Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Stiffness of clays and silts: Normalizing shear modulus and shear strain

An analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p9 (i.e., G=p9 versus log g) or undrained shear strength cu (i.e., G=cu versus log g) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus,Gmax, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions forGmax is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is normalized with respect to its small-strain value Gmax, and shear strain g is normalized with respect to a reference strain gref at which this stiffness has halved. The data are corrected to two standard strain rates to reduce the discrepancy between data obtained from static and cyclic testing. The reference strain gref is approximated as a function of the plasticity index.Aunique normalized shear modulus reduction curve in the shape of a modified hyperbola is fitted to all the available data up to shear strains of the order of 1%. As a result, good estimates can be made of the modulus reduction G/Gmax ±30% across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves. © 2013 American Society of Civil Engineers.

Stack ventilation in multi-storey atrium buildings: A dimensionless design approach

Using a simplified mathematical model, a preliminary design strategy for steady stack ventilation in multi-storey atrium buildings is developed. By non-dimensionalising the governing equations of flow, two key dimensionless parameters are identified - a ventilation performance indicator, λ, and atrium enhancement parameter, E - which quantify the performance of the ventilation system and the effectiveness of the atrium in assisting flows. Analytical expressions are determined to inform the vent sizes needed to provide the desired balance between indoor air temperature, ventilation flow rate and heat inputs for any distribution of occupants within the building, and also to ensure unidirectional flow. Dimensionless charts for determining the required combination of design variables are presented with a view to informing first-order design guidance for naturally ventilated buildings. © 2013 Elsevier Ltd.

Shock amplification, curve veering and the role of damping

The circumstances are investigated under which high peak acceleration can occur in the internal parts of a system when subjected to impulsive driving on the outside. Previous work using a coupled beam model has highlighted the importance of veering pairs of modes. Such a veering pair can be approximated by a lumped system with two degrees of freedom. The worst case of acceleration amplification is shown to occur when the two oscillators are tuned to the same frequency, and for this case closed-form expressions are derived to show the parameter dependence of the acceleration ratio on the mass ratio and coupling strength. Sensitivity analysis of the eigenvalues and eigenvectors indicates that mass ratio is the most sensitive parameter for altering the veering behaviour in an undamped system. Non-proportional damping is also shown to have a strong influence on the veering behaviour. The study gives design guidelines to allow permissible acceleration levels to be achieved by the choice of the effective mass and damping of the indirectly driven subsystem relative to the directly driven subsystem. © 2013 Elsevier Ltd.

Symmetry-extended counting rules for periodic frameworks.

A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Fracture of brittle lattice materials: A review

The mechanics of failure for elastic-brittle lattice materials is reviewed. Closed-form expressions are summarized for fracture toughness as a function of relative density for a wide range of periodic lattices. A variety of theoretical and numerical approaches has been developed in the literature and in the main the predictions coincide for any given topology. However, there are discrepancies and the underlying reasons for these are highlighted. The role of imperfections at the cell wall level can be accounted for by Weibull analysis. Nevertheless, defects can also arise on the meso-scale in the form of misplaced joints, wavy cell walls and randomly distributed missing cell walls. These degrade the macroscopic fracture toughness of the lattice. © 2010 Springer Science+Business Media B.V.

Toll-like receptor 4 signaling pathway can be triggered by grass carp reovirus and Aeromonas hydrophila infection in rare minnow Gobiocypris rarus

Toll-like receptor 4 (TLR4) is critical for LPS recognition and cellular responses. It also recognizes some viral envelope proteins. Detection mostly results in the inflammation rather than specific antiviral responses. However, it's unclear in fish. In this report, a TLR4 gene (named as GrTLR4b) was cloned and characterized from rare minnow Gobiocypris rarus. The full length of GrTLR4b cDNA consists of 2766 nucleotides and encodes a polypeptide of 818 amino acids with an estimated molecular mass of 94,518 Da and a predicted isoelectric point of 8.41. The predicted amino acid sequence comprises a signal peptide, six leucine-rich repeat (LRR) motifs, one leucine-rich repeat C-terminal (LRRCT) motif, followed by a transmembrane segment of 23 amino acids, and a cytoplasmic region of 167 amino acids containing one Toll - interleukin 1 - receptor (TIR) motif. It's closely similar to the zebrafish (Danio rerio) TLR4b amino acid sequence with an identity of 77%. Quantitative RT-PCR analysis showed GrTLR4b mRNA was constitutive expression in gill, heart, intestine, kidney, liver, muscle and spleen tissues in healthy animals and up-regulated by viruses and bacteria. After being infected by grass carp reovirus or Aeromonas hydrophila, GrTLR4b expressions were up-regulated from 24 h post-injection and lasted until the fish became moribund (P < 0.05). These data implied that TLR4 signaling pathway could be activated by both viral and bacterial infection in rare minnow. (C) 2009 Elsevier Ltd. All rights reserved.

Allelopathic mechanism of pyrogallol to Microcystis aeruginosa PCC7806 (Cyanobacteria): From views of gene expression and antioxidant system

Pyrogallol is a potent allelochemical on Microcystis aeruginosa, but its allelopathic mechanism is not fully known. In order to explore this mechanism, gene expressions for prx, mcyB, psbA, recA, grpE, fabZ under pyrogallol stress were studied, and activities of the main antioxidant enzymes were also measured. The results showed that expression of grpE and recA showed no significant change under pyrogallol stress, while psbA and mcyB were up-regulated at 4 mg L-1. Both prx and fabZ were up-regulated even under exposure to 1 mg L-1 pyrogallol concentration. The activities of superoxide dismutase (SOD) and catalase (CAT) were enhanced under pyrogallol stress. Levels of malodialdehyde (MDA) at 2 and 4 mg L-1 pyrogallol were significantly higher than those of the controls. It was concluded that oxidant damage is an important mechanism for the allelopathic effect of pyrogallol on M. aeruginosa. (c) 2009 Elsevier Ltd. All rights reserved.

Reactive Many-Body Expansion for a Protonated Water Cluster.

We generalize the standard many-body expansion technique that is used to approximate the total energy of a molecular system to enable the treatment of chemical reactions by quantum chemical techniques. By considering all possible assignments of atoms to monomer units of the many-body expansion and associating suitable weights with each, we construct a potential energy surface that is a smooth function of the nuclear positions. We derive expressions for this reactive many-body expansion energy and describe an algorithm for its evaluation, which scales polynomially with system size, and therefore will make the method feasible for future condensed phase simulations. We demonstrate the accuracy and smoothness of the resulting potential energy surface on a molecular dynamics trajectory of the protonated water hexamer, using the Hartree-Fock method for the many-body term and Møller-Plesset theory for the low order terms of the many-body expansion.

Student-t processes as alternatives to Gaussian processes

We investigate the Student-t process as an alternative to the Gaussian process as a non-parametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the co-variance kernel of a Gaussian process model. We show surprising equivalences between different hierarchical Gaussian process models leading to Student-t processes, and derive a new sampling scheme for the inverse Wishart process, which helps elucidate these equivalences. Overall, we show that a Student-t process can retain the attractive properties of a Gaussian process - a nonparamet-ric representation, analytic marginal and predictive distributions, and easy model selection through covariance kernels - but has enhanced flexibility, and predictive covariances that, unlike a Gaussian process, explicitly depend on the values of training observations. We verify empirically that a Student-t process is especially useful in situations where there are changes in covariance structure, or in applications such as Bayesian optimization, where accurate predictive covariances are critical for good performance. These advantages come at no additional computational cost over Gaussian processes.

The cytomegalovirus promoter-driven short hairpin RNA constructs mediate effective RNA interference in zebrafish in vivo

The ability to utilize the RNA interference (RNAi) machinery for silencing target-gene expression has created a lot of excitement in the research community. In the present study, we used a cytomegalovirus (CMV) promoter-driven DNA template approach to induce short hairpin RNA (shRNA) triggered RNAi to block exogenous Enhanced Green Fluorescent Protein (EGFP) and endogenous No Tail (NTL) gene expressions. We constructed three plasmids, pCMV-EGFP-CMV-shGFP-SV40, pCMV-EGFP-CMV-shNTL-SV40, and pCMV-EGFP-CMV-shScrambled-SV40, each containing a CMV promoter driving an EGFP reporter cDNA and DNA coding for one shRNA under the control of another CMV promoter. The three shRNA-generating plasmids and pCMV-EGFP control plasmid were introduced into zebrafish embryos by microinjection. Samples were collected at 48 h after injection. Results were evaluated by phenotype observation and real-time fluorescent quantitative reverse-transcription polymerase chain reaction (Q-PCR). The shGFP-generating plasmid significantly inhibited the EGFP expression viewed under fluorescent microscope and reduced by 70.05 +/- 1.26% of exogenous EGFP gene mRNA levels compared with controls by Q-PCR. The shRNA targeting endogenous NTL gene resulted in obvious NTL phenotype of 30 +/- 4% and decreased the level of their corresponding mRNAs up to 54.52 +/- 2.05% compared with nontargeting control shRNA. These data proved the feasibility of the CMV promoter-driven shRNA expression technique to be used to inhibit exogenous and endogenous gene expressions in zebrafish in vivo.

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.

Short and long peptidoglycan recognition proteins (PGRPs) in zebrafish, with findings of multiple PGRP homologs in teleost fish

Peptidoglycan recognition protein (PGRP) specifically binds to peptidoglycan and is considered to be one of the pattern recognition proteins in the innate immunity of insect and mammals. Using a database mining approach and RT-PCR, multiple peptidoglycan recognition protein (PGRP) like genes have been discovered in fish including zebrafish Danio rerio, Japanese pufferfish TakiFugu rubripes and spotted green pufferfish Tetraodon nigroviridis. They share the common features of those PGRPs in arthropod and mammals, by containing a conserved PGRP domain. Based on the predicted structures, the identified zebrafish PGRP homologs resemble short and long PGRP members in arthropod and mammals. The identified PGRP genes in T. nigroviridis and TakiFugu rubripes resemble the long PGRPs, and the short PGRP genes have not been found in T. nigroviridis and TakiFugu rubripes databases. Computer modelling of these molecules revealed the presence of three alpha-helices and five or six beta-strands in all fish PGRPs reported in the present study. The long PGRP in teleost fish have multiple alternatively spliced forms, and some of the identified spliced variants, e.g., tnPGRP-L3 and tnPGRP-L4 (in: Tetraodon nigroviridis), exhibited no characters present in the PGRP homologs domain. The coding regions of zfPGRP6 (zf: zebrafish), zfPGRP2-A, zfPGRP2-B and zfPGRP-L contain five exons and four introns; however, the other PGRP-like genes including zfPGRPSC1a, zfPGRPSC2, tnPGRP-L1-, tnPGRP-L2 and frPGRP-L (fr: Takifugu rubripes) contain four exons and three introns. In zebrafish, long and short PGRP genes identified are located in different chromosomes, and an unknown locus containing another long PGRP-like gene has also been found in zebrafish, demonstrating that multiple PGRP loci may be present in fish. In zebrafish, the constitutive expressions of zfPGRP-L, zfPGRP-6 and zfPGRP-SC during ontogeny from unfertilized eggs to larvae, in different organs of adult, and the inductive expression following stimulation by Flavobacterium columnare, were detected by real-time PCR, but the levels and patterns varied for different PGRP genes, implying that different short and long PGRPs may play different roles in innate immune response. (c) 2007 Elsevier Ltd. All rights reserved.

Difterentially expressed genes of Tetrahymena thermophila in response to tributyltin (TBT) identified by suppression subtractive hybridization and real time quantitative PCR

Tributyltin (TBT) is widely used as antifouling paints, agriculture biocides, and plastic stabilizers around the world, resulting in great pollution problem in aquatic environments. However, it has been short of the biomonitor to detect TBT in freshwater. We constructed the suppression subtractive hybridization library of Tetrahymena thermophila exposed to TBT, and screened out 101 Expressed Sequence Tags whose expressions were significantly up- or down-regulated with TBT treatment. From this, a series of genes related to the TBT toxicity were discovered, such as glutathione-S-transferase gene (down-regulated), plasma membrane Ca2+ ATPase isoforms 3 gene (up-regulated) and NgoA (up-regulated). Furthermore, their expressions under different concentrations of TBT treatment (0.5-40 ppb) were detected by real time fluorescent quantitative PCR. The differentially expressed genes of T thermophila in response to TBT were identified, which provide the basic to make Tetrahymena as a sensitive, rapid and convenient TBT biomonitor in freshwater based on rDNA inducible expression system. (c) 2006 Elsevier B.V. All rights reserved.

Scaling arguments for the fluxes in turbulent miscible fountains

For established axisymmetric turbulent miscible Boussinesq fountains in quiescent uniform environments, expressions are developed for the fluxes of volume, momentum and buoyancy at the outflow from the fountain: the outflow referring to the counterflow at the horizontal plane of the source. The fluxes are expressed in terms of the fountain source conditions and two dimensionless functions of the source Froude number, Fr0: a radial function (relating a horizontal scale of the outflow to the source radius) and a volume flux function (relating the outflow and source volume fluxes). The forms taken by these two functions at low Fr0 and high Fr0 are deduced, thereby providing the outflow fluxes and outflow Froude number solely in terms of the source conditions. For high Fr0, the outflow Froude number, Frout, is shown to be invariant, indicating (by analogy with plumes for which the 'far-field' Froude number is invariant with source Froude number) that the outflow may be regarded as 'far-field' since the fluxes within the fountain have adjusted to attain a balance which is independent of the source conditions. Based on Frout, the fluxes in the plume that forms beyond the fountain outflow are deduced. Finally, from the results of previously published studies, we show that the scalings deduced for fountains are valid for 0.0025 ≲ Fr0 ≲ 1.0 for low Fr0 and Fr0≳ 3.0 for high Fr0. © 2014 Cambridge University Press.