Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film

It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting counter-rotating vortices form a very simple convection pattern and exhibit a variety of interesting nonlinear effects. The linear stability problem for this system has recently been solved. The convection mechanism, which involves charge separation at the free surfaces of the film, is applicable to any sufficiently two-dimensional fluid. In this paper, we derive an amplitude equation which describes the weakly nonlinear regime, by starting from the basic electrohydrodynamic equations. This regime has been the subject of several recent experimental studies. The lowest order amplitude equation we derive is of the Ginzburg-Landau form, and describes a forward bifurcation as is observed experimentally. The coefficients of the amplitude equation are calculated and compared with the values independently deduced from the linear stability calculation.Comment: 26 pages, 2 included eps figures, submitted to Phys Rev E. For more information, see http://mobydick.physics.utoronto.c

Simulation-based model course to demonstrate seafarers' competence for deck officers' discipline

Postprint (published version

Prediction of landing gear loads using machine learning techniques

This article investigates the feasibility of using machine learning algorithms to predict the loads experienced by a landing gear during landing. For this purpose, the results on drop test data and flight test data will be examined. This article will focus on the use of Gaussian process regression for the prediction of loads on the components of a landing gear. For the learning task, comprehensive measurement data from drop tests are available. These include measurements of strains at key locations, such as on the side-stay and torque link, as well as acceleration measurements of the drop carriage and the gear itself, measurements of shock absorber travel, tyre closure, shock absorber pressure and wheel speed. Ground-to-tyre loads are also available through measurements made with a drop test ground reaction platform. The aim is to train the Gaussian process to predict load at a particular location from other available measurements, such as accelerations, or measurements of the shock absorber. If models can be successfully trained, then future load patterns may be predicted using only these measurements. The ultimate aim is to produce an accurate model that can predict the load at a number of locations across the landing gear using measurements that are readily available or may be measured more easily than directly measuring strain on the gear itself (for example, these may be measurements already available on the aircraft, or from a small number of sensors attached to the gear). The drop test data models provide a positive feasibility test which is the basis for moving on to the critical task of prediction on flight test data. For this, a wide range of available flight test measurements are considered for potential model inputs (excluding strain measurements themselves), before attempting to refine the model or use a smaller number of measurements for the prediction

The Spatio-Temporal Structure of Spiral-Defect Chaos

We present a study of the recently discovered spatially-extended chaotic state known as spiral-defect chaos, which occurs in low-Prandtl-number, large-aspect-ratio Rayleigh-Benard convection. We employ the modulus squared of the space-time Fourier transform of time series of two-dimensional shadowgraph images to construct the structure factor ${S}({\vec k},\omega )$. This analysis is used to characterize the average spatial and temporal scales of the chaotic state. We find that the correlation length and time can be described by power-law dependences on the reduced Rayleigh number ${\epsilon}$. These power laws have as yet no theoretical explanation.Comment: RevTex 38 pages with 13 figures. Due to their large size, some figures are stored as separate gif images. The paper with included hi-res eps figures (981kb compressed, 3.5Mb uncompressed) is available at ftp://mobydick.physics.utoronto.ca/pub/MBCA96.tar.gz An mpeg movie and samples of data are also available at ftp://mobydick.physics.utoronto.ca/pub/. Paper submitted to Physica

The Forms of Bullying Scale (FBS): Validity and reliability estimates for a measure of bullying victimization and perpetration in adolescence

The study of bullying behavior and its consequences for young people depends on valid and reliable measurement of bullying victimization and perpetration. Although numerous self-report bullying-related measures have been developed, robust evidence of their psychometric properties is scant, and several limitations inhibit their applicability. The Forms of Bullying Scale (FBS), with versions to measure bullying victimization (FBS-V) and perpetration (FBS-P), was developed on the basis of existing instruments, for use with 12-to 15-year-old adolescents to economically, yet comprehensively measure both bullying perpetration and victimization. Measurement properties were estimated. Scale validity was tested using data from 2 independent studies of 3,496 Grade 8 and 783 Grade 8-10 students, respectively. Construct validity of scores on the FBS was shown in confirmatory factor analysis. The factor structure was not invariant across gender. Strong associations between the FBS-V and FBS-P and separate single-item bullying items demonstrated adequate concurrent validity. Correlations, in directions as expected with social-emotional outcomes (i.e., depression, anxiety, conduct problems, and peer support), provided robust evidence of convergent and discriminant validity. Responses to the FBS items were found to be valid and concurrently reliable measures of self-reported frequency of bullying victimization and perpetration, as well as being useful to measure involvement in the different forms of bullying behaviors

Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca

Apollo Lightcraft project

The detailed design of a beam-powered transatmospheric vehicle, the Apollo Lightcraft, was selected as the project for the design course. The principal goal is to reduce the LEO payload delivery cost by at least three orders of magnitude below the Space Shuttle Orbiter in the post 2020 era. The completely reusable, single-stage-to-orbit shuttlecraft will take off and land vertically, and have a reentry heat shield integrated with its lower surface. At appropriate points along the launch trajectory, the combined cycle propulsion system will transition through three or four airbreathing modes, and finally use a pure rocket mode for orbital insertion. The objective for the Spring semester propulsion source was to design and perform a detailed theoretical analysis on an advanced combined-cycle engine suitable for the Apollo Lightcraft. The preliminary theoretical analysis of this combined-cycle engine is now completed, and the acceleration performance along representative orbital trajectories was simulated. The total round trip cost is $3430 or$686 per person. This represents a payload delivery cost of $3.11/lb, which is a factor of 1000 below the STS. The Apollo Lightcraft concept is now ready for a more detailed investigation during the Fall semester Transatmosphere Vehicle Design course

Annular electroconvection with shear

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $\eta \sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see http://mobydick.physics.utoronto.c