In situ 2-D piezoelectric wafer active sensors arrays for guided wave damage detection

This paper presented development work of an in situ method for damage detection in thin-wall structures using embedded two-dimensional ultrasonic phased arrays. Piezoelectric wafer active sensors were used to generate and receive guided Lamb waves propagating in the plate-like structure. The development of a generic beamforming algorithm that does not require parallel ray assumption through using full wave propagation paths is described. A virtual beam steering method and device, the embedded ultrasonic structural radar, was implemented as a signal post-processing procedure. Several two-dimensional configurations were investigated and compared with beamforming simulation. Finally, rectangular shape arrays were developed for verifying the generic formulas and omnidirectionality. The rectangular arrays yield good directionality within the 360° full range and are able to detect damage anywhere in the entire plate.     

Gallai’s path decomposition conjecture for triangle-free planar graphs

A path decomposition of a graph $G$ is a collection of edge-disjoint paths of $G$ that covers the edge set of $G$. Gallai (1968) conjectured that every connected graph on $n$ vertices admits a path decomposition of cardinality at most $?(n+1)∕2?$. Gallai’s Conjecture has been verified for many classes of graphs. In particular, Lovász (1968) verified this conjecture for graphs with at most one vertex with even degree, and Pyber (1996) verified it for graphs in which every cycle contains a vertex with odd degree. Recently, Bonamy and Perrett (2016) verified Gallai’s Conjecture for graphs with maximum degree at most 5, and Botler et al. (2017) verified it for graphs with treewidth at most 3. In this paper, we verify Gallai’s Conjecture for triangle-free planar graphs.     

Linearizability of planar polynomial Hamiltonian systems

Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for the linearization of a polynomial system. Using computer algebra systems we provide necessary and sufficient conditions for linearizability of Hamiltonian systems with homogeneous non-linearities of degrees 5, 6 and 7. We also present some sufficient conditions for systems with nonhomogeneous nonlinearities of degrees two, three and five.     

Studying the Electrically Driven Switching of the Planar Light Guide

Liquid crystalline materials can be used as an active media for the new generation of planar light guides. The main characteristics which governs light-guiding and switching abilities of such devices are the spatial distributions of the refraction indices (defined via the distribution of nematic director) for the liquid crystal confined within a light-guiding pore. We aim to obtain these distributions from the molecular dynamics simulation of the liquid crystalline cell with the homeotropic boundary conditions being applied. We discuss the reorientation kinetics of the homeotropic-planar transition and obtain the equilibrium director profile upon application of the planar reorienting field.     

Existence and stability of spatially localized patterns

Spatially localized patterns have been observed in numerous physical contexts, and their bifurcation diagrams often exhibit similar snaking behavior: symmetric solution branches, connected by bifurcating asymmetric solution branches, wind back and forth in an appropriate parameter. Previous papers have addressed existence of such solutions; here we address their stability, taking the necessary first step of unifying existence and uniqueness proofs for symmetric and asymmetric solutions. We then show that, under appropriate assumptions, temporal eigenvalues of the front and back underlying a localized solution are added with multiplicity in the right half plane. In a companion paper, we analyze the behavior of eigenvalues at $\lambda =0$ and inside the essential spectrum. Our results show that localized snaking solutions are stable if, and only if, the underlying fronts and backs are stable: unlike localized non-oscillatory solutions, no interaction eigenvalues are present. We use the planar Swift–Hohenberg system to illustrate our results.     

Emergence of a non-Fowler-Nordheim-type behavior for a general planar tunneling barrier

In this work we investigate a generalized tunneling barrier for planar emitters at zero-temperature. We present the evidence of the emergence of a non-Fowler-Nordheim-type general behavior for the field emission current density in the case that the Fermi energy (μ) is comparable with or smaller that the decay width ($d_F$). Therefore, for some non-metals or materials that have very small Fermi energy the standard Fowler-Nordheim-type theory may require a correction. In the opposite regime, i.e., for μ much larger that $d_F$, we confirm that the conventional theory is suitable for metals.     

Simplified fabrication of high areal capacitance all-solid-state micro-supercapacitors based on graphene and MnO2 nanosheets

A universal simplified strategy was developed to fabricate all-solid-state planar micro-supercapacitors with high areal capacitance (~355 mF/cm²), based on interdigital patterned films of 2D pseudocapacitive MnO₂ nanosheets and electrochemically exfoliated graphene.     

Model Biological Membranes and Possibilities of Application of Electrochemical Impedance Spectroscopy for their Characterization

Biological membranes are essential parts of living systems. They represent an interface between intracellular and extracellular space. Depending on their structure, they often perform very complex functions and play an important role in the transport of both charged and uncharged particles in any organism. Structure of the biological membranes, which play very important role in electrochemical processes inside living organisms, is very complicated and still not precisely defined and explained. Model lipid membranes are used to gain detail information about properties of real biological membranes and about associated electrochemical processes. Electrochemistry, especially electrochemical impedance spectroscopy (EIS), can play a useful role in the characterization of properties of model lipid membranes (planar and supported lipid bilayers, tethered lipid membranes, liposomes, etc.). This review is focused on model biological membranes and the possibilities and limitations of electrochemical methods and namely of EIS in this field.     

Intramolecular N−H...O hydrogen bonding,quinoid effect,and partial π-electron delocalization in N-aryl Schiff bases of 2-hydroxy-1-naphthaldehyde: the crystal structures of planar N-(α-naphthyl)- and N-(β-naphthyl)-2-oxy-1-naphthaldimine

The structures of N-(-naphthyl)-2-oxy-1-naphthaldimine1 and N-(-naphthyl)-2-oxy-1-naphthaldimine2 have been investigated by X-ray analysis and by spectroscopic methods. Crystals of1 are monoclinic, space groupPn, with cell dimensionsa=10.823(3),b=5.826(2),c=11.899 (3) Å, and =99.66(3)°. Compound2 crystallizes in the orthorhombic space groupPca2₁ witha=17.564(3),b=6.314(2), andc=13.663(4) Å. The IR spectra exhibited neither N–H nor O–H stretching frequencies. The existence of theintramolecular hydrogen bonding of N–H...O type was predicted by spectroscopic experiment but unequivocally established by diffraction experiment in both cases1 and2. The molecules1 and2 are significantly planar with considerable quinoid effect at the 2-oxy-naphthaldimine moiety. Although essentially planar, both molecules1 and2 show the delocalization of -electrons only in the central part of the molecules including C=N imino group with pendent ring carbon atoms.Intermolecular attractions in the crystals belong to weak van der Waals interactions-between discrete planar molecules spatially arranged into the expectedherringbone motif in the solid state.     

Progress in planar electrochromatography

Developments in planar electrochromatography in open (PEC) and closed (PPEC) systems are reviewed. The discussion focuses on progress in chamber construction for planar electrochromatography, separating system performance, equilibration of the PPEC process, separation time and selectivity, and the general advantages, disadvantages and prospects of this separation mode. Presented at the 11th International Conference on Chemistry and the Environment, 9–12 September 2007, Torum, Poland.