Preliminary Investigation of Cyclic De-Icing of an Airfoil Using an External Electric Heater

An investigation was conducted in the NACA Lewis icing research tunnel to determine the characteristics and requirements of cyclic deicing of a 65,2-216 airfoil by use of an external electric heater. The present investigation was limited to an airspeed of 175 miles per hour. Data are presented to show the effects of variations in heat-on and heat-off periods, ambient air temperature, liquid-water content, angle of attack, and. heating distribution on the requirements for cyclic deicing. The external heat flow at various icing and heating conditions is also presented. A continuously heated parting strip at the airfoil leading edge was found necessary for quick, complete, and consistent ice removal. The cyclic power requirements were found to be primarily a function of the datum temperature and heat-on time, with the other operating and meteorological variables having a second-order effect. Short heat-on periods and high power densities resulted in the most efficient ice removal, the minimum energy input, and the minimum runback ice formations. The optimum chordwise heating distribution pattern was found to consist of a uniform distribution of cycled power density in the impingement region. Downstream of the impingement region the power density decreased to the limits of heating which, for the conditions investigated, extended from 5.7 percent chord on the upper surface of the airfoil to 8.9 percent chord on the lower surface. Ice removal did not take place at a heater surface temperature of 32 F; surface temperatures of approximately 50 to 100 F were required to effect removal. Better de-icing performance and greater energy savings would be possible with a heater having a higher thermal efficiency

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

Adaptive cancelation of self-generated sensory signals in a whisking robot

Sensory signals are often caused by one's own active movements. This raises a problem of discriminating between self-generated sensory signals and signals generated by the external world. Such discrimination is of general importance for robotic systems, where operational robustness is dependent on the correct interpretation of sensory signals. Here, we investigate this problem in the context of a whiskered robot. The whisker sensory signal comprises two components: one due to contact with an object (externally generated) and another due to active movement of the whisker (self-generated). We propose a solution to this discrimination problem based on adaptive noise cancelation, where the robot learns to predict the sensory consequences of its own movements using an adaptive filter. The filter inputs (copy of motor commands) are transformed by Laguerre functions instead of the often-used tapped-delay line, which reduces model order and, therefore, computational complexity. Results from a contact-detection task demonstrate that false positives are significantly reduced using the proposed scheme

Visibility Representations of Boxes in 2.5 Dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane $z=0$ and edges are unobstructed lines of sight parallel to the $x$- or $y$-axis. We prove that: $(i)$ Every complete bipartite graph admits a 2.5D-BR; $(ii)$ The complete graph $K_n$ admits a 2.5D-BR if and only if $n \leq 19$; $(iii)$ Every graph with pathwidth at most $7$ admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an $n$-vertex graph that admits a 2.5D-GBR has at most $4n - 6 \sqrt{n}$ edges and this bound is tight. Finally, we prove that deciding whether a given graph $G$ admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR $\Gamma$ is the set of bottom faces of the boxes in $\Gamma$.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Continuum Derrida Approach to Drift and Diffusivity in Random Media

By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8

Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style

Dynamical transition for a particle in a squared Gaussian potential

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.Comment: 18 pages, 4 figures .eps, JPA styl

Radar signal categorization using a neural network

Neural networks were used to analyze a complex simulated radar environment which contains noisy radar pulses generated by many different emitters. The neural network used is an energy minimizing network (the BSB model) which forms energy minima - attractors in the network dynamical system - based on learned input data. The system first determines how many emitters are present (the deinterleaving problem). Pulses from individual simulated emitters give rise to separate stable attractors in the network. Once individual emitters are characterized, it is possible to make tentative identifications of them based on their observed parameters. As a test of this idea, a neural network was used to form a small data base that potentially could make emitter identifications

A Level-Set Hit-And-Run Sampler for Quasi-Concave Distributions

We develop a new sampling strategy that uses the hit-and-run algorithm within level sets of a target density. Our method can be applied to any quasi-concave density, which covers a broad class of models. Standard sampling methods often perform poorly on densities that are high-dimensional or multi-modal. Our level set sampler performs well in high-dimensional settings, which we illustrate on a spike-and-slab mixture model. We also extend our method to exponentially-tilted quasi-concave densities, which arise in Bayesian models consisting of a log-concave likelihood and quasiconcave prior density. We illustrate our exponentially-tilted level-set sampler on a Cauchy-normal model where our sampler is better able to handle a high-dimensional and multi-modal posterior distribution compared to Gibbs sampling and Hamiltonian Monte Carlo