Sum Of Harmonic Functions Research Articles

High‐spatial‐resolution velocity measurements derived using Local Divergence‐Free Fitting of SuperDARN observations

AbstractA new technique for analysis of Super Dual Auroral Radar Network (SuperDARN) line‐of‐sight velocity observations enables resolving plasma convection with unprecedented spatial resolution. The technique, Local Divergence‐Free Fitting (LDFF), can be used to produce maps with a spatial resolution that is determined by the resolution of the observations rather than an arbitrary fit order. Other techniques, which express the potential as a sum of harmonic functions, limit the number of functions in the expansion to the fit order. Doing so imposes a limit on the minimum size of features that will be represented in the results. The LDFF technique is not limited by this constraint. Rather, it is limited by the resolution of the observations and the amount of regularization required by the observed noise level, which generally allows finer‐scale features to be represented. The LDFF technique is described and then applied to a synthetic data set to demonstrate its validity. Then high‐resolution convection maps are presented from an interval during which auroral observations over Alaska showed poleward boundary intensifications (PBIs) and auroral streamers. Overlays of the convection vectors on the auroral images illustrate correspondence between flow features and the auroral luminosity. Detailed comparison between the flows and images showed that the PBIs originated from polar cap boundary arcs that extended away from midnight toward earlier local times. As the arcs extended they were accompanied by enhanced shear flow. The arcs intensified then moved equatorward becoming streamers. As the arcs moved, the region of shear flow followed their motion, indicating a pattern of field‐aligned current associated with the moving arc. The observations are the most comprehensive and detailed known to the authors for such an interval and agree well with the expected plasma flows based upon magnetospheric simulations. Flow vectors generated for the interval by the spherical harmonic fit technique for the most part do not show the direct relationship between the convection and the localized luminosity features nearly as well as the LDFF results. Some of the features found in the LDFF fitting are simply not present in the results from the global fits. The LDFF technique should find application in a variety of studies where high‐spatial‐resolution estimates of plasma flows are required. The example study presented here, which examined the details of flows in the region of auroral arcs, is representative of such problems.

Parameter estimation of sub-Gaussian stable distributions

In this paper, we present a parameter estimation method for sub-Gaussian stable distributions. Our algorithm has two phases: in the first phase, we calculate the average values of harmonic functions of observations and in the second phase, we conduct the main procedure of asymptotic maximum likelihood where those average values are used as inputs. This implies that the main procedure of our method does not depend on the sample size of observations. The main idea of our method lies in representing the partial derivative of the density function with respect to the parameter that we estimate as the sum of harmonic functions and using this representation for finding this parameter. For fifteen summands we get acceptable precision. We demonstrate this methodology on estimating the tail index and the dispersion matrix of sub-Gaussian distributions.

Action of Individual Bouncing on Structures

This paper investigates the action of an individual bouncing on a structure, including the load generated and the effect on the dynamic behavior of the structure. A simply supported beam at The University of Manchester is used as a supporting structure for an individual bouncing and its responses to bouncing are recorded. Four hundred thirty three tests were conducted ranging bouncing frequency from 0.4to3.2Hz for determining the load factors of individual bouncing loads. Over 7,300 bouncing frequencies are identified from the tests and analyzed statistically for examining how well people respond to metronome or music beats. The frequency range for coordinated bouncing between individuals is determined and is between 1.0 and 3.1Hz. The first four dynamic load factors or Fourier coefficients are determined based on the measurements and the concept that dynamic responses induced by the sum of harmonic functions are at discrete loading frequencies. The proposed load model is validated by comparing the predicted responses and measurements on another beam. Two hundred forty human-structure interaction tests for an individual bouncing are also conducted. It reveals that a bouncing person interacts with the test rig, but the degree of the human-structure interaction is less significant than that between a standing person and the rig.

Dielectric permittivity simulation of random irregularly shaped particle composites and approximation using modified dielectric mixing laws

Finite difference quasielectrostatic modeling is used to predict the dielectric permittivity of composites consisting of irregular particles in a background matrix. Representations of particles having undulating surfaces described by sums of harmonic functions are created on the computer and subsequently packed into a three-dimensional cellular model space. Composite dielectric permittivities as a function of volumetric filling fraction and particle undulation amplitude were simulated using constituent permittivities similar to the low-field behavior of barium titanium oxide (particles) and polyvinylidene fluoride-trifluoroethylene-chlorofluoroethylene (terpolymer matrix). An increase in particle roughness (undulation amplitude) causes a more rapid increase in composite permittivity than that predicted by random spherical particle simulations. The dielectric behavior of irregular particle composites is also simulated over a wide range of ratios of particle permittivity to matrix permittivity, where both permittivities are purely real. An empirical mixing law, which is a modification of the Hanai equation with an exponent 1/μ instead of 1/3, is investigated and found to be in excellent agreement with the simulations. Additional empirical expressions that provide approximate values of μ in terms of the particle undulation amplitude and the ratio of constituent permittivities are developed. Together, the empirical expressions are potentially useful as a predictive mixing law for irregular particle systems.

Probabilistic Models and Simulation of Irregular Masonry Walls

A method is proposed for generating samples of irregular masonry walls that capture the essential statistics of a given population. The method first entails characterizing the geometry of scaled star-like inclusions by means of a non-Gaussian random field model and second packing these inclusions together to form a virtual material specimen. The model used in the first step is a nonlinear memoryless mapping of a sum of harmonic functions with Gaussian coefficients while in the second step the model proposed transforms Poisson fields into a domain of inclusions with a sieving curve that matches the sample specimen. The two random field models are used to develop Monte Carlo algorithms which produce virtual material specimens that include two levels of probabilistic characterization, a first level that is correlated to the inclusion geometry, and a second that is dictated by the global morphology of the sample material specimen.