Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Long-range interactions in turbulence and the energy decay problem.

We discuss the long-range interactions that arise in homogeneous turbulence as a consequence of the Biot-Savart law. We note that, somewhat surprisingly, these long-range correlations are very weak in decaying, isotropic turbulence, and we argue that this should also be true for magnetohydrodynamic, rotating and stratified turbulence. If this is indeed the case, it is possible to make explicit predictions for the rate of decay of energy in these anisotropic systems, and it turns out that these predictions are consistent with the available numerical and experimental evidence.

Numerical modelling of dynamic response of loss modulated monolithic multisection mode-locked semiconductor lasers

Monolithic multisection mode-locked semiconductor lasers with an integrated distributed Bragg reflector (DBR) have recently been demonstrated to generate stable picosecond pulses at high repetition rates suitable for optical communication systems. However, there has been very little theoretical work on understanding the physical mechanisms of the device and on optimisation of the absorber modulator design. This article presents numerical modeling of the loss modulated mode-locking process in these lasers. The model predicts most aspects experimentally observed within this type of device, and the results show the output waveform, optical spectrum, instantaneous frequency chirp, and stable operating range.

Numerical analysis of the coupled circuit and cooling holes for an electromagnetic shaker

This paper presents a time-stepping shaker modeling scheme. The new method improves the accuracy of analysis of armature-position-dependent inductances and force factors, analysis of axial variation of current density in copper plates (short-circuited turns), and analysis of cooling holes in the magnetic circuit. Linear movement modeling allows armature position to be precisely included in the shaker analysis. A more accurate calculation of eddy currents in the coupled circuit is in particular crucial for the shaker analysis in a mid-or high-frequency operation range. Large currents in a shaker, including eddy currents, incur large Joule losses, which in turn require the use of a cooling system to keep temperature at bay. Sizable cooling holes have influence on the saturation state of iron poles, and hence have to be properly taken into account.

Numerical simulations of unsteady wet steam flows with non-equilibrium condensation in the nozzle and the steam turbine

Numerical techniques for non-equilibrium condensing flows are presented. Conservation equations for homogeneous gas-liquid two-phase compressible flows are solved by using a finite volume method based on an approximate Riemann solver. The phase change consists of the homogeneous nucleation and growth of existing droplets. Nucleation is computed with the classical Volmer-Frenkel model, corrected for the influence of the droplet temperature being higher than the steam temperature due to latent heat release. For droplet growth, two types of heat transfer model between droplets and the surrounding steam are used: a free molecular flow model and a semi-empirical two-layer model which is deemed to be valid over a wide range of Knudsen number. The computed pressure distribution and Sauter mean droplet diameters in a convergent-divergent (Laval) nozzle are compared with experimental data. Both droplet growth models capture qualitatively the pressure increases due to sudden heat release by the non-equilibrium condensation. However the agreement between computed and experimental pressure distributions is better for the two-layer model. The droplet diameter calculated by this model also agrees well with the experimental value, whereas that predicted by the free molecular model is too small. Condensing flows in a steam turbine cascade are calculated at different Mach numbers and inlet superheat conditions and are compared with experiments. Static pressure traverses downstream from the blade and pressure distributions on the blade surface agree well with experimental results in all cases. Once again, droplet diameters computed with the two-layer model give best agreement with the experiments. Droplet sizes are found to vary across the blade pitch due to the significant variation in expansion rate. Flow patterns including oblique shock waves and condensation-induced pressure increases are also presented and are similar to those shown in the experimental Schlieren photographs. Finally, calculations are presented for periodically unsteady condensing flows in a low expansion rate, convergent-divergent (Laval) nozzle. Depending on the inlet stagnation subcooling, two types of self-excited oscillations appear: a symmetric mode at lower inlet subcooling and an asymmetric mode at higher subcooling. Plots of oscillation frequency versus inlet sub-cooling exhibit a hysteresis loop, in accord with observations made by other researchers for moist air flow. Copyright © 2006 by ASME.

Numerical simulation of the growth of ZnO nanostructures in a tube furnace by physical vapour deposition

Zinc oxide is a versatile II-VI naturally n-type semiconductor that exhibits piezoelectric properties. By controlling the growth kinetics during a simple carbothermal reduction process a wide range of 1D nanostructures such as nanowires, nanobelts, and nanotetrapods have been synthesized. The driving force: for the nanostructure growth is the Zn vapour supersaturation and supply rate which, if known, can be used to predict and explain the type of crystal structure that results. A model which attempts to determine the Zn vapour concentration as a function of position in the growth furnace is described. A numerical simulation package, COMSOL, was used to simultaneously model the effects of fluid flow, diffusion and heat transfer in a tube furnace made specifically for ZnO nanostructure growth. Parameters such as the temperature, pressure, and flow rate are used as inputs to the model to show the effect that each one has on the Zn concentration profile. An experimental parametric study of ZnO nanostructure growth was also conducted and compared to the model predictions for the Zn concentration in the tube. © 2008 Materials Research Society.

An experimental and numerical study of an oscillating transonic shock wave in a duct

A combined experimental and numerical study of a transonic shock wave in a parallel walled duct subject to downstream pressure perturbations has been conducted. Experiments and simulations have been carried out with a shock strength of M∞ = 1.4 for pressure perturbation frequencies in the range 16-90 Hz. The dynamics of unsteady shock motion and the interaction structure between the unsteady transonic shock wave and the turbulent tunnel floor boundary layer have been investigated. It is found that the (experimentally measured) dynamics of shock motion are generally well predicted by the computational scheme, especially at relatively low (≈ 40 Hz) frequencies. However, at higher frequencies (≈ 90 Hz), some subtle differences between the shock dynamics measured in experiments and those predicted by Computational Fluid Dynamics (CFD) exist. There is evidence from experiments that variations in shock / boundary layer interaction (SBLI) structure caused by shock motion are responsible for a change in the nature of shock dynamics between low and high frequency. In contrast, numerical results at low and high frequencies do not differ significantly and this suggests that the numerical method is not fully capturing the physics of the unsteady flow. Possible reasons for this are considered and a number of areas where CFD is unable to replicate experimental observations are identified. Significantly, CFD predicts changes in SBLI structure due to shock motion that are much too large and this may explain why none of the subtle effects on shock dynamics seen in experiments occur in CFD. Further work developing numerical methods that demonstrate a more realistic sensitivity of SBLI structure to unsteady shock motion is required. Copyright © 2010 by P.J.K. Bruce.

Effects of turbulent reynolds number on the performance of algebraic flame surface density models for large eddy simulation in the thin reaction zones regime: A direct numerical simulation analysis

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Ret has been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Ret and Ka before reaching an asymptotic value for large values of Ret and Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel'dovich flame thickness ηi/δz does not exhibit any significant dependence on Ret for the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width. © 2012 Mohit Katragadda et al.

Numerical study of the shielding properties of macroscopic hybrid ferromagnetic/superconductor hollow cylinders

We study the magnetic shielding properties of hybrid ferromagnetic/ superconductor (F/S) structures consisting of two coaxial cylinders, with one of each material. We use an axisymmetric finite-element model in which the electrical properties of the superconducting tube are modeled by a nonlinear E-J power law with a magnetic-field-dependent critical current density whereas the magnetic properties of the ferromagnetic material take saturation into account. We study and compare the penetration of a uniform axial magnetic field in two cases: 1) a ferromagnetic tube placed inside a larger superconducting tube (Ferro-In configuration) and 2) a ferromagnetic tube placed outside the superconducting one (Ferro-Out configuration). In both cases, we assess how the ferromagnetic tube improves the shielding properties of the sole superconducting tube. The influence of the geometrical parameters of the ferromagnetic tube is also studied: It is shown that, upon an optimal choice of the geometrical parameters, the range of magnetic fields that are efficiently shielded by the high-temperature superconductor tube alone can be increased by a factor of up to 7 (2) in a Ferro-Out (Ferro-In) configuration. The optimal configuration uses a 1020 carbon steel with a thickness of 2 mm and a height that is half that of the superconducting cylinder (80 mm). © 2009 IEEE.

Direct numerical simulation of turbulent flows over superhydrophobic surfaces with gas pockets using linearized boundary conditions

Superhydrophobic surfaces are shown to be effective for surface drag reduction under laminar regime by both experiments and simulations (see for example, Ou and Rothstein, Phys. Fluids 17:103606, 2005). However, such drag reduction for fully developed turbulent flow maintaining the Cassie-Baxter state remains an open problem due to high shear rates and flow unsteadiness of turbulent boundary layer. Our work aims to develop an understanding of mechanisms leading to interface breaking and loss of gas pockets due to interactions with turbulent boundary layers. We take advantage of direct numerical simulation of turbulence with slip and no-slip patterned boundary conditions mimicking the superhydrophobic surface. In addition, we capture the dynamics of gas-water interface, by deriving a proper linearized boundary condition taking into account the surface tension of the interface and kinematic matching of interface deformation and normal velocity conditions on the wall. We will show results from our simulations predicting the dynamical behavior of gas pocket interfaces over a wide range of dimensionless surface tensions.

An investigation into numerical analysis alternatives for predicting reingestion in turbine disc rim cavities

Reliable means of predicting ingestion in cavities adjacent to the main gas path are increasingly being sought by engineers involved in the design of gas turbines. In this paper, analysis is to be presented that results from an extended research programme, MAGPI, sponsored by the EU and several leading gas turbine manufactures and universities. Extensive use is made of CFD modelling techniques to understand the aerodynamic behaviour of a turbine stator well cavity, focusing on the interaction of cooling air supply with the main annulus gas. The objective of the study has been to benchmark a number of CFD codes and numerical techniques covering RANS and URANS calculations with different turbulence models in order to assess the suitability of the standard settings used in the industry for calculating the mechanics of the flow travelling between cavities in a turbine through the main gas path. The modelling methods employed have been compared making use of experimental data gathered from a dedicated two-stage turbine rig, running at engine representative conditions. Extensive measurements are available for a range of flow conditions and alternative cooling arrangements. The limitations of the numerical methods in calculating the interaction of the cooling flow egress and the main stream gas, and subsequent ingestion into downstream cavities in the engine (i.e. re-ingestion), have been exposed. This has been done without losing sight of the validation of the CFD for its use for predicting heat transfer, which was the main objective of the partners of the MAGPI Work- Package 1 consortium. Copyright © 2012 by ASME.

Numerical study of the impact of process variations on the motional resistance of weakly coupled MEMS resonators

This paper presents a numerical study of the impact of process-induced variations on the achievable motional resistance Rx of one-dimensional, cyclic and cross-coupled architectures of electrostatically transduced MEMS resonators operating in the 250 kHz range. Monte Carlo numerical simulations which accounted for up to 0.75% variation in critical resonator feature sizes were initiated on 1, 2, 3, 4, 5 and 9 coupled MEMS resonators for three distinct coupling architectures. Improvements of 100X in the spread of Rx and 2.7X in mean achievable Rx are reported for the case of 9 resonators when implemented in the cross-coupled topology, as opposed to the traditional one-dimensional chain. © 2013 IEEE.

Cellular contractility and substrate elasticity: A numerical investigation of the actin cytoskeleton and cell adhesion

Numerous experimental studies have established that cells can sense the stiffness of underlying substrates and have quantified the effect of substrate stiffness on stress fibre formation, focal adhesion area, cell traction, and cell shape. In order to capture such behaviour, the current study couples a mixed mode thermodynamic and mechanical framework that predicts focal adhesion formation and growth with a material model that predicts stress fibre formation, contractility, and dissociation in a fully 3D implementation. Simulations reveal that SF contractility plays a critical role in the substrate-dependent response of cells. Compliant substrates do not provide sufficient tension for stress fibre persistence, causing dissociation of stress fibres and lower focal adhesion formation. In contrast, cells on stiffer substrates are predicted to contain large amounts of dominant stress fibres. Different levels of cellular contractility representative of different cell phenotypes are found to alter the range of substrate stiffness that cause the most significant changes in stress fibre and focal adhesion formation. Furthermore, stress fibre and focal adhesion formation evolve as a cell spreads on a substrate and leading to the formation of bands of fibres leading from the cell periphery over the nucleus. Inhibiting the formation of FAs during cell spreading is found to limit stress fibre formation. The predictions of this mutually dependent material-interface framework are strongly supported by experimental observations of cells adhered to elastic substrates and offer insight into the inter-dependent biomechanical processes regulating stress fibre and focal adhesion formation. © 2013 Springer-Verlag Berlin Heidelberg.