Impact of mode localization on the motional resistance of coupled MEMS resonators

This paper investigates the effect of mode-localization that arises from structural asymmetry induced by manufacturing tolerances in mechanically coupled, electrically transduced Si MEMS resonators. We demonstrate that in the case of such mechanically coupled resonators, the achievable series motional resistance (R x) is dependent not only on the quality factor (Q) but also on the variations in the eigenvector of the chosen mode of vibration induced by mode localization due to manufacturing tolerances during the fabrication process. We study this effect of mode-localization both theoretically and experimentally in two pairs of coupled double-ended tuning fork resonators with different levels of initial structural asymmetry. The measured series R x is minimal when the system is close to perfect symmetry and any deviation from structural symmetry induced by fabrication tolerances leads to a degradation in the effective R x. Mechanical tuning experiments of the stiffness of one of the coupled resonators was also conducted to study variations in R x as a function of structural asymmetry within the system, the results of which demonstrated consistent variations in motional resistance with predictions. © 2012 IEEE.

A Stochastic Model for Electron Multiplication Charge-Coupled Devices - From Theory to Practice

Electron multiplication charge-coupled devices (EMCCD) are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images. © 2013 Hirsch et al.

Theory of high-power mode-locked lasers with a slow absorber

We develop an analytical theory of high-power passively mode-locked lasers with a slow absorber; the theory is valid at pulse energies well exceeding the saturation energy. We analyze the Haus modelocking master equation in the pulse-energy-domain representation, approximating the intensity profile function by a series in the vicinity of its peak value. We consider the high-power operation regime of subpicosecond blue-violet GaN mode-locked diode lasers, using the approach developed. © 2010 Springer Science+Business Media, Inc.

Evanescent-wave coupled right angled buried waveguide: Applications in carbon nanotube mode-locking

We present an evanescent-field device based on a right-angled waveguide. This consists of orthogonal waveguides, with their points of intersection lying along an angled facet of the chip. Light guided along one waveguide is incident at the angled dielectric-air facet at an angle exceeding the critical angle, so that the totally internally reflected light is coupled into the second waveguide. By depositing a nanotube film on the angled surface, the chip is then used to mode-lock an Erbium doped fiber ring laser with a repetition rate of 26 MHz, and pulse duration of 800 fs. © 2013 AIP Publishing LLC.

Passively harmonically mode-locked vertical-external-cavity surface-emitting laser emitting 1.1 ps pulses at 147 GHz repetition rate

Coupled-cavity passive harmonic mode-locking of a quantum well based vertical-external-cavity surface-emitting laser has been demonstrated, yielding an output pulse train of 1.5 ps pulses at a repetition rate of 80 GHz and with an average power of 80 mW. Harmonic mode-locking results from coupling between the main laser cavity and a cavity formed within the substrate of the saturable absorber structure. Mode-locking on the second harmonic of the substrate cavity allows a train of 1.1 ps pulses to be generated at a repetition rate of 147 GHz with 40 mW average power. © 2010 American Institute of Physics.

Effects of mechanical and electrical coupling on the parametric sensitivity of mode localized sensors

We compare and contrast the effects of two distinctly different mechanisms of coupling (mechanical and electrical) on the parametric sensitivity of micromechanical sensors utilizing mode localization for sensor applications. For the first time, the strong correlation between mode localization and the phenomenon of 'eigenvalue loci-veering' is exploited for accurate quantification of the strength of internal coupling in mode localized sensors. The effects of capacitive coupling-spring tuning on the parametric sensitivity of electrically coupled resonators utilizing this sensing paradigm is also investigated and a mass sensor with sensitivity tunable by over 400% is realized. ©2009 IEEE.

169 GHz repetition rate passively harmonically mode-locked VECSEL emitting 265 fs pulses

High repetition rate passively mode-locked sources are of significant interest due to their potential for applications including optical clocking, optical sampling, communications and others. Due to their short excited state lifetimes mode-locked VECSELs are ideally suited to high repetition rate operation, however fundamentally mode-locked quantum well-based VECSELs have not achieved repetition rates above 10 GHz due to the limitations placed on the cavity geometry by the requirement that the saturable absorber saturates more quickly than the gain. This issue has been overcome by the use of quantum dot-based saturable absorbers with lower saturation fluences leading to repetition rates up to 50 GHz, but sub-picosecond pulses have not been achieved at these repetition rates. We present a passively harmonically mode-locked VECSEL emitting pulses of 265 fs duration at a repetition rate of 169 GHz with an output power of 20 mW. The laser is based around an antiresonant 6 quantum well gain sample and is mode-locked using a semiconductor saturable absorber mirror. Harmonic modelocking is achieved by using an intracavity sapphire etalon. The sapphire then acts as a coupled cavity, setting the repetition rate of the laser while still allowing a tight focus on the saturable absorber. RF spectra of the laser output show no peaks at harmonics of the fundamental repetition rate up to 26 GHz, indicating stable harmonic modelocking. Autocorrelations reveal groups of pulses circulating in the cavity as a result of an increased tendency towards Q-switched modelocking due to the low pulse energies.

Shock transmission and eigenvalue veering within a coupled system.

The operation of dynamical systems in harsh environments requires continuous monitoring. Internal sensors may be used to monitor the conditions in real time. A typical example is the sensor and electronic components used in space structures which, especially during launch, are subject to huge g force. The paper will present an experimental and theoretical study on a simplified model used to analyze the possible cause of high acceleration on the enclosed sensors and equipments due to impulsive loading. The model system consists of two beams coupled using compliant connections. An impulse hammer excites one beam, and vibrations are transmitted to the indirectly driven beam. A theoretical model is developed using a Rayleigh-Ritz approach and validated using experimental results in both the frequency and time domains. Monto Carlo simulation was done with random masses positioned on the indirectly driven beam to determine the worst-case conditions for maximum peak acceleration. Highest acceleration levels were found when mode matching in the two beams led to veering behavior in the coupled modes. The results suggest guidelines for the detailed design of internal components of a structure exposed to shock loading from its environment. [The authors thank Schlumberger Cambridge Research for financial support.].

Vibrations of coupled cylindrical-conical shells

The free vibrational characteristics of coupled conical-cylindrical shells is presented. The equations of motion for the cylindrical shell are solved using a wave approach while the equations of motion for the conical shells are solved using a power series solution. The use of both Donnell-Mushtari and Flügge equations of motion are investigated and their limitations are discussed. Results are presented in terms of natural frequencies for different boundary conditions and the purely torsional mode solution is described. The results from the analytical model presented are compared with those obtained from a finite element model solved with Nastran and other data available in literature.

Classical plume theory: 1937-2010 and beyond

Developing a theoretical description of turbulent plumes, the likes of which may be seen rising above industrial chimneys, is a daunting thought. Plumes are ubiquitous on a wide range of scales in both the natural and the man-made environments. Examples that immediately come to mind are the vapour plumes above industrial smoke stacks or the ash plumes forming particle-laden clouds above an erupting volcano. However, plumes also occur where they are less visually apparent, such as the rising stream of warmair above a domestic radiator, of oil from a subsea blowout or, at a larger scale, of air above the so-called urban heat island. In many instances, not only the plume itself is of interest but also its influence on the environment as a whole through the process of entrainment. Zeldovich (1937, The asymptotic laws of freely-ascending convective flows. Zh. Eksp. Teor. Fiz., 7, 1463-1465 (in Russian)), Batchelor (1954, Heat convection and buoyancy effects in fluids. Q. J. R. Meteor. Soc., 80, 339-358) and Morton et al. (1956, Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A, 234, 1-23) laid the foundations for classical plume theory, a theoretical description that is elegant in its simplicity and yet encapsulates the complex turbulent engulfment of ambient fluid into the plume. Testament to the insight and approach developed in these early models of plumes is that the essential theory remains unchanged and is widely applied today. We describe the foundations of plume theory and link the theoretical developments with the measurements made in experiments necessary to close these models before discussing some recent developments in plume theory, including an approach which generalizes results obtained separately for the Boussinesq and the non-Boussinesq plume cases. The theory presented - despite its simplicity - has been very successful at describing and explaining the behaviour of plumes across the wide range of scales they are observed. We present solutions to the coupled set of ordinary differential equations (the plume conservation equations) that Morton et al. (1956) derived from the Navier-Stokes equations which govern fluid motion. In order to describe and contrast the bulk behaviour of rising plumes from general area sources, we present closed-form solutions to the plume conservation equations that were achieved by solving for the variation with height of Morton's non-dimensional flux parameter Γ - this single flux parameter gives a unique representation of the behaviour of steady plumes and enables a characterization of the different types of plume. We discuss advantages of solutions in this form before describing extensions to plume theory and suggesting directions for new research. © 2010 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

Material point method for coupled hydromechanical problems

This paper describes a new formulation of the material point method (MPM) for solving coupled hydromechanical problems of fluid-saturated soil subjected to large deformation. A soil-pore fluid coupled MPM algorithm based on Biot's mixture theory is proposed for solving hydromechanical interaction problems that include changes in water table location with time. The accuracy of the proposed method is examined by comparing the results of the simulation of a one-dimensional consolidation test with the corresponding analytical solution. A sensitivity analysis of the MPM parameters used in the proposed method is carried out for examining the effect of the number of particles per mesh and mesh size on solution accuracy. For demonstrating the capability of the proposed method, a physical model experiment of a large-scale levee failure by seepage is simulated. The behavior of the levee model with time-dependent changes in water table matches well to the experimental observations. The mechanisms of seepage-induced failure are discussed by examining the pore-water pressures, as well as the effective stresses computed from the simulations © 2013 American Society of Civil Engineers.