Toward automated analysis of particle holograms

A preliminary study of approaches for extracting and analyzing data from particle holograms is discussed. It concludes that: (1) for thin spherical particles, out-of-focus methods are optimum; (2) for thin nonspherical particles, out-of-focus methods are useful but must be supplemented by in-focus methods; (3) a complex method of projection and back projection can remove out-of-focus data for deep particles

Automatic holographic droplet analysis for liquid fuel sprays

The basic scheme for automated holographic analysis involves an optical system for reconstruction of the three dimensional real image of the droplet field, a spatial scanning system to transport a digitizing X-y image sensor through the real image, and processing algorithms for droplet recognition which establish the droplet sizes and positions. The hardware for system demonstrated includes the expanded and collimated beam from a 5 mW helium-neon laser for hologram reconstruction, an imaging lens for magnification of the real image field, and a video camera and digitizer providing 512-by-512 pixel resolution with 8-bit digitization. A mechanical stage is used to scan the hologram in three dimensional space, maintaining constant image magnification. A test droplet hologram is used for development and testing of the image processing algorithms

Decisions, Decisions: How Should The Votes Be Counted?

It is a simple matter for the members of a group to decide among two options. When there are three or more options among which to choose, the situation is much more complicated. This is precisely what faces the electorate each time there are more than two candidates running for a single office. And while there is debate over which voting method should be used, there is wide agreement over the method that should not be used: plurality, the most common approach taken in the United States. This article presents a simple classroom activity which provides students the opportunity to explore this issue in the context of a group of friends deciding which movie to watch. The methods of plurality, Borda count, approval, Condorcet, and Instant Runoff are discussed, along with advantages and disadvantages of each. All theoretical discussions are illustrated with voting data collected from fifty-eight students; an accompanying spreadsheet contains the data and the tabulations corresponding to each method

A variational framework for flow optimization using semi-norm constraints

When considering a general system of equations describing the space-time evolution (flow) of one or several variables, the problem of the optimization over a finite period of time of a measure of the state variable at the final time is a problem of great interest in many fields. Methods already exist in order to solve this kind of optimization problem, but sometimes fail when the constraint bounding the state vector at the initial time is not a norm, meaning that some part of the state vector remains unbounded and might cause the optimization procedure to diverge. In order to regularize this problem, we propose a general method which extends the existing optimization framework in a self-consistent manner. We first derive this framework extension, and then apply it to a problem of interest. Our demonstration problem considers the transient stability properties of a one-dimensional (in space) averaged turbulent model with a space- and time-dependent model "turbulent viscosity". We believe this work has a lot of potential applications in the fluid dynamics domain for problems in which we want to control the influence of separate components of the state vector in the optimization process.Comment: 30 page

Dependence on aspect ratio of symmetry breaking for oscillating foils: Implications for flapping flight

Using two-dimensional direct numerical simulations, we investigate the flow in a fluid of kinematic viscosity ${\it\nu}$ and density ${\it\rho}$ around elliptical foils of density ${\it\rho}_{s}$ with major axis $c$ and minor axis $b$ for three different aspect ratios: $AR=b/c=1$ (a circle); $AR=0.5$; and $AR=0.1$. The vertical location of these foils $y_{s}(t)=A\sin (2{\rm\pi}f_{0}t)$ oscillates with amplitude $A$ and frequency $f_{0}$ in two distinct ways: ‘pure’ oscillation, where the foils are constrained to remain in place; and ‘flying’ oscillation, where horizontal motion is allowed. We simulate the flow for a range of the two appropriate control parameters, the non-dimensional amplitude, or Keulegan–Carpenter number $KC=2{\rm\pi}A/c$, and the non-dimensional frequency, or Stokes number ${\it\beta}=f_{0}c^{2}/{\it\nu}$. We observe three distinct patterns of asymmetry, labelled ‘S-type’ for synchronous asymmetry, ‘$\text{QP}_{\text{H}}$-type’ and ‘$\text{QP}_{\text{L}}$-type’ for quasi-periodic asymmetry at sufficiently high and sufficiently low (i.e. $AR=0.1$) aspect ratios, respectively. These patterns are separated at the critical locus in $KC$–${\it\beta}$ space by a ‘freezing point’ where the two incommensurate frequencies of the QP-type flows combine, and we show that this freezing point tends to occur at smaller values of $KC$ as $AR$ decreases. We find for the smallest aspect ratio case ($AR=0.1$) that the transition to asymmetry, for all values of $KC$, occurs for a critical value of an ‘amplitude’ Stokes number ${\it\beta}_{A}={\it\beta}(KC)^{2}=4{\rm\pi}^{2}f_{0}A^{2}/{\it\nu}\simeq 3$. The $\text{QP}_{\text{L}}$-type asymmetry for $AR=0.1$ is qualitatively different in physical and mathematical structure from the $\text{QP}_{\text{H}}$-type asymmetry at higher aspect ratio. The flows at the two ends of the ellipse become essentially decoupled from each other for the $\text{QP}_{\text{L}}$-type asymmetry, the two frequencies in the horizontal force signature being close to the primary frequency, rather than twice the primary frequency as in the $\text{QP}_{\text{H}}$-type asymmetry. Furthermore, the associated coefficients arising from a Floquet stability analysis close to the critical thresholds are profoundly different for low aspect ratio foils. Freedom to move slightly suppresses the transition to S-type asymmetry, and for certain parameters, if a purely oscillating foil subject to S-type asymmetry is released to move, flow symmetry is rapidly recovered due to the negative feedback of small horizontal foil motion. Conversely, for the ‘higher’ aspect ratios, the transition to $\text{QP}_{\text{H}}$-type asymmetry is encouraged when the foil is allowed to move, with strong positive feedback occurring between the shed vortices from successive oscillation cycles. For $AR=0.1$, freedom to move significantly encourages the onset of asymmetry, but the newly observed ‘primary’ $\text{QP}_{\text{L}}$-type asymmetry found for pure oscillation no longer occurs when the foil flies, with S-type asymmetry leading ultimately to locomotion at a constant speed occurring all along the transition boundary for all values of $KC$ and ${\it\beta}$.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.66

Optical implementation of systolic array processing

Algorithms for matrix vector multiplication are implemented using acousto-optic cells for multiplication and input data transfer and using charge coupled devices detector arrays for accumulation and output of the results. No two dimensional matrix mask is required; matrix changes are implemented electronically. A system for multiplying a 50 component nonnegative real vector by a 50 by 50 nonnegative real matrix is described. Modifications for bipolar real and complex valued processing are possible, as are extensions to matrix-matrix multiplication and multiplication of a vector by multiple matrices

Horizontal locomotion of a vertically flapping oblate spheroid

We consider the self-induced motions of three-dimensional oblate spheroids of density \unicode[STIX]{x1D70C}_{s} with varying aspect ratios $AR=b/c\leqslant 1$, where $b$ and $c$ are the spheroids’ centre-pole radius and centre-equator radius, respectively. Vertical motion is imposed on the spheroids such that y_{s}(t)=A\sin (2\unicode[STIX]{x03C0}ft) in a fluid of density \unicode[STIX]{x1D70C} and kinematic viscosity \unicode[STIX]{x1D708}. As in strictly two-dimensional flows, above a critical value $Re_{C}$ of the flapping Reynolds number Re_{A}=2Afc/\unicode[STIX]{x1D708}, the spheroid ultimately propels itself horizontally as a result of fluid–body interactions. For $Re_{A}$ sufficiently above $Re_{C}$, the spheroid rapidly settles into a terminal state of constant, unidirectional velocity, consistent with the prediction of Deng et al. (Phys. Rev. E, vol. 94, 2016, 033107) that, at sufficiently high $Re_{A}$, such oscillating spheroids manifest $m=1$ asymmetric flow, with characteristic vortical structures conducive to providing unidirectional thrust if the spheroid is free to move horizontally. The speed $U$ of propagation increases linearly with the flapping frequency, resulting in a constant Strouhal number $St(AR)=2Af/U$, characterising the locomotive performance of the oblate spheroid, somewhat larger than the equivalent $St$ for two-dimensional spheroids, demonstrating that the three-dimensional flow is less efficient at driving locomotion. $St$ decreases with increasing aspect ratio for both two-dimensional and three-dimensional flows, although the relative disparity (and hence relative inefficiency of three-dimensional motion) decreases. For flows with $Re_{A}\gtrsim Re_{C}$, we observe two distinct types of inherently three-dimensional motion for different aspect ratios. The first, associated with a disk of aspect ratio $AR=0.1$ at $Re_{A}=45$, consists of a ‘stair-step’ trajectory. This trajectory can be understood through consideration of relatively high azimuthal wavenumber instabilities of interacting vortex rings, characterised by in-phase vortical structures above and below an oscillating spheroid, recently calculated using Floquet analysis by Deng et al. (Phys. Rev. E, vol. 94, 2016, 033107). Such ‘in-phase’ instabilities arise in a relatively narrow band of $Re_{A}\gtrsim Re_{C}$, which band shifts to higher Reynolds number as the aspect ratio increases. (Indeed, for horizontally fixed spheroids with aspect ratio $AR=0.2$, Floquet analysis actually predicts stability at $Re_{A}=45$.) For such a spheroid ($AR=0.2$, $Re_{A}=45$, with sufficiently small mass ratio m_{s}/m_{f}=\unicode[STIX]{x1D70C}_{s}V_{s}/(\unicode[STIX]{x1D70C}V_{s}), where $V_{s}$ is the volume of the spheroid) which is free to move horizontally, the second type of three-dimensional motion is observed, initially taking the form of a ‘snaking’ trajectory with long quasi-periodic sweeping oscillations before locking into an approximately elliptical ‘orbit’, apparently manifesting a three-dimensional generalisation of the $QP_{H}$ quasi-periodic symmetry breaking discussed for sufficiently high aspect ratio two-dimensional elliptical foils in Deng &amp; Caulfield (J. Fluid Mech., vol. 787, 2016, pp. 16–49).</jats:p

The Dimer Model for k-phase Organic Superconductors

We prove that the upper electronic bands of k-phase BEDT-TTF salts are adequately modeled by an half-filled tight-binding lattice with one site per cell. The band parameters are derived from recent ab-initio calculations, getting a very simple but extremely accurate one-electron picture. This picture allows us to solve the BCS gap equation adopting a real-space pairing potential. Comparison of the calculated superconducting properties with the experimental data points to isotropic s_0-pairing. Residual many-body or phonon-mediated interactions offer a plausible explanation of the large variety of physical properties observed in k-phase BEDT-TTF salts.Comment: 8 pages, 6 PostScript figures, uses RevTe