Size-dependent piezoelectricity

In this paper, a consistent theory is developed for size-dependent piezoelectricity in dielectric solids. This theory shows that electric polarization can be generated as the result of coupling to the mean curvature tensor, unlike previous flexoelectric theories that postulate such couplings with other forms of curvature and more general strain gradient terms ignoring the possible couple- stresses. The present formulation represents an extension of recent work that establishes a consistent size-dependent theory for solid mechanics. Here by including scale-dependent measures in the energy equation, the general expressions for force- and couple-stresses, as well as electric displacement, are obtained. Next, the constitutive relations, displacement formulations, the uniqueness theorem and the reciprocal theorem for the corresponding linear small deformation size-dependent piezoelectricity are developed. As with existing flexoelectric formulations, one finds that the piezoelectric effect can also exist in isotropic materials, although in the present theory the coupling is strictly through the skew-symmetric mean curvature tensor. In the last portion of the paper, this isotropic case is considered in detail by developing the corresponding boundary value problem for two dimensional analyses and obtaining a closed form solution for an isotropic dielectric cylinder.Comment: 37 pages, 4 figure

Asymptotics of Nonlinear LSE Precoders with Applications to Transmit Antenna Selection

This paper studies the large-system performance of Least Square Error (LSE) precoders which~minimize~the~input-output distortion over an arbitrary support subject to a general penalty function. The asymptotics are determined via the replica method in a general form which encloses the Replica Symmetric (RS) and Replica Symmetry Breaking (RSB) ans\"atze. As a result, the "marginal decoupling property" of LSE precoders for $b$-steps of RSB is derived. The generality of the studied setup enables us to address special cases in which the number of active transmit antennas are constrained. Our numerical investigations depict that the computationally efficient forms of LSE precoders based on "$\ell_1$-norm" minimization perform close to the cases with "zero-norm" penalty function which have a considerable improvements compared to the random antenna selection. For the case with BPSK signals and restricted number of active antennas, the results show that RS fails to predict the performance while the RSB ansatz is consistent with theoretical bounds.Comment: 5 pages; 2 figures; to be presented at ISIT 201

ESRI vs BREWER: An Evaluation of Map Use with Alternative Colour Schemes amongst the General Public

This small study evaluates the effectiveness of selected sets of colour schemes used in ESRI‟s ArcMap and ColorBrewer in communicating information on choropleth maps. Subjects conducted map reading tasks using online questionnaires and their performance was captured. The results did not show significant differences in performance associated with colour scheme - subjects were highly successful in direct acquisition tasks irrespective of the set(s) of scheme used. However, performances were consistently poor for „distribution‟ tasks. The results suggest limited spatial capabilities in the sample and highlight the need to test for general spatial ability in such experiments