On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.

Decay of vibrations along deepwater mooring lines

Model tests for global design verification of deepwater floating structures cannot be made at reasonable scales. An overview of recent research efforts to tackle this challenge is given first, introducing the concept of line truncation techniques. In such a method the upper sections of each line are modelled in detail, capturing the wave action zone and all coupling effects with the vessel. These terminate to an approximate analytical model, that aims to simulate the remainder of the line. The rationale for this is that in deep water the transverse elastic waves of a line are likely to decay before they are reflected at the seabed. The focus of this paper is the verification of this rationale and the ongoing work, which is considering ways to produce a truncation model. Transverse dynamics of a mooring line are modelled using the equations of motion of an inextensible taut string, submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. Nonlinear hydrodynamic damping is included; bending and VIV effects are neglected. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a universal curve for the decay of transverse vibrations along the line, which is suitable for any kind of line with any top motion. This has a significant engineering benefit, allowing for a rapid assessment of line dynamics - it is very useful in deciding whether a truncated line model is appropriate, and if so, at which point truncation might be applied. Initial efforts in developing a truncated model show that a linearized numerical solution in the frequency domain matches very closely the exact benchmark. Copyright © 2011 by ASME.

Structural sensitivity of spiral vortex breakdown

Previous numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier-Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the m=-1 azimuthal mode is the most unstable and that the wavemaker regions of the m=-1 mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown. © 2013 Cambridge University Press.

Controlling the phase of an oscillator: A phase response curve approach

The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC) calculated from the linearized model. The performance is evaluated on a popular model of circadian oscillations. ©2009 IEEE.

Minimum maneuver time calculation using convex optimization

The problem of calculating the minimum lap or maneuver time of a nonlinear vehicle, which is linearized at each time step, is formulated as a convex optimization problem. The formulation provides an alternative to previously used quasi-steady-state analysis or nonlinear optimization. Key steps are: the use of model predictive control; expressing the minimum time problem as one of maximizing distance traveled along the track centerline; and linearizing the track and vehicle trajectories by expressing them as small displacements from a fixed reference. A consequence of linearizing the vehicle dynamics is that nonoptimal steering control action can be generated, but attention to the constraints and the cost function minimizes the effect. Optimal control actions and vehicle responses for a 90 deg bend are presented and compared to the nonconvex nonlinear programming solution. Copyright © 2013 by ASME.

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.

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg-Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor-Couette-Poiseuille flow. © 2014 Elsevier Masson SAS. All rights reserved.

Finding resonance: Adaptive frequency oscillators for dynamic legged locomotion

There is much to gain from providing walking machines with passive dynamics, e.g. by including compliant elements in the structure. These elements can offer interesting properties such as self-stabilization, energy efficiency and simplified control. However, there is still no general design strategy for such robots and their controllers. In particular, the calibration of control parameters is often complicated because of the highly nonlinear behavior of the interactions between passive components and the environment. In this article, we propose an approach in which the calibration of a key parameter of a walking controller, namely its intrinsic frequency, is done automatically. The approach uses adaptive frequency oscillators to automatically tune the intrinsic frequency of the oscillators to the resonant frequency of a compliant quadruped robot The tuning goes beyond simple synchronization and the learned frequency stays in the controller when the robot is put to halt. The controller is model free, robust and simple. Results are presented illustrating how the controller can robustly tune itself to the robot, as well as readapt when the mass of the robot is changed. We also provide an analysis of the convergence of the frequency adaptation for a linearized plant, and show how that analysis is useful for determining which type of sensory feedback must be used for stable convergence. This approach is expected to explain some aspects of developmental processes in biological and artificial adaptive systems that "develop" through the embodied system-environment interactions. © 2006 IEEE.

Cloning of rainbow trout (Oncorhynchus mykiss) histone H3 promoter and the activity analysis in rare minnow (Gobiocypris rarus)

Rainbow trout historic H3 (RH3) promoter was cloned via high fidelity PCR. The cloned RH3 promoter was inserted into a promoter-lacked vector pEGFP-1, resulting in an expression vector pRH3FGFP-1. The linearized pRH3EGFP-1 was microinjected into fertilized eggs of rare minnows and the sequential embryogenetic processes were monitored under a fluorescent microscope. Strong green fluorescence was ubiquitously observed at as early as the gastrula stage and then in various tissues at the fry stage. The results indicate that RH3 promoter, as a piscine promoter, could serve in producing transgenic Cyprinoid such as rare minnow. Promoter activity of RH3, CMV and common carp beta-actin (CA) were compared in rare minnow by the expression of respective recombinant EGFP vectors. The expression of pCMVEGFP occurred earlier than the following one, pRH3EGFP-1, and then pCAEGFP during the embryogenesis of the transgenics. Their expression activities demonstrated that the CMV promoter is the strongest one, followed by the CA and then the RH3.

Development of a positive-negative selection procedure for gene targeting in fish cells

The gene targeting technique is a powerful tool for analyzing functions of cloned genes and for generating transgenic animals with site-directed integration of foreign genes. In order to develop this technique in fish, positive-negative selection (PNS) and homologous recombination vectors were constructed, and their expression was examined in fish cells. A vector (pNK) for PNS consists of the neomycin resistance gene (neo) as a positive selectable marker gene and the herpes simplex virus (HSV) thymidine kinase (tk) gene as a negative selectable marker gene. Positive selection with geneticin (G418) of epithelioma papulosum of carp (EPC) cells transfected with linearized pNK vector yielded 350 colonies, while double selection of transfected EPC cells with G418 and gancyclovir (Gc) resulted in nearly complete cell death, demonstrating that the PNS procedure is effective in fish cells. Homologous recombination vectors consist of the Xiphophorus melanoma receptor kinase (X mrk(Y)) gene as homologous sequence in addition to the neo and tk genes. Conditions for homologous recombination vector transfection and drug selection were established. After verification of the feasibility of expression of homologous recombination vectors in EPC cells, the first gene targeting experiments were attempted in the Xiphophorus melanoma cell line, PSM. Positive-negative selection of the targeting vector-transfectants led to a low enrichment in this particular cell line. The reasons for the low enrichment in PSM cells were discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Introduction of the human lactoferrin gene into grass carp (Ctenopharyngodon idellus) to increase resistance against GCH virus

Haemorrhage can be an epidemic and fatal condition in grass carp. It is known now that the Grass Carp Haemorrhage Virus (GCHV) triggers haemorrhage. Human lactoferrin (hLF) plays an important role in the non-specific immune system, making some organisms more resistant to some viruses. Sperm of grass carp was mixed with linearized pCAhLFc, which is a DNA construct containing an hLF cDNA and the promoter of common carp beta-actin gene, and then electroporated. Then, mature eggs were fertilized in vitro with the treated sperm cells. The fry were sampled and analyzed by polymerase chain reaction (PCR). Results indicated that the foreign gene had been transferred successfully into the cells of some fry. Under optimal electroporation conditions, the efficiency of gene transfer was as high as 46.8%. About 35.7% of treated 5-month-old grass carp contained foreign genes. Most transgenic fry demonstrated significant delays in onset of symptoms of haemerrhage after injection of GCHV, suggesting a significant positive relationship between hLF cDNA and levels of disease resistance (P < 0.01). Results suggest that transgenic grass carp could be bred for increased resistance to haemorrhage. (C) 2002 Elsevier Science B.V. All rights reserved.

HORMONAL REPLACEMENT THERAPY IN FISH - HUMAN GROWTH-HORMONE GENE-FUNCTION IN HYPOPHYSECTOMIZED CARP

Transgenic common carp, Cyprinus carpio, produced by the microinjection of fertilized eggs with a linearized chimeric plasmid pMThGH, a human growth hormone (hGH) gene with a mouse metallothionein-I (MT) gene promoter in pBR322, were used to produce F1 and F2 transgenics. Following hypophysectomy of the transgenic F2 common carp, non-transgenic common carp and non-transgenic crucian carp, growth was monitored for up to 110 days. In addition, recombinant hGH was injected subcutaenously into a group of the non-transgenic crucian carp. Growth rate analyses indicated that (1) hypophysectomy of non-transgenic common carp and crucian carp results in the cessation of growth, (2) hGH administration can stimulate the growth of hypophysectomized crucian carp and (3) hypophysectomized hGH-transgenic common carp continue to grow in the absence of their own growth hormone, suggesting that the hGH-transgene is being expressed in tissues other than the pituitary.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

无指盘臭蛙皮肤抗菌肽Odorgrin A和Odorgrin C基因表达载体的构建及其在毕赤酵母中的表达

研究背景与目的：近二十年来，抗生素的广泛使用以及一些不当应用导致临床上出现大量的耐药性病原菌，所以不易产生耐药性的抗菌肽就成为目前研究的热点。本课题组此前的研究表明无指盘臭蛙（Odorrana grahami）皮肤抗菌肽具有广谱抗菌活性，但对真核细胞没有毒性，因此有成为新型药物的潜力。本研究采用毕赤酵母真核表达系统来生物合成抗菌肽Odorgrin A和Odorgrin C，为大量获取抗菌肽资源提供技术支撑。 方法：依照Odorgrin A和C的氨基酸序列、采用酵母偏爱密码子分别设计并化学合成了相应的目的基因序列。目的片段从合成质粒上用Xho Ι和EcoR Ι双酶切下后，与经同样限制酶完全酶切pPIC9K载体所获得的两个大片段直接连接，并转化至大肠杆菌DH5α。用PCR扩增、酶切及测序检测，鉴定正确的重组质粒。提取大量表达载体pPIC9K - Odo A和C并使之线性化后经电击法分别转化毕赤酵母（Pichia pastoris）GS115宿主菌，用营养缺陷型筛选、遗传霉素抗性筛选、PCR扩增和测序检测，鉴定并筛选出对G418具高抗性的Odorgrin A和C重组酵母菌。用甲醇对之进行诱导表达，SDS - PAGE电泳及反相层析检测表达产物，并做抑菌活性检测。 成果：PCR扩增、酶切及测序等结果表明表达载体pPIC9K - Odo A和C构建成功。营养缺陷型筛选、遗传霉素抗性筛选、PCR扩增和测序等证实pPIC9K - Odo A和C已整合入酵母基因组中。SDS - PAGE电泳及反相层析结果表明抗菌肽Odorgrin A和C成功地获得了分泌表达。而抑菌活性实验则检测到部分阳性克隆菌诱导分泌表达的抗菌肽Odorgrin A和C都对测试菌的生长具有较高（>94%）的抑制率。 结论：无指盘臭蛙皮肤抗菌肽Odorgrin A和Odorgrin C基因的表达载体都构建成功，并且都在毕赤酵母系统中获得了成功表达。 Background ＆ Objective: In the recent twenty years, a lot of pathogenic bacteria have come forth in clinic with durable trait derived from making use of and abusing the traditional antibiotics. Therefore, studying antimicrobial peptides, not be easy to be invalidated by durable bacteria, are becomimg popular and important. The skin antimicrobial peptides of Odorrana grahami with broad spectrum antibacterial activity and no toxicity to eukaryotic cell, discovered by previous research work of our workgroup, are looked forward to being potential medication. Pichia pastoris expressional system was used for biosynthesis antimicrobial peptides Odorgrin A and Odorgrin C in this study, for producing abundant antimicrobial peptides. Methods: The foreign fragments which included Odorgrin A or Odorgrin C gene according to their amino acid sequence respectively were synthesized based on the biased codon usage of yeast. The DNA fragments, obtained from the plasmids containing them by digested with Xho Ι and EcoR Ι, were directly ligated with the two bigger fragments obtained from the vector pPIC9K by digested with the same restriction enzymes. And then they were transformed into Escherichia coli DH5α to be selected and amplified positive colonies. The recombinants were testified by using PCR amplification, enzymes digestion and sequencing of the foreign fragment. After the expressional vector pPIC9K - Odo A and pPIC9K - Odo C were linearized, they were transformed into Pichia pastoris GS115 strain by the electroporation. Then the positive colonies which were of the highest geneticin resistant were selected through auxotrophic screening, genetic resistant screening, PCR amplification and sequencing of the inserted fragment. Methanol was used to induce the recombinant yeasts to express the foreign gene. SDS-PAGE electrophoresis, reversed phase chromatography and antibacterial activity experiment were used to testify the expressional products. Results: The evidences of PCR, enzymes digestion and sequence analysis confirmed that the expressional vector pPIC9K - Odo A and pPIC9K - Odo C have been constructed correctly. The results of auxotrophic screening, of genetic resistant screening, of PCR and sequencing of the foreign fragment showed that Odorgrin A and Odorgrin C gene have been homologous integrated with the Pichia pastoris genome. And it was also testified that antimicrobial peptides Odorgrin A and Odorgrin C have been expressed successfully by using SDS - PAGE electrophoresis, reversed phase chromatography and antibacterial activity experiment. Conclusion: The expressional vector of the skin antimicrobial peptides Odorgrin A and Odorgrin C gene of Odorrana grahami have been constructed correctly and both of the genes have been expressed successfully in Pichia pastoris system in this study.