A differential lyapunov framework for contraction analysis

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. © 2013 IEEE.

Control of material transport through pulse shape manipulation-a development toward designer pulses

The variety of laser systems available to industrial laser users is growing and the choice of the correct laser for a material target application is often based on an empirical assessment. Industrial master oscillator power amplifier systems with tuneable temporal pulse shapes have now entered the market, providing enormous pulse parameter flexibility in an already crowded parameter space. In this paper, an approach is developed to design interaction parameters based on observations of material responses. Energy and material transport mechanisms are studied using pulsed digital holography, post process analysis techniques and finite-difference modelling to understand the key response mechanisms for a variety of temporal pulse envelopes incident on a silicon (1/1/1) substrate. The temporal envelope is shown to be the primary control parameter of the source term that determines the subsequent material response and the resulting surface morphology. A double peak energy-bridged temporal pulse shape designed through direct application of holographic imaging data is shown to substantially improve surface quality. © 2014 IEEE.

Generation of 140 fs pulse train with widely tunable repetition rate through cascaded fibre compression techniques

The authors present numerical simulations of ultrashort pulse generation by a technique of linear spectral broadening in phase modulators and compression in dispersion compensating fibre, followed by a further stage of soliton compression in dispersion shifted fibre. This laser system is predicted to generate pulses of 140 fs duration with a peak power of 1.5 kW over a wide, user selectable repetition rate range while maintaining consistent characteristics of stability and pulse quality. The use of fibre compressors and commercially available modulators is expected to make the system setup compact and cost-effective. © The Institution of Engineering and Technology 2014.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Differential expression and dynamic changes of SOX3 during gametogenesis and sex reversal in protogynous hermaphroditic fish

SOX3 has been suggested to play significant roles in gametogenesis and gonad differentiation of vertebrates, but the exact cellular localization evidence is insufficient and controversial. In this study, a protogynous hermaphrodite fish Epinephelus coioides is selected to analyze EcSox3 differential expression and the expression pattern in both processes of oogenesis and spermatogenesis by utilizing the advantages that gonad development undergoes transition from ovary to intersexual gonad and then to testis, and primordial germ cells and different stage cells during oogenesis and spermatogenesis are synchronously observed in the transitional gonads. The detailed and clear immunofluoresence localization indicates that significantly differential expression and dynamic changes of Sox3 occur in the progresses of gametogenesis and sex reversal, and EcSOX3 protein exists in the differentiating primordial germ cells, oogonia, and different stage oocytes of ovaries, and also in the differentiating primordial germ cells and the Sertoli cells of testis. One important finding is that the EcSox3 expression is a significant time point for enterable gametogenesis of primordial germ cells because EcSOX3 is obviously expressed and localized in primordial germ cells. As EcSox3 continues to express, the EcSOX3-positive primordial germ cells develop toward oogonia and then oocytes, whereas when EcSox3 expression is ceased, the EcSOX3-positive primordial germ cells develop toward spermatogonia. Therefore, the current finding of EcSOX3 in the differentiating primordial germ cells again confirms the potential regulatory role in oogenesis and germ cell differentiation. The data further suggest that SOX3, as a transcription factor, might have more important roles in oogenesis than in spermatogenesis.

Differential and spermatogenic cell-specific expression of DMRT1 during sex reversal in protogynous hermaphroditic groupers

DMRT1 has been suggested to play different roles in sex determination and gonad differentiation, because different expression patterns have been reported among different vertebrates. The groupers, since their gonads first develop as ovary and then reverse into testis, have been thought as good models to study sex differentiation and determination. In this study, we cloned the full-length cDNAs of DMRT] gene from orange-spotted grouper (Epinephelus coioides), and prepared corresponding anti-EcDMRT1] antiserum to study the relationship of DMRT] to sex reversal. One important finding is that the grouper DMRT] is not only differentially expressed in different stage gonads, but also restricted to specific stages and specific cells of spermatogenesis. Grouper DMRT1 protein exists only in spermatogonia, primary spermatocytes and secondary spermatocytes, but not in the supporting Sertoli cells. Moreover, we confirmed that EcSox3 is expressed not only in oogonia and different stage oocytes, but also in Sertoli cells and spermatogonia, and EcSox9 is expressed only in Sertoli cells. The data suggested that grouper DMRT1 might be a more specific sex differentiation gene for spermatogenesis, and play its role at the specific stages from spermatogonia to spermatocytes. In addition, no introns were found in the grouper DMRT1, and no duplicated DMRT1, genes were detected. The finding implicates that the intronless DMRT1 that is able to undergo rapid transcriptional turnover might be a significant gene for stimulating spermatogenesis in the protogynous hermaphroditic gonad. (c) 2006 Published by Elsevier Ireland Ltd.

Double-wall carbon nanotubes for wide-band, ultrafast pulse generation.

We demonstrate wide-band ultrafast optical pulse generation at 1, 1.5, and 2 μm using a single-polymer composite saturable absorber based on double-wall carbon nanotubes (DWNTs). The freestanding optical quality polymer composite is prepared from nanotubes dispersed in water with poly(vinyl alcohol) as the host matrix. The composite is then integrated into ytterbium-, erbium-, and thulium-doped fiber laser cavities. Using this single DWNT-polymer composite, we achieve 4.85 ps, 532 fs, and 1.6 ps mode-locked pulses at 1066, 1559, and 1883 nm, respectively, highlighting the potential of DWNTs for wide-band ultrafast photonics.

270GHz, 580fs Optical Pulse Generation from a single-section quantum-dash fabry-pérot laser using frequency multiplication

Pulse generation from a mode-locked single-section 1.55μm quantum-dash FP laser is demonstrated under continuous-wave operation. A 270GHz, 580fs pulse train is achieved by applying frequency multiplication using fiber dispersion. ©2009 Optical Society of America.

Differential equation based length scales to improve DES and RANS simulations

Surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models. Potentially economical, accuracy improving differential equation based distance algorithms are considered. These involve elliptic Poisson and hyperbolic natured Eikonal equation approaches. Numerical issues relating to non-orthogonal curvilinear grid solution of the latter are addressed. Eikonal extension to a Hamilton-Jacobi (HJ) equation is discussed. Use of this extension to improve turbulence model accuracy and, along with the Eikonal, enhance Detached Eddy Simulation (DES) techniques is considered. Application of the distance approaches is studied for various geometries. These include a plane channel flow with a wire at the centre, a wing-flap system, a jet with co-flow and a supersonic double-delta configuration. Although less accurate than the Eikonal, Poisson method based flow solutions are extremely close to those using a search procedure. For a moving grid case the Poisson method is found especially efficient. Results show the Eikonal equation can be solved on highly stretched, non-orthogonal, curvilinear grids. A key accuracy aspect is that metrics must be upwinded in the propagating front direction. The HJ equation is found to have qualitative turbulence model improving properties. © 2003 by P. G. Tucker.

Differential expression of three Paralichthys olivaceus Hsp40 genes in responses to virus infection and heat shock

Heat shock proteins (Hsps) are a family of highly conserved cellular proteins present in all organisms, mediating a range of essential housekeeping and cytoprotective functions as well-known molecular chaperons and recently as regulators of the immune response. By subtractive suppression hybridization, three Hsp40 homologues have been identified in the flounder (Paralichthys olivaceus) embryonic cells (FEC) after treatment with UV-inactivated turbot (Scophthalmus maximus L.) rhabdovirus (SMRV), termed PoHsp40A4, PoHsp40B6 and PoHsp40B11, whose encoded proteins all possess the conserved DnaJ domain, a signature motif of the Hsp40 family. Based on different protein structure and phylogenetic analysis, they can be categorized into two subfamilies, PoHsp40A4 for Type I Hsp40, PoHsp40B6 and PoHsp40B11 for Type 11 Hsp40. Further expression analysis revealed two very different types of kinetics in response either to heat shock or to virus infection, with a marked induction for PoHsp4OA4 and a weak one for both PoHsp40B6 and PoHsp40B11. A very distinct tissue distribution of mRNA was also revealed among the three genes, even between PoHsp40B6 and PoHsp40B11. This is the first report on the transcriptional induction of Hsp40 in virally stimulated fish cells, and the differential expressions might reflect their different roles in unstressed and stressed cells. (c) 2005 Elsevier Ltd. All rights reserved.