Linear stability of miscible two-fluid flow down an incline

We show that miscible two-layer free-surface flows of varying viscosity down an inclined substrate are different in their stability characteristics from both immiscible two-layer flows, and flows with viscosity gradients spanning the entire flow. New instability modes arise when the critical layer of the viscosity transport equation overlaps the viscosity gradient. A lubricating configuration with a less viscous wall layer is identified to be the most stabilizing at moderate miscibility (moderate Peclet numbers). This also is in contrast with the immiscible case, where the lubrication configuration is always destabilizing. The co-existence that we find under certain circumstances, of several growing overlap modes, the usual surface mode, and a Tollmien-Schlichting mode, presents interesting new possibilities for nonlinear breakdown. © 2013 AIP Publishing LLC.

What is the weakest topology in which feedback stability is robust?

Mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations. The space of systems with transfer functions in ℋ∞, for example, has many advantages mathematically, but includes large classes of non-physical systems, and one must be careful in drawing inferences from results in that setting. Similarly, the graph topology has long been known to be the weakest, or coarsest, topology in which (1) feedback stability is a robust property (i.e. preserved in small neighbourhoods) and (2) the map from open-to-closed-loop transfer functions is continuous. However, it is not known whether continuity is a necessary part of this statement, or only required for the existing proofs. It is entirely possible that the answer depends on the underlying classes of systems used. The class of systems we concern ourselves with here is the set of systems that can be approximated, in the graph topology, by real rational transfer function matrices. That is, lumped parameter models, or those distributed systems for which it makes sense to use finite element methods. This is precisely the set of systems that have continuous frequency responses in the extended complex plane. For this class, we show that there is indeed a weaker topology; in which feedback stability is robust but for which the maps from open-to-closed-loop transfer functions are not necessarily continuous. © 2013 Copyright Taylor and Francis Group, LLC.

Otolith characteristics and age determination of an endemic Ptychobarbus dipogon (Regan, 1905) (Cyprinidae: Schizothoracinae) in the Yarlung Tsangpo River, Tibet

We describe the microincrements, checks and annuli in the lapilli of the schizothoracine Ptychobarbus dipogon, an endemic species of the Tibetan plateau. We collected samples in the Yarlung Tsangpo River and its tributaries on a monthly basis (from April 2004 to August 2006). We describe the shape features of the three pairs of otoliths and document the full trajectory of lapillus development. We found that five to seven checks were clearly visible in the opaque zone of the first annulus. The pattern of 21-23 daily growth increments within each check might be explained as a lunar-induced deposition. We counted between 137 and 154 increments within the first annulus. Annuli appeared as a sequence of gradually declining increment widths, whereas false rings were characterized by abrupt checks. Our oldest estimates were 23(+)years for males and 44(+) for females. The time of annulus completion was clearly between March and April each year using monthly marginal increments analysis. We consider the factors responsible for daily increment formation as an endogenous circadian rhythm. Environmental information, such as strong sunlight and cold water temperatures in the Tibetan Plateau, could reinforce the endogenous daily cycle. Our results provided important data addressing the ecology and population dynamics of P. dipogon.

Age structure, growth and mortality estimates of an endemic Ptychobarbus dipogon (Regan, 1905) (Cyprinidae: Schizothoracinae) in the Lhasa River, Tibet

Ptychobarbus dipogon is an endemic fish in the Yarlung Tsangpo River, but its biology is poorly known. We sampled 582 specimens (total length, TL, between 70.6 and 593.0 mm) from April 2004 to August 2006 in the Lhasa River, Tibet. We estimated ages based on the counts of alternating opaque and translucent zones (annuli) in thin transverse sections of lapilli otoliths. Ages ranged from 1(+) to 23(+) years for males and 1(+) to 44(+) for females. The observed 44(+) years was the oldest reported for schizothoracine fishes. Females attained a larger size than males. The TL weight relationship was W=7.12 x 10(-6)TL(3.006) for combined sexes. The growth parameters fitted von Bertalanffy growth functions were L-infinity = 598.66 mm, k=0.0898 year(-1), t(0)=-0.7261 year and W-infinity = 1585.38 g for females and L-infinity = 494.23mm, k=0.1197 year(-1), t(0)=-0.7296 year and W-infinity = 904.88g for males. The longevities of 32.7 year for females and 24.3 year for males were similar to the observed ages. Using an empirical model we estimated the instantaneous rate of total mortality (Z) at 0.28 per year in the lower reaches. Z in the upper and middle stocks was close to the M because of unexploited or lightly exploited stock. Protracted longevity, slow growth, low natural mortality and large body size were typical characteristics of P. dipogon. The current declining trend of P. dipogon could be prevented by altering fishing regulations.

Genetic Stability of Progeny from an Artificial Allotetraploid Carp Using Sperm from Five Fish Species

Microsatellite markers and D-loop sequences of mtDNA from a female allotetraploid parent carp and her progenies of generations 1 and 2 induced by sperm of five distant fish species were analyzed. Eleven microsatellite markers were used to identify 48 alleles from the allotetraploid female. The same number of alleles (48) appeared in the first and second generations of the gynogenetic offspring, regardless of the source of the sperm used as an activator. The mtDNA D-loop analysis was performed on the female tetraploid parent, 25 gynogenetic offspring, and 5 sperm-donor species. Fourteen variable sites from the 1,018 bp sequences were observed in the offspring as compared to the female tetraploid parent. Results from D-loop sequence and microsatellite marker analysis showed exclusive maternal transmission, and no genetic information was derived from the father. Our study suggests that progenies of artificial tetraploid carp are genetically stable, which is important for genetic breeding of this tetraploid fish.

Age and Growth of an Endemic Tibetan Fish, Schizothorax o'connori, in the Yarlung Tsangpo River

We investigated the age and growth of Schizothorax o'connori in the Yarlung Tsangpo River by examination of annuli from otoliths. The von Bertalanffy model was the most acceptable statistical growth model. Its parameters were as follows: SL infinity = 492.4 mm, K = 0.1133, t(0) = -0.5432 year and W-infinity = 1748.9 g for females; SL infinity = 449.0 mm, K = 0.1260, t(0) = -0.4746 year and W-infinity = 1287.0 g for males. Theoretical longevity was 25.9 years for the female and 23.3 years for the male. Moreover, females had larger asymptotic length and weight compared with males.

Relaxed purifying selection of rhodopsin gene within a Chinese endemic cavefish genus Sinocyclocheilus (Pisces: Cypriniformes)

The cyprinid fish genus Sinocyclocheilus, as the most cavefish rich genus, includes many species showing striking adaptation to caves and convergent reduction or even loss of eyes and pigmentation. RH1 is responsible for dim vision. In order to explore the evolution of RH1 gene in this genus, we sequenced the complete gene from 28 individuals of 16 representative species of Sinocyclocheilus, with cave and surface species included. Phylogenetic analyses supported the monophyly of Sinocyclocheilus and polyphyly of the cave species. Codon models implemented in PAML were used to infer the evolution of RH1. We found that Sinocyclocheilus had a significantly higher evolutionary rate for amino acids than other cyprinid fishes compared, which might be the result of relaxation of purifying selection and could be ascribed to cave habit of this genus. In contrast to previous hypotheses, both cave and surface lineages exhibited a similar rate of molecular evolution, so the RH1 of cave species may still be functional, although these species were highly adapted to cave environment. Two amino acid substitutions (D83G and E122V) that were not reported before were found, which may be useful for site-directed mutagenesis in the future.

Noise and stability in giant-chirp oscillators mode-locked with a nanotube-based saturable absorber

We compare experimental results showing stable dissipative-soliton solutions exist in mode-locked lasers with ultra-large normal dispersion (as large as 21.5 ps2), with both the analytic framework provided by Haus' master-equation and full numerical simulations. © 2010 Optical Society of America.

Global linear stability of the boundary-layer flow over a rotating sphere

We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°-65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk. © 2014 Elsevier Masson SAS. All rights reserved.

Diet overlap between the endemic fish Anablariflus grahami(Cyprinidae) and the exotic noodlefish Neosalanx taihuensis (Salangidae) in lake Fuxian, China

We studied diet composition and overlap of the exotic noodlefish (Neosalanx taihuensis) and the endemic fish Anaborilius grahami in a deep, oligotrophic lake in the Yunnan Plateau. A. grahami dominated the fish community in Lake Fuxian before the invasion of N. taihuensis in 1982, but it is now in the process of extinction, corresponding with an explosive increase in N. taihuensis population. Schoener's index (alpha=0.773) indicate that N. taihuensis and A. grahami have significant diet overlap, with both fish feeding mainly on zooplankton. An increased proportion of littoral prey, such as Procladius spp., Coleoptera, and epiphytes, in the diet of A. grahami indicated that this endemic fish shifted its main habitat from the off-shore zone in the late 1980s to the littoral zone at the present. A difference in reproduction between the two fishes, along with the overfishing, may have exacerbated the occupation of A. grahami's pelagic niche by N. taihuensis. The endemic species has shown large competitive disadvantage for food and space in the presence of N. taihuensis.

Modal stability theory

This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spatio-temporal stability, the linearized Navier-Stokes equations, the Orr-Sommerfeld equation, the Rayleigh equation, the Briggs-Bers criterion, Poiseuille flow, free shear flows, and secondary modal instability. It also covers the parabolized stability equation (PSE), temporal and spatial biglobal theory, 2D eigenvalue problems, 3D eigenvalue problems, spectral collocation methods, and other numerical solution methods. Computer codes are provided for tutorials described in the article. These tutorials cover the main topics of the article and can be adapted to form the basis of research codes. Copyright © 2014 by ASME.

Distribution and morphology of two endemic gomphonemoid species, Gohphonema kaznakowi Mereschkowsky and G-yangtzensis Li nov sp in China

The morphology of Gomphonema kaznakowi Mereschkowsky was investigated using light microscopy. This species has two morphologically distinct areas near the headpole; an unornamented and an ornamented area. The two areas are distinguished from each other by the combination of size and striae number. A new species, Gomphonema yangtzensis Li nov. sp. is identified based on an ornamented area near the headpole. G. kaznakowi is reported from the upper and middle part of the Yangtze River, and was also found in the upper section of the Yellow River. G. yangtzensis was found in the upper area of the Yellow River and the middle of the Yangtze River. Their limited distribution may be due to certain environmental conditions or a different dispersal rate. Both species are illustrated.

Age and growth of an endemic cyprinid fish, Spinibarbus yunnanensis, from Lake Fuxian, China

Age and growth of Spinibarbus yunnanensis Tsu in Lake Fuxian were investigated by examination of annuli from scales, dorsal fin spines, and otoliths. Sectioned otoliths exhibited the clearest and the most regular annuli. The formation of false annuli, which regularly arose on scales and dorsal fin spines during the juvenile stage, may be caused by a change in diet during development. The parameters for the von Bertalanffy growth curve were: K = 0.105, L-infinity = 950 mm, t(0) = -0.22 year for both sexes. W-infinity, calculated from the relationship W-infinity = aL(infinity)(b), was 10,352 g.