurements of the interface in polyacrylate and epoxy interpenetrating networks with fractal geometry

The interface thickness in two-component interpenetrating polymer networks (IPN) system based on polyacrylate and epoxy were determined using small-angle X-ray scattering (SAXS) in terms of the theory proposed by Ruland. The thickness was found to be nonexistent for the samples at various compositions and synthesized at variable conditions-temperature and initiator concentration. By viewing the system as a two-phase system with a sharp boundary, the roughness of the interface was described by fractal dimension, D, which slightly varies with composition and synthesis condition. Length scales in which surface fractals are proved to be correct exist for each sample and range from 0.02 to 0.4 Angstrom(-1). The interface in the present IPN system was treated as fractal, which reasonably explained the differences between Pored's law and experimental data, and gained an insight into the interaction between different segments on the interface. (C) 1997 Elsevier Science Ltd.

SURFACE FRACTALS IN BLOCK-COPOLYMERS

A surface fractal model was presented to describe the interface in block copolymers. It gives a simple power-law relationship between the scattering intensity I(q) and the wave vector q in a relatively wide range as qxi >> 1, I(q) is-proportional-to q(D-6