Revisiting the cutting of the firing squad synchronization

Various synchronization algorithms have been introduced in literature during the last decades to deal with the firing squad synchronization problem on cellular automata (CA). Among others defective CA algorithms, where the CA cell is able to transmit information without previous processing, have been also presented. In our case, originating from the classical Mazoyer’s paper, where a minimum-time solution is presented with 6 states, a one-dimensional CA where one cell may permanently fail is presented. In the proposed algorithm, the defective cell can neither process nor transmit information any longer, while it is considered that such dynamic defects may become apparent in any time step of computation. A thorough analysis of the synchronization, in terms of location and time at which cell fails, for the cells found in both sides of defective cell is delivered to decipher the corresponding maximal possible number of synchronized cells in each part of the cut, due to defect, CA array. The proposed algorithm is properly extended to consider more than one defective cells that may occur in the under study one-dimensional CA. Based on the aforementioned analysis, we provide the generalization of synchronization with multiple totally defective cells, while application examples of the generalized CA algorithm in case of two defective cells are also presented. Finally, another intriguing aspect refers to handling of states that could be tentatively characterized as unknown, in a confrontation similar to the previous defective state but also different, since now this(these) cell(s) are not stated as faulty but unknown. As a result, a new one-dimensional CA with less states, compared to the previous CA defective algorithms, able to synchronize the maximal possible number of cells in each part occurs.     

On the gradient elastic wave propagation in cylindrical waveguides with microstructure

The present work describes the development of a complete theoretical framework of wave propagation in cylindrical waveguides possessing microstructure. In parallel, a thorough investigation of the full 3-D model of wave propagation in cylinders is presented. The first step is the spectral decomposition of the boundary value problem emerging via wave propagation analysis. The spectral representation of the specific gradient elasticity problem reflects the ability to construct all the possible propagating modes in cylindrical geometry. Several byproducts arise along the present work, which constitute generalizations of well known important features of classical elasticity and are indispensable for modeling the gradient elasticity problem. We note the construction of the set of dyadic Navier eigenfunctions which constitute the generalization of the Navier eigenvectors. The restriction of the Navier eigendyadics on cylindrical surfaces gives birth to the dyadic cylindrical harmonics, which constitute the generalization of the well known vector harmonics. This set is also a basis in the sense that the trace of every dyadic field on a cylindrical surface can be represented as a countable superposition of dyadic cylindrical harmonics. The method aims at providing the necessary theoretical establishment for the determination of the dispersion curves emerging in cortical bones.     

Mathematical investigation of interfacial property in fiber reinforced model composites

In the current paper, we have investigated the dependence of the effective elastic properties of a composite material on the fiber/matrix interface elastic property. The model composite consists of a single cylindrical fiber embedded in a concentric cylindrical matrix material. A three dimensional mathematical method has been developed connecting the interface properties with the effective axial Young’s modulus of the composite structure. Special effort has been devoted to decode information about the quality of the interface by exploiting the information provided by the elastic effective parameters. In particular, the effective modulus vs. stiffness coefficient curves have been generated for Ti/SiC composites. The aforementioned curves reveal the characteristics of the transition from the regime of perfect interface to the realm of complete debonding.     

A model for the dc electrical behavior of bulk-barrier diodes

Contents  This paper presents an analytical model for the dc electrical behavior of bulk barrier diodes (BBD's). The proposed model extends previously published models, and includes analytical expressions for all significant quantities of the device dc performance, i.e. barrier height, current density and ideality factor, with respect to the technological parameters and the applied voltage in both bias conditions. The analytical results have been compared with those obtained using the 2-D device simulator S-PISCES, which takes into account the drift–diffusion theory, as well as a concentration and field dependent mobility, the Shockley–Read–Hall and Auger carrier recombination, and the band gab narrowing. Good agreement was obtained between theory and simulation. The device simulation played a very important role in best understanding BBD's behavior, because it could easily take into account parameters strongly affecting the behavior of BBD's, e.g. the free carrier presence in depletion layers, which was very difficult for the analytical model to include. Received: 15 January 2001     

The effect of acetylation on the Janka hardness of pine wood

This paper addressed the effect of chemical modification with acetic anhydride on Janka hardness of pine wood, a less studied mechanical property. It was found that acetylation did not significantly affect the hardness of wood.     

Simulation,model‐reduction,and state estimation of a two‐component coagulation process

The issue of state estimation of an aggregation process through (1) using model reduction to obtain a tractable approximation of the governing dynamics and (2) designing a fast moving‐horizon estimator for the reduced‐order model is addressed. The method of moments is first used to reduce the governing integro‐differential equation down to a nonlinear ordinary differential equation. This reduced‐order model is then simulated for both batch and continuous processes and the results are shown to agree with constant Number Monte Carlo simulation results of the original model. Next, the states of the reduced order model are estimated in a moving horizon estimation approach. For this purpose, Carleman linearization is first employed and the nonlinear system is represented in a bilinear form. This representation lessens the computation burden of the estimation problem by allowing for analytical solution of the state variables as well as sensitivities with respect to decision variables. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1557–1567, 2016