Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Determination of solid fraction evolution during solidification of aluminum alloy in presence of linear electromagnetic stirring

In many industrial casting processes, knowledge of the solid fraction evolution during the solidification process is a key factor in determining the process parameters such as cooling rate, stirring intensity and in estimating the total solidification time. In the present work, a new method of estimating solid fraction is presented, which is based on calorimetric principles. In this method, the cooling curve data at each point in the melt, along with the thermal boundary conditions, are used to perform energy balance in the mould, from which solid fraction generation during any time interval can be estimated. This method is applied to the case of a rheocasting process, in which Al-Si alloy (A356 alloy) is solidified by stirring in a cylindrical mould placed in the annulus of a linear electromagnetic stirrer. The metal in the mould is simultaneously cooled and stirred to produce a cylindrical billet with non-dendritic globular microstructure. Temperature is measured at key locations in the mould to assess the various heat exchange processes prevalent in the mould and to monitor the solidification rate. The results obtained by energy balance method are compared with those by the conventional procedure of calculating solid fraction using the Schiel equation.

Performance Evaluation of Distance-Hop Proportionality on Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approach- ing unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c q ln n n . We show that, for a given hop distance h of a node from a fixed anchor on the unit square,the Euclidean distance lies within [(1−ǫ)(h−1)r(n), hr(n)],for ǫ > 0, with probability approaching unity as n → ∞.This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this an- nulus centred at the anchor location, and of width roughly r(n), rather than close to a circle whose radius is exactly proportional to h. We show that if the radius r of the ge- ometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that il- lustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.

EXPERIMENTAL INVESTIGATION OF UNSTEADY FLOW IN A TRANSONIC UNI-STAGE AXIAL COMPRESSOR

Detailed steady and unsteady experimental measurements and analysis were performed on a Single stage Transonic Axial Compressor with asymmetric rotor tip clearance for studying the compressor stall phenomena. The installed compressor had asymmetric tip clearance around the rotor casing varying from about 0.65mm to 1.25mm. A calibrated 5-hole aerodynamic probe was traversed radially at exit of rotor and showed the characteristics of increased flow angle at lower mass flow rates for all the speeds. Mach number distribution and boundary layer effects were also clearly captured. Unsteady measurements for velocity were carried out to study the stall cell behavior using a single component calibrated hotwire probe oriented in axial and tangential directions for choke/free flow and near stall conditions. The hotwire probe was traversed radially across the annulus at inlet to the compressor and showed that the velocity fluctuations were dissimilar when probe was aligned axial and tangential to the flow. Averaged velocities across the annulus showed the reduction in velocity as stall was approached. Axial mean flow velocity decreased across the annulus for all the speeds investigated. Tangential velocity at free flow condition was higher at the tip region due to larger radius. At stall condition, the tangential velocity showed decreased velocities at the tip and slightly increased velocities at the hub section indicating that the flow has breakdown at the tip region of the blade and fluid is accelerated below the blockage zone. The averaged turbulent intensity in axial and tangential flow directions increased from free flow to stall condition for all compressor rated speeds. Fast Fourier Transform (FFT) of the raw signals at stall flow condition showed stall cell and its corresponding frequency of occurrence. The stalling frequency of about half of rotational speed of the rotor along with large tip clearance suggests that modal type stall inception was occurring.

Novel Investigation on Principle of Similarity for Microgravity Two-Phase Flow

根据两流体同心环状流线性稳定性分析的结果 ,对微重力气 /液两相流地面模拟实验所应遵循的相似准则进行了探讨 ,得到了一个新的重力无关性准则 ,即Bond数和环形区流体相的毛细数之比的绝对值不大于 1 .此外 ,微重力气 /液两相流模拟实验还必须满足两个条件 ,即流量比和气相表观Weber数应与所模拟的流动中对应数值相等 . In the present paper, the principle of similarity for two phase flows at microgravity is studied based on the results of the linear stability analysis of the two fluid concentric annular flow configuration. A new criterion of gravity independence, namely the absolute value of the ratio between the Bond number and the capillary number of the phase flowing in the annulus is no more than one, is achieved. It is also pointed out that the flowrate ratio and the gas superficial Weber number must have the same ...

固井工程中的流动问题

同井是油气在建过程中的重要工程，一般分下套管和注水泥两个过程．本文结合作者近年来的研究，着重阐述了钻井液、前置液、水泥浆在环形空间中流动的流体力学问题，包括：高温高压下的水泥浆流变性、偏心环形空间中浆液的流动特性、钻井液-前置液和前置液-水泥浆界面的稳定性等，介绍了国内外学者对这些问题的研究进展，提出了今后应深入研究的问题.

Generation and scattering of sound in vortical flow

We present solutions to scattering problems for unsteady disturbances to a mean swirling flow in an annular duct with a rigid 'splitter'. This situation has application to rotor-stator interaction noise in aeroengines, where the flow downstream of the fan is swirling and bifurcates into the by-pass duct and the engine core. We also consider the trailing edge extension of this problem. Inviscid mean flow in a cylindrical annulus is considered, with both axial and swirling (azimuthal) velocity components. The presence of vorticity in the mean flow couples the acoustic and vorticity modes of irrotational flow. Instead we have one combined spectrum of acoustic-vorticity waves in which the 'sonic' and 'nearly-convected' modes are fully coupled. In addition to the aeroacoustics application the results offer insight into the behaviour of these acoustic-vorticity waves, and the precise nature of the coupling between the two types of mode. Two regimes are discussed in which progress has been made, one for a specialised mean flow, uniform axial flow and rigid body swirl, and a second regime in which the frequency is assumed large, valid for any axisymmetric mean flow. The Wiener-Hopf technique is used to solve the scattering problems mathematically, and we present numerical evaluations of these solutions. Several new effects are seen to arise due to the mean vorticity, in particular the generation of sound at a trailing edge due to the scattering of a nearly convected disturbance, in contrast to the way a convected gust silently passes a trailing edge in uniform mean flow.

Topological strings, double affine Hecke algebras, and exceptional knot homology

In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.

Análise da função diastólica em mulheres medicadas com antraciclínicos no tratamento do câncer de mama

O Câncer de mama é um dos problemas de saúde pública mais importantes em nosso país. São estimados, para 2010, 49.400 novos casos de câncer de mama no Brasil, com um risco estimado de 51 casos a cada 100 mil mulheres. A estratégia de tratamento das pacientes com tumores de mama pode passar pelo uso de quimioterapia. A doxorrubicina é uma das drogas mais ativas para o câncer de mama, pertencendo ao grupo das antraciclinas. A família das antraciclinas apresenta como efeito colateral dano ao miocárdio que pode chegar a 36% dependendo da dose utilizada. O efeito sobre o miocárdio costuma ocorrer mais comumente durante ou logo após o último ciclo de quimioterapia podendo, entretanto ocorrer após vários anos do último ciclo de quimioterapia. O objetivo deste estudo foi analisar as alterações da função diastólica ventricular esquerda em mulheres usuárias de antraciclínicos no tratamento do câncer de mama. Realizamos um estudo prospectivo, em uma coorte de mulheres entre 18 e 69 anos, com câncer de mama e indicação de quimioterapia com doxorrubicina. Acompanhamos por período não inferior a 18 meses um grupo de 38 pacientes que cumpriram os critérios de elegibilidade. A dose de doxorrubicina utilizada variou de 50 a 60 mg/m/SC. Todos os pacientes são do sexo feminino, e portadores do tipo histológico carcinoma ductal infiltrante. Duas pacientes faleceram durante o estudo, de causa não cardíaca. Em nossa avaliação, ao final do estudo observamos que os parâmetros: dimensões do átrio esquerdo, dimensões do ventrículo esquerdo na diástole, dimensões do ventrículo esquerdo na sístole, velocidade da onda E, relação da fase de enchimento rápido pela sístole atrial, velocidade diastólica tardia do anel mitral, velocidade diastólica precoce do anel mitral, tempo de desaceleração e a relação da velocidade de enchimento rápido precoce de VE pela velocidade diastólica precoce do anel mitral demonstraram serem parâmetros de grande utilidade para seguimento da lesão cardíaca por antraciclínicos. Já o que não ocorreu com: a fração de encurtamento, fração de ejeção, volume do AE, volume do AE corrigido pela superfície corporal, velocidade diastólica tardia, tempo de relaxamento isovolumétrico, velocidade sistólica do anel mitral, que não apresentaram alterações significativas neste estudo. A análise da função diastólica utilizando o ecocardiograma mostrou ser um método eficaz, que em conjunto com a da função sistólica possibilita detectar precocemente o possível dano miocárdico, oriundo ao uso da quimioterapia com antraciclínicos, favorecendo uma intervenção terapêutica precoce e adequada.

Integrating methods for determining length-at-age to improve growth estimates for two large scombrids

Fish growth is commonly estimated from length-at-age data obtained from otoliths. There are several techniques for estimating length-at-age from otoliths including 1) direct observed counts of annual increments; 2) age adjustment based on a categorization of otolith margins; 3) age adjustment based on known periods of spawning and annuli formation; 4) back-calculation to all annuli, and 5) back-calculation to the last annulus only. In this study we compared growth estimates (von Bertalanffy growth functions) obtained from the above five methods for estimating length-at-age from otoliths for two large scombrids: narrow-barred Spanish mackerel (Scomberomorus commerson) and broad-barred king mackerel (Scomberomorus semifasciatus). Likelihood ratio tests revealed that the largest differences in growth occurred between the back-calculation methods and the observed and adjusted methods for both species of mackerel. The pattern, however, was more pronounced for S. commerson than for S. semifasciatus, because of the pronounced effect of gear selectivity demonstrated for S. commerson. We propose a method of substituting length-at-age data from observed or adjusted methods with back-calculated length-at-age data to provide more appropriate estimates of population growth than those obtained with the individual methods alone, particularly when faster growing young fish are disproportionately selected for. Substitution of observed or adjusted length-at-age data with back-calculated length-at-age data provided more realistic estimates of length for younger ages than observed or adjusted methods as well as more realistic estimates of mean maximum length than those derived from backcalculation methods alone.

Age and growth of swordfish (Xiphias gladius) caught by the Hawaii-based pelagic longline fishery

We verified the age and growth of swordfish (Xiphias gla-dius) by comparing ages determined from annuli in fin ray sections with daily growth increments in otoliths. Growth of swordfish of exploitable sizes is described on the basis of annuli present in cross sections of the second ray of the first anal fins of 1292 specimens (60−260 cm eye-to-fork length, EFL) caught in the region of the Hawaii-based pelagic longline fishery. The position of the initial fin ray annulus of swordfish was verified for the first time with the use of scanning electron micrographs of presumed daily growth increments present in the otoliths of juveniles. Fish growth through age 7 was validated by marginal increment analysis. Faster growth of females was confirmed, and the standard von Bertalanffy growth model was identified as the most parsimonious for describing growth in length for fish greater than 60 cm EFL. The observed growth of three fish, a year-old in size when first caught and then recaptured from 364 to1490 days later, is consistent with modeled growth for fish of this size range. Our novel approach to verifying age and growth should increase confidence in conducting an age-structured stock assessment for swordfish in the North Pacific Ocean.

Revisão taxonômica das espécies brasileiras de Funariaceae Schwagr. (Bryophyta)

Funariaceae Schwägrichen é uma família de musgos cosmopolita que crescem em diversos habitats, por um ou raramente dois anos, mas algumas espécies podem ser perenes. Possuem como característica marcante o gametófito uniforme e uma ampla diversidade na arquitetura do esporófito. Este estudo realizou a revisão taxonômica da família Funariaceae no Brasil através da análise dos espécimes-tipos de coleções de herbários, nacionais e internacionais, e consulta a literatura específica sobre os táxons. É apresentada uma listagem revista e atualizada da família Funariaceae que ocorrem no Brasil, chaves de identificação para gêneros e espécies, descrições morfológicas, distribuição geográfica, status de conservação, ecologia, comentários, relação do material examinado e ilustrações. Para o Brasil eram citados 51 binômios agrupados em três gêneros: Entosthodon Schwagr. (11 binômios), Funaria Hedw. (20 binômios) e Physcomitrium (Brid.) Brid. (20 binômios). Os gêneros são taxonomicamente distintos pelo tipo de ornamentação dos esporos, forma da cápsula, forma das células do exotécio, presença ou ausência de peristômio, comprimento da seta, forma do ânulo e forma da caliptra. Após a revisão dos nomes foi estabelecida uma combinação nova a partir de Funaria ramulosa (Hampe) Paris: Entosthodon ramulosus (Hampe) M. S. Dias & D. F. Peralta. Foram estabelecidos 10 novos sinônimos: Funaria luteolimbata Broth. F. obtusa-apiculata Müll. Hal. e F. ramulosa (Hampe) Paris como sinônimos de Entosthodon ramulosus (Hampe) M. S. Dias & D. F. Peralta; Physcomitrium flavum (Müll. Hal.) Broth. como sinônimo de E. bonplandii (Hook.) Mitt.; Physcomitrium badium Broth. como sinônimo de P. umbonatum Mitt.; P. lindmanii Broth., P. sylvestre Müll. Hal. e P. convolutaceum Müll. Hal. como sinônimos de P. thieleanum Hampe. P. serrulatum Mitt., P. cupulare Müll Hal. e P. platyphylloides Paris como sinônimos de P. subsphaericum Schimp. Entosthodon puiggarii Geh. & Hampe é o nome legítimo do táxon Physcomitrium puiggarii Geh & Hampe e foi constatado que Funaria capillipes (Müll. Hal. ex Broth.) Broth., é uma combinação inválida. Seis táxons foram excluídos de Funariaceae por não possuírem os caracteres morfológicos diagnósticos da família e seis espécies não foram incluídas no tratamento taxonômico por falta de informação sobre as mesmas e foram consideradas como espécies duvidosas. Portanto, são reconhecidos para o Brasil 11 táxons em Funariaceae: quatro de Entosthodon (E. bonplandii (Hook.) Mitt., E. obtusifolius Hook. f. in Hooker, E. puiggarii Geh. & Hampe in Hampe & Geheeb. e E. ramulosus (Hampe) M. S. Dias & D. F. Peralta); dois de Funaria (F. calvescens Schwagr. e F. hygrometrica Hedw.) e cinco de Physcomitrium (P. capillipes Müll. Hal. ex Broth., P. falcifolium Müll. Hal. in Brotherus, P. umbonatum Mitt., P. subsphaericum Schimp. e P. thieleanum Hampe). Cinco táxons são endêmicos do Brasil: Entosthodon puiggarii, E. ramulosus, Physcomitrium capillipes, P. falcifolium, P. umbonatum e a espécie P. capillipes é conhecida apenas pelo tipo nomenclatural. A partir da análise de diversos materiais originais, é apresentada aqui uma nova reinterpretação da família Funariaceae do Brasil, com novas sinonimizações, reconhecimento de uma nova combinação, e lectótipos

Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field.

We investigate the evolution of localized blobs of swirling or buoyant fluid in an infinite, inviscid, electrically conducting fluid. We consider the three cases of a strong imposed magnetic field, a weak imposed magnetic field, and no magnetic field. For a swirling blob in the absence of a magnetic field, we find, in line with others, that the blob bursts radially outward under the action of the centrifugal force, forming a thin annular vortex sheet. A simple model of this process predicts that the vortex sheet thins exponentially fast and that it moves radially outward with constant velocity. These predictions are verified by high-resolution numerical simulations. When an intense magnetic field is applied, this phenomenon is suppressed, with the energy and angular momentum of the blob now diffusing axially along the magnetic field lines, converting the blob into a columnar structure. For modest or weak magnetic fields, there are elements of both types of behavior, with the radial bursting dominating over axial diffusion for weak fields. However, even when the magnetic field is very weak, the flow structure is quite distinct to that of the nonmagnetic case. In particular, a small but finite magnetic field places a lower bound on the thickness of the annular vortex sheet and produces an annulus of counter-rotating fluid that surrounds the vortex core. The behavior of the buoyant blob is similar. In the absence of a magnetic field, it rapidly develops the mushroomlike shape of a thermal, with a thin vortex sheet at the top and sides of the mushroom. Again, a simple model of this process predicts that the vortex sheet at the top of the thermal thins exponentially fast and rises with constant velocity. These predictions are consistent with earlier numerical simulations. Curiously, however, it is shown that the net vertical momentum associated with the blob increases linearly in time, despite the fact that the vertical velocity at the front of the thermal is constant. As with the swirling blob, an imposed magnetic field inhibits the formation of a vortex sheet. A strong magnetic field completely suppresses the phenomenon, replacing it with an axial diffusion of momentum, while a weak magnetic field allows the sheet to form, but places a lower bound on its thickness. The magnetic field does not, however, change the net vertical momentum of the blob, which always increases linearly with time.

Age and growth of the bastard grunt (Pomadasys incisus: Haemulidae) inhabiting the Canarian archipelago, Northwest Africa

The bastard grunt (Pomadasys incisus) is one of the most abundant coastal demersal fishes inhabiting the Canary Islands. Age and growth were studied from samples collected between October 2000 and September 2001. Growth analysis revealed that this species is a fast growing and moderately short-lived species (ages up to seven years recorded). Length-at-age was described by the von Bertalanffy growth model (L∞=309.58 mm; k=0.220/year; t0=–1.865 year), the Schnute growth model (y1=126.66 mm; y2=293.50 mm; a=–0.426; b= 5.963), and the seasonalized von Bertalanffy growth model (L∞=309.93 mm; k=0.218/ year; t0= –1.896 year; C=0.555; ts=0.652). Individuals grow quickly in their first year, attaining approximately 60% of their maximum length; after the first year, their growth rate drops rapidly as energy is probably diverted to reproduction. The parameters of the von Bertalanffy weight growth curve were W∞=788.22 mm; k=0.1567/year; t0= –1.984 year. Fish total length and otolith radius were closely correlated, r2=0.912. A power relationship was estimated between the total length and the otolith radius (a=49.93; ν=0.851). A year’s growth was represented by an opaque and hyaline (translucent) zone—an annulus. Backcalculated lengths were similar to those predicted by the growth models. Growth parameters estimated from the backcalculated sizes at age were L∞=315.23 mm; k=0.217/year; and t0= –1.73 year.