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.     

Synthesis and mesomorphic properties of bent-shaped molecule with low bent-angle central core and long alkylthio tail

Two homologous series of bent-shaped molecules composed of low bent-angle naphthalene central core and long alkoxy tail or alkylthio tail,N（1,7）-n-OPIMB and N（1,7）-n-SPIMB（n = 20,22）,respectively,were synthesized.The mesomorphic properties were investigated by differential scanning calorimetry（DSC）,polarizing optical microscopy（POM） and X-ray diffraction（XRD）. Compared to the direct transition from the isotropic phase to the chiral B4 phase examined in N（1,7）-n-OPIMB,N（1,7）-n-SPIMB exhibited a rare Iso-N_col-Col_h-B4 phase sequence.The combination of the asymmetric low bent-angle 1,7-naphathalene central core and the flexible long alkylthio tail is considered to play an important role in the formation of such a novel phase sequence.     

Experimental investigation and modelling of compressibility induced by damage in carbon black-reinforced natural rubber

While natural rubber is commonly considered as an incompressible material, this study shows how carbon black-reinforced natural rubber (NR-CB), when subjected to various mechanical loading conditions (uniaxial, hydrostatic, monotonic, cyclic), is affected by volume change. Experiments show a volume variation even for low straining values and a significant volume change for large elongations. Moreover, volume change can be either reversible or not, depending on the loading conditions. It is related to a competition between void growth, chain orientation, and stress softening. At a microscopic scale, in situ Scanning Electron Microscopy (SEM) examinations and image analysis allow one to record damage and microscopic volume change as a function of elongation. Therefore the volume change measured at the microscopic scale is equal to the macroscopic one. Based on the experimental results, this paper shows that the hypothesis of incompressibility is worth being revisited. Thus, a nearly compressible approach was considered, where the strain energy is assumed to be the sum of spherical and deviatoric parts that are both affected by damage. The model was then implemented in a finite-element code. Good agreement was obtained between experimental results and model predictions for low triaxiality test conditions.     

Control of a novel fractional hyperchaotic system using a located control method

Fractional order dynamics and chaotics systems have been recently combined, yielding interesting behaviours. In this paper, a novel integer order hyperchaotic system is considered. Then, a fractional order hyperchaotic representation of said system is proposed using a natural fractionalization. Two different linear control methodologies to deal with the complexity which introduce such systems are proposed. Those methods are able to modify the hyperchaotic behaviour of the system and force it to move towards a fixed point; i.e. steady state. These approaches give a general framework for taming such complex systems using simple linear controllers. The main tools for analysing the controlled system are Matignon stability criterion and RouthHurwitz test. Using a reliable numerical simulation, the designed system is simulated to verify the theoretical analysis.