A ternary square-free sequence avoiding factors equivalent to abcacbaabcacba

We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern $xyzxzyx$. In fact, we: (1) characterize all the (two-way) infinite ternary square-free words avoiding letter pattern $xyzxzyx$ (2) characterize the lexicographically least (one-way) infinite ternary square-free word avoiding letter pattern $xyzxzyx$ (3) show that the number of ternary square-free words of length $n$ avoiding letter pattern $xyzxzyx$ grows exponentially with $n$.Comment: 7 pages, 1 figur

Computing the Partial Word Avoidability Indices of Ternary Patterns

We study pattern avoidance in the context of partial words. The problem of classifying the avoidable binary patterns has been solved, so we move on to ternary and more general patterns. Our results, which are based on morphisms (iterated or not), determine all the ternary patterns' avoidability indices or at least give bounds for them

Understanding the Effect of Caesium Promotion on the Preparation and Activation of Copper-Based Low-Temperature Water-Gas Shift Catalysts

The water-gas shift (WGS) reaction has been extensively researched due to its widespread application. Its purpose is to yield the maximum amount of hydrogen, thermodynamically favoured at low temperatures, making the efficiency and stability of the Cu-based low-temperature shift (LTS) catalyst a necessity. Typically, commercial LTS catalysts are composed of CuO/ZnO/Al2O3 (molar ratio 0.6:0.3:0.1); however, this catalyst formulation is also used for methanol synthesis, making MeOH an undesirable by-product which can cause reactor degradation. Caesium promotion (ca. 1 wt.%) has been reported to inhibit this side reaction but is thought to lead to instability in the catalyst early on, making activation crucial. Initially, alterations to the CuO/ZnO/Al2O3 (molar ratio 0.6:0.3:0.1) coprecipitation method were investigated to determine which conditions afforded catalysts with comparable properties to those employed in industry. This ensured all activation tests were commercially relevant. Understanding how the microstructure of the active Cu0 component in the commercially applicable CuO/ZnO/Al2O3(-Cs2O) catalyst evolves under various H2 partial pressures in the presence/absence of Cs was determined at beamline ID15A, ESRF, where time-resolved 1D XRD and spatially-resolved XRD-CT (X-ray diffraction computed tomography) data were collected for [H2] of 1, 2.5 and 5 %. These were compared to catalysts with higher copper loading (CuO/ZnO/Al2O3(-Cs2O), molar ratio 0.8:0.1:0.1) to elucidate the importance of the zincite support and the effect of the promoter on sintering mechanisms, dislocation character and stacking fault probability. Steam incorporation during activation was also investigated in a commissioned reactor set-up to elucidate possible early onset deactivation mechanisms resulting from the Cs-promoter. The coprecipitation method was scaled-up in order to produce industrially relevant pellets for activation testing, which were then characterised using XRD, Hg porosimetry and mechanical strength testing. This highlighted the effects of phase segregation caused by Cs-incorporation, and the susceptibility of the ZnO support sintering in wet environments

A Ternary Square-free Sequence Avoiding Factors Equivalent to abcacba

We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern xyzxzyx. In fact, we characterize all the (two-way) infinite ternary square-free words avoiding letter pattern xyzxzyx characterize the lexicographically least (one-way) infinite ternary square-free word avoiding letter pattern xyzxzyx show that the number of ternary square-free words of length n avoiding letter pattern xyzxzyx grows exponentially with n.http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i2p4

A study of InAs based quantum structures for use in optoelectronic devices

Due to increasing demand of nanowires (NWs) in the areas of electrical and photonic devices applications, it is imperative to try to improve their properties that are found to degrade their device performances. This thesis provides an extensive investigation of InAs based NWs for use in the photodetection applications. To achieve this goal, the structural and optical properties of InAs NWs and InAs NW-based quantum materials (e.g., InAsSb NWs, InAs/AlSb NWs and InAs/GaSb core-shell NWs) have been investigated. The NW samples were grown by molecular beam epitaxy (MBE); self-catalysed droplet epitaxy was used as the growth mechanism for them. To improve the optical properties of InAs NWs, we further optimised the MBE growth for the NWs based on our previous growth understanding, which resulted in InAs NWs give strong room temperature photoluminescence (PL) at room temperature. We also notified that the substrate doping type gives significant effect on PL emission. In order to improve the axial growth rate for the epitaxy of NW devices, we developed a new 3-step growth technique: step 1 – droplet seeding, step – 2: NW growth initiation, step - 3 NW growth at high growth rate. The above new growth method yielded high quality InAs NWs with much higher axial growth rate compared to conventional growth methods. This method offers cost-effectiveness and reduction in time consumption. The NW samples grown by this method demonstrated denser, longer and enhanced optical properties. The thesis also studied the incorporation of Sb into the InAs NWs to synthesis InAsSb NWs which is very challenging but has many interesting device applications. Through comprehensive growth study, we demonstrated the realization of InAsSb NWs with increased Sb content through reducing growth rate of the NWs. For the first time, we produced optically active InAsSb NWs with 19% of Sb content which gives PL emission at a long wavelength of 5.1 훍m at 10 K. This achievement reveals that our InAsSb NWs could be used for infrared photodetectors and emitters operating in entire mid wavelength infrared spectral range (MWIR), e.g. 3-5 훍m. It is well known that NW structures suffer from severe surface states which degrade the resulting devices performance, due to the large surface to volume ratio. To overcome this problem, in this thesis, we developed several advanced NW-based quantum materials with a core-shell structure (heterojunction), e.g., the NW core is passivated with shell layer of different material. Two novel core-shell NW materials namely, InAs/AlSb and InAs/GaSb were grown. Transmission electron microscopy (TEM) and electron diffraction x-ray (EDX) confirmed the success of the core-shell structure. More importantly, the PL study indicates a massive enhancement in the PL emission, by 5 times in comparison with the bare InAs NWs. Temperature dependence PL measurements proved that surface states were significantly eliminated. Our core-shell NW structure is a great success in surface passivation. Mesa device of bare InAs NWs were fabricated and its current-voltage (I-V) were tested in room temperature. I-V measurements showed that the NW device is a working device with relatively high dark current of 0.0011A and negative photocurrent of (-8.9526×104A). Single NW field effect transistors (FET) were fabricated using bare InAs NWs and InAs/ AlSb core-shell NWs and operated as photodetectors. The dark current measurements reveal that the bare InAs NW device gives a high dark current 1.5×10-6 A, while the core-shell NW device has a much more supressed dark current of 2.8×10-8 A, which is 186 times less than bare InAs NW device. This is a further evidence of the surface passivation induced by the shell layer, which is important for fabricating photodetectors with high directivity. The photocurrent study show that the bare InAs device gives a photocurrent of 0.2 um leading to a signal-to-noise ratio of 13%, while core-shell NW devices exhibited anomalous photocurrent behaviour, e.g. The device gives a signal-to-noise ratio of 80%, which is 6 times higher than the bare InAs NW device. These striking device properties were attributed to the efficient surface passivation caused by the shell layer of the materials. The anomalous photocurrent behavior was attributed to the trap centres in the shell layer. Our study demonstrates the great potential of the core-shell structure in the use of highly efficient infrared photodetectors