Modelling and simulation of gas dynamics in an exhaust pipe

The gas dynamics in an exhaust pipe is studied. In particular we focus on the warm up of the catalytic converter in very short times after the engine start. This is done by combustion a small unburnt part of the exhaust gas. This process is classically modelled by gas dynamic equations. Compared to the existing literature we improve the (one-dimensional) modelling approach using a small Mach number technique and a network ansatz for the full exhaust pipe. The final simplified model on one hand still describes the main features and on the other hand it is computationally a few orders of magnitude faster than the original model. Performing numerical simulations we compare the new model to the (classical) full model and to experimental results in the literature.     

A note on commutators of Hardy operators

Fu and Lu et al. 7 showed that the commutator $\mathcal {H}_{\beta ,b}$ generated by the fractional Hardy operator and a locally integrable function b is bounded on the homogenous Herz spaces if and only if b is a central bounded mean oscillation function. We show that their result is optimal by giving a counterexample.     

Investigation on slot-die coating of hybrid material structure for OLED lightings

With an attempt to fabricate large-area OLED lighting panels, we investigate slot-die coating of a small molecule (SM) hole transport layer (HTL). It is observed that SM HTL films formed by spin coating exhibit pinhole-like surface, whereas the films by slot-die coating show micro-sized hillocks due to agglomeration. As the plate temperature of the slot coater is increased, smaller hillocks appear more densely. To tackle it, a small amount of a polymer HTL is added into the SM HTL (Hybrid HTL). By the aid of entangled polymer chains, small molecules are prohibited from migrating and thus agglomerations disappear. The peak-to-peak roughness of the slot-coated hybrid HTL films is measured to be about 11.5 nm, which is slightly higher than that (~7 nm) of the polymer HTL film, but much lower than that (~1071 nm) of the SM HTL film. Similar results are also observed in spin-coated films. It is also addressed that OLED with the hybrid HTL shows higher luminous efficacy, compared to OLED with the SM HTL or the polymer HTL. We have further demonstrated that the dissolution problem occurring between two stacked layers with different solvents during slot-die coating can be suppressed to a great extent using such a combination of materials in hybrid structure.     

On actions of Drinfel'd doubles on finite dimensional algebras

Let q be an nth root of unity for $n>2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of $T_n(q)$. We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel $u_q({\mathfrak{sl}}_2)$.     

Quasipatterns versus superlattices resulting from the superposition of two hexagonal patterns

We present a short review of the experimental observations and mechanisms related to the generation of quasipatterns and superlattices by the Faraday instability with two-frequency forcing. We show how two-frequency forcing makes possible triad interactions that generate hexagonal patterns, twelvefold quasipatterns or superlattices that consist of two hexagonal patterns rotated by an angle α relative to each other. We then consider which patterns could be observed when α does not belong to the set of prescribed values that give rise to periodic superlattices. Using the Swift–Hohenberg equation as a model, we find that quasipattern solutions exist for nearly all values of α. However, these quasipatterns have not been observed in experiments with the Faraday instability for $\alpha \ne \mathrm{\pi }/6$. We discuss possible reasons and mention a simpler framework that could give some hint about this problem.     

Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Tailoring the morphology and properties of waterborne polyurethanes by the procedure of cellulose nanocrystal incorporation

Polyurethane waterborne synthesis was performed using a two-step method, commonly referred to as a prepolymer method. Nanocomposites based on waterborne polyurethane and cellulose nanocrystals were prepared by the prepolymer method by altering the mode and step in which the nanofillers were incorporated during the polyurethane formation. The morphology, structural, thermal, and mechanical properties of the resulting nanocomposite films were evaluated by Fourier transform infrared spectroscopy (FTIR), small angle X-ray scattering (SAXS), scanning electron microscopy (SEM), and tensile tests. FTIR results indicated that the degree of interaction between the nanofillers and the WPU through hydrogen bonds could be controlled by the method of cellulose nanocrystal incorporation. Data obtained from SAXS experiments showed that the cellulose nanocrystals as well as the step of the reaction in which they are added influenced the morphology of the polyurethane. The reinforcing effect of CNCs on the nanocomposites depends on their morphology.     

Chiral bidiaziridines by a two-step domino aziridination of meso-α-diimines

Chiral racemic α-diimines, tested in aziridination reactions with NsONHCO₂Et, for the first time led to the synthesis of (±)-bidiaziridines, stereoselectively derived from the corresponding meso (E-s-trans-E)-α-diimines. Moreover, a minor bidiaziridine isomer, probably a meso form that was lost under classical work-up conditions, can be obtained by adding water to the crude mixtures at the end of amination reactions. The results definitively prove that the imine aziridination by carbamates is a two-step domino process. The structures of the compounds were determined using 2D NMR on purified bidiaziridines.     

Small‐Angle Neutron Scattering (SANS) Study of Magneto‐Vesicles

Small‐angle neutron scattering from magneto‐vesicles (MVs) prepared by extrusion was studied. Contrast variation allowed the determination of structure and sizes of the vesicles and the encapsulated magnetic nanoparticles, respectively. The results from MVs synthesized with a 0.3% volume fraction of citrate‐coated magnetic nanoparticles are compared to those of similarly prepared vesicles of the neutral lipid 1,2‐Dioleoyl‐sn‐Glycero‐3‐Phosphocholine (DOPC) (without magnetic particles), and magnetic particles not encapsulated in vesicles. It is observed that the bilayers of the as‐prepared MVs, and the encapsulated nanoparticles retain their structural properties, highlighting the suitability of the MVs for applications.     

An infrared small target detection algorithm based on high-speed local contrast method

Small-target detection in infrared imagery with a complex background is always an important task in remote sensing fields. It is important to improve the detection capabilities such as detection rate, false alarm rate, and speed. However, current algorithms usually improve one or two of the detection capabilities while sacrificing the other. In this letter, an Infrared (IR) small target detection algorithm with two layers inspired by Human Visual System (HVS) is proposed to balance those detection capabilities. The first layer uses high speed simplified local contrast method to select significant information. And the second layer uses machine learning classifier to separate targets from background clutters. Experimental results show the proposed algorithm pursue good performance in detection rate, false alarm rate and speed simultaneously.