An analytical approach to evaluate effective coefficients of 1–3 piezoelectric composites

In this paper, a micromechanics method is developed to evaluate effective coefficients of piezoelectric fiber-reinforced composites. An exact solution is derived for effective elastic, piezoelectric and dielectric coefficients of such piezocomposites subjected to the applied load in the direction transverse to the fiber orientation. Simultaneously, based on finite element method, a numerical study is performed on a representative volume element of such piezo composite containing fiber in square packing arrangement. The finite element method provides a numerical solution to evaluate effective elastic, piezoelectric and dielectric coefficients for discrete volume fraction of fiber, the range being 0.1–0.6 for this study. The results are interpolated to understand the overall behavior of such piezocomposites. The results obtained from the micromechanics method and the finite element method are compared with the results obtained from other models based on strength of materials method given in the literature. It is observed that the method developed in this study provides better results for effective coefficients susceptible to fiber packing arrangements.

A Reinterpretation of Evidence for the Endothelial Glycocalyx Filtration Structure

The endothelial glycocalyx (eGlx) is thought to be the primary macromolecular filter for fluid flux out of the vasculature. This filter maintains the higher protein concentration within the vessel lumen relative to the tissue. Whilst the arguments for the eGlx being the size filter are convincing the structural evidence has been limited to specialized stains of perfusion fixed tissue, which are further processed for resin embedding for transmission electron microscopy. The staining and processing of the delicate pore structure has left many researchers struggling to interpret the observed surface coat. Previous work has alluded to a 19.5 nm spacing between fibers; however, whilst repeatable it does not give an eGlx pore size consistent with known glycosaminoglycan (GAG) molecular structure due to the required fiber thickness of >10 nm. Here a new interpretation is proposed based on the likelihood that the electron micrographs of are often of collapsed eGlx. The 19.5 nm spacing measured may therefore be the core protein of the proteoglycans (PGs) with the GAGs wrapped up around them rather than in an expanded in vivo state. The concept is explored to determine that this is indeed consistent with experimental measurements of permeability if the syndecans are predominately dimerized. Further an alteration of core protein lattice from hexagonal packing to square packing dramatically changes the permeability which could be facilitated via known mechanisms such as transient actin binding.

Prices of Anarchy of Selfish 2D Bin Packing Games

We consider a game-theoretical problem called selfish 2-dimensional bin packing game, a generalization of the 1-dimensional case already treated in the literature. In this game, the items to be packed are rectangles, and the bins are unit squares. The game starts with a set of items arbitrarily packed in bins. The cost of an item is defined as the ratio between its area and the total occupied area of the respective bin. Each item is a selfish player that wants to minimize its cost. A migration of an item to another bin is allowed only when its cost is decreased. We show that this game always converges to a Nash equilibrium (a stable packing where no single item can decrease its cost by migrating to another bin). We show that the pure price of anarchy of this game is unbounded, so we address the particular case where all items are squares. We show that the pure price of anarchy of the selfish square packing game is at least [Formula: see text] and at most [Formula: see text]. We also present analogous results for the strong Nash equilibrium (a stable packing where no nonempty set of items can simultaneously migrate to another common bin and decrease the cost of each item in the set). We show that the strong price of anarchy when all items are squares is at least [Formula: see text] and at most [Formula: see text].

Improved Online Algorithms for 2-Space Bounded 2-Dimensional Bin Packing

A 3.8165-competitive 2-space bounded 2-dimensional bin packing algorithm is described. Moreover, a 3.6-competitive online square packing algorithm with two active bins is presented.

Fibonacci or quasi-symmetric phyllotaxis. Part I: why?

The study of phyllotaxis has focused on seeking explanations for the occurrence of consecutive Fibonacci numbers in the number of helices paving the stems of plants in the two opposite directions. Using the disk-accretion model, first introduced by Schwendener and justified by modern biological studies, we observe two distinct types of solutions: the classical Fibonacci-like ones, and also more irregular configurations exhibiting nearly equal number of helices in a quasi-square packing, the quasi-symmetric ones, which are a generalization of the whorled patterns. Defining new geometric tools allowing to work with irregular patterns and local transitions, we provide simple explanations for the emergence of these two states within the same elementary model. A companion paper will provide a wide array of plant data analyses that support our view.