Three‐dimensional sloshing: A consistent finite element approach

This paper presents a new computational methodology based on Legendre's polynomials to predict the slosh and acoustic motion in nearly incompressible fluids in both rigid and flexible structures with free surface. Here, we have used a finite element formulation based on Lagrangian frame of reference to model the fluid motion derived using Hamiltonian equation of the fluid system. We formulated three hexahedral finite elements based on strain fields expressed in terms of extended Legendre's polynomials. Sloshing and acoustic motion of liquid is investigated using these newly formulated elements and inf–sup test is performed on these new elements to check the performance of these elements in modeling sloshing under two severe constraints, namely incompressibility and irrotationality. Comparisons of slosh and acoustic frequencies, and mode shapes with exact solutions are given. Dynamic analysis with earthquake and harmonic kind of forcing function is carried out to validate the formulated hexahedral elements to analyze the sloshing response. Numerical results obtained with these new finite elements, and with the present finite element formulation of the mathematical model agree well with the exact solution and as well as with published experimental literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Hille and Nehari type criteria for third-order delay dynamic equations

The objective of this note is to present new Hille and Nehari type asymptotic criteria for a class of third-order delay dynamic equations on a time scale. Assumptions in our theorems are less restrictive, whereas the proofs are significantly simpler compared to those reported in the literature. The results obtained extend and improve some previous results.     

Main-chain biodegradable liquid crystal derived from cholesteryl derivative end-capped poly(trimethylene carbonate): synthesis and characterisation

Main-chain biodegradable liquid crystal derived from cholesteryl derivative end-capped poly(trimethylene carbonate) was investigated. The novel liquid crystal was synthesised via ring-opening polymerisation of trimethylene carbonate initiated by cholesteryl derivative with an alkyl spacer and end primary hydroxyl group, without any catalyst. The chemical structure of resulting polymers was verified by ¹H NMR. Liquid crystalline properties were validated by X-ray diffraction, differential scanning calorimetry, and polarising optical microscopy. The results showed that all the synthesised polymers Chol-(CH₂)₂-(TMC)_n exhibited mesomorphism in particular temperature ranges because of the introduction of the cholesteryl derivative moiety.     

Network dilution and asymmetry in an efficient brain

ABSTRACT

The ultimate goal of neuroscience is to ultimately understand how the brain functions. The advancement of brain imaging shows us how the brain continuously alternates complex activity patterns and experimentally reveals how these patterns are responsible for memory, association, reasoning, and countless other tasks. Two fundamental parameters, dilution (the number of connections per node), and symmetry (the number of bidirectional connections of the same weight) characterise two fundamental features underlying the networks that connect the single neurons in the brain and generate these patterns. Mammalian brains show large variations of dilution, and mostly asymmetric connectivity, unfortunately the advantages which drove evolution to these state of network dilution and asymmetry are still unknown. Here, we studied the effects of symmetry and dilution on a discrete-time recurrent neural network with McCulloch–Pitts neurons. We use an exhaustive approach, in which we probe all possible inputs for several randomly connected neuron networks with different degrees of dilution and symmetry. We find an optimum value for the synaptic dilution and symmetry, which turns out to be in striking quantitative agreement with what previous researchers have found in the brain cortex, neocortex and hippocampus. The diluted asymmetric brain shows high memory capacity and pattern recognition speed, but most of all it is the less energy-consumptive with respect to fully connected and symmetric network topologies.     

On the rates of decay to equilibrium in degenerate and defective Fokker–Planck equations

We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker–Planck equations and show that, much like defective finite dimensional ODEs, their decay rate is an exponential multiplied by a polynomial in time. The novelty of our study lies in the amalgamation of spectral theory and a quantitative non-symmetric hypercontractivity result, as opposed to the usual approach of the entropy method.     

Multiscale characterization of dislocation processes in Al 5754

Multiscale characterization was performed on an Al–Mg alloy, Al 5754 O-temper, including in situ mechanical deformation in both the scanning electron microscope and the transmission electron microscope. Scanning electron microscopy characterization showed corresponding inhomogeneity in the dislocation and Mg distribution, with higher levels of Mg correlating with elevated levels of dislocation density. At the nanoscale, in situ transmission electron microscopy straining experiments showed that dislocation propagation through the Al matrix is characterized by frequent interactions with obstacles smaller than the imaging resolution that resulted in the formation of dislocation debris in the form of dislocation loops. Post-mortem chemical characterization and comparison to dislocation loop behaviour in an Al–Cr alloy suggests that these obstacles are small Mg clusters. Previous theoretical work and indirect experimental evidence have suggested that these Mg nanoclusters are important factors contributing to strain instabilities in Al–Mg alloys. This study provides direct experimental characterization of the interaction of glissile dislocations with these nanoclusters and the stress needed for dislocations to overcome them.     

Effect of relative humidity on mechanical properties of a woven thermoplastic composite for automotive application

The purpose of this work is to characterise the influence of moisture content in a woven glass fibre reinforced polyamide 6,6 composite. Two different stacking sequences are studied: [(0/90)₃] and [(±45)₃] as well as the neat PA6,6 matrix. Samples have been conditioned through three ways: either water immersed, left at ambient temperature and humidity or dried in 35 °C oven. A one dimensional Fick's law has been used to model the water uptake in immersed samples. The glass transition temperature is highly affected by the presence of water and has been measured using modulated DSC technique. Finally, the effects of water on these composite materials have been investigated through tensile tests instrumented with acoustic emission monitoring (AE). Mechanical properties are highly affected by the presence of water in the composite. This result is even more visible on [(±45)₃] sample because of the preferential loading of the matrix.     

Kojic acid—a new fragment for the preparation of bent‐core mesogens

Kojic acid was used to synthesize bent‐core mesogens. Antiferroelectric polar smectic mesophases, an oblique and a rectangular columnar mesophase were found. The mesophases were characterized by X‐ray scattering, electro‐optical measurements, polarizing microscopy and DSC. On the base of these measurements, models of the mesophases are proposed.