Localization Properties of a Quasiperiodic Ladder under Physical Gain and Loss: Tuning of Critical Points, Mixed-Phase Zone and Mobility Edge

We explore the localization properties of a double-stranded ladder within a tight-binding framework where the site energies of different lattice sites are distributed in the cosine form following the Aubry–André–Harper (AAH) model. An imaginary site energy, which can be positive or negative, referred to as physical gain or loss, is included in each of these lattice sites which makes the system a non-Hermitian (NH) one. Depending on the distribution of imaginary site energies, we obtain balanced and imbalanced NH ladders of different types, and for all these cases, we critically investigate localization phenomena. Each ladder can be decoupled into two effective one-dimensional (1D) chains which exhibit two distinct critical points of transition from metallic to insulating (MI) phase. Because of the existence of two distinct critical points, a mixed-phase (MP) zone emerges which yields the possibility of getting a mobility edge (ME). The conducting behaviors of different energy eigenstates are investigated in terms of inverse participation ratio (IPR). The critical points and thus the MP window can be selectively controlled by tuning the strength of the imaginary site energies which brings a new insight into the localization aspect. A brief discussion on phase transition considering a multi-stranded ladder was also given as a general case, to make the present communication a self-contained one. Our theoretical analysis can be utilized to investigate the localization phenomena in different kinds of simple and complex quasicrystals in the presence of physical gain and/or loss.

Comparison of the focused optical vortices produced by high-aperture phase conventional and spiral zone plates

Using the FDTD simulation, sharp focusing of a linearly polarized Gaussian beam with an embedded topological charge m = 3 by a phase zone plate and focusing of a Gaussian beam by a phase spiral zone plate with topological charge m = 3 were studied. The obtained results showed that proposed elements formed different patterns of intensity at a focal plane. The spiral zone plate forms a focal spot with three petals. At a distance of 13.5 μm from the focus, the lobe structure of the intensity (and energy flux) is replaced by an annular distribution.

A Multi-Level Non-Linear Solver for Complex Well Modelling

Complex well model has proved to be important for capturing the full physics in wellbore, including pressure losses, multiphase effects, and advanced device modelling. Numerical instability may be observed especially when the well is produced at a low rate from a highly productive multi-phase zone. In this paper, a new multi-level nonlinear solver is presented in a state-of-the-art parallel complex wellbore model for addressing some difficult numerical convergence problems. A sequential two-level nonlinear solver is implemented, where the inner solver is used to address the convergence in the constraint rate equation, and then the entire complex network is solved using an outer solver. Finally, the wellbore model is coupled with the grid solution explicitly, sequentially, or implicitly. This novel formulation is robust enough to greatly improve the numerical stability due to the lagging in the computation of mixture density in wellbore constraint rate equation and the variation in the fluid composition over Newton iterations in network nonlinear solver. The numerical challenge in the complex well model and the improvement of performance with the new nonlinear solver are demonstrated using reservoir simulation. Models with complex wells running into convergence problems are constructed and simulated. With this novel nonlinear solver, simulation gives much more reliable results on well productions without numerical oscillations and computational cost is much less.

Reusable rainwater quality at the Ikorodu area of Lagos, Nigeria: impact of first-flush and household treatment techniques

Water scarcity is a huge problem in Africa, and hence rainwater becomes a crucial water source for fulfilling basic human needs. However, less attention has been given by African countries to the effectiveness of common rainwater treatments to ensure the population's health. This study investigates the impact of different household treatment techniques (HHTTs), i.e. treatments by chlorine, boiling, alum, and combination of alum and chlorine, on its storage system using a case study at the Ikorodu area of Lagos state, which is a rural area in Nigeria. The first-flush quality has been particularly studied here, where the microbial reduction through its practice has been examined from five different roofs. One of the investigated roofs was from a residential building, and four were constructed for the purpose of this study. In this study, the physical parameters (i.e. total suspended solids and turbidity) and the microbial parameters (i.e. total coliform and Escherichia coli) of the collected rainwater have been investigated. From the results, it has been observed that: (1) the water quality at the free phase zone is better than that at the tank's bottom; (2) the combination of chlorine and alum gives the best rainwater quality after comparing the application of different HHTTs; and (3) a reduction of about 40% from the original contaminant load occurs in every 1 mm diversion.

The Theory of Naphthidogenesis: A Quantitative Model of the Catagenetic Evolution of Aquatic Organic Matter

—This study discusses the evolution of the composition of dispersed organic matter from the Bazhenov Formation (West Siberian petroleum basin) and the products of its catagenetic transformation on the basis of the balance and kinetic approaches to modeling of the catagenetic transformation of organic matter and its individual components, primarily kerogen. The results show that the variations in the elemental composition of kerogen and the extent of generation of both hydrocarbons and nonhydrocarbons can be quantitatively described using a simplified kinetic model. Preliminary estimates of the model parameters are given for the averaged Bazhenov-type kerogen. It is shown that numerical modeling of the catagenetic transformation of dispersed organic matter confirms the validity of the recognition of the main phase (zone) of oil generation and the main phase (zone) of gas generation.

Radial integral boundary element method for simulating phase change problem with mushy zone

A radial integral boundary element method (BEM) is used to simulate the phase change problem with a mushy zone in this paper. Three phases, including the solid phase, the liquid phase, and the mushy zone, are considered in the phase change problem. First, according to the continuity conditions of temperature and its gradient on the liquid-mushy interface, the mushy zone and the liquid phase in the simulation can be considered as a whole part, namely, the non-solid phase, and the change of latent heat is approximated by heat source which is dependent on temperature. Then, the precise integration BEM is used to obtain the differential equations in the solid phase zone and the non-solid phase zone, respectively. Moreover, an iterative predictor-corrector precise integration method (PIM) is needed to solve the differential equations and obtain the temperature field and the heat flux on the boundary. According to an energy balance equation and the velocity of the interface between the solid phase and the mushy zone, the front-tracking method is used to track the move of the interface. The interface between the liquid phase and the mushy zone is obtained by interpolation of the temperature field. Finally, four numerical examples are provided to assess the performance of the proposed numerical method.

Numerical Modeling of Sublimation of Ammonium Carbamate Applied to Supply System of NOx Reductant

Recently, ammonium carbamate (AC) has attracted attention as a substitute for urea, which is a commonly used reductant for NOx emitted from combustion engines. The AC exists as a solid at room temperature, and it is decomposed to NH3 and CO2 gases by heating. Therefore, adequate heat transfer is an essential issue in the design of AC pyrolysis reactor. In this study, a numerical model that describes the sublimation of AC was developed. For modeling, this study considered the three different calculation zones: solid-phase zone, gas-phase zone, and sublimation zone. Additionally, during the sublimation process, collapse of upper solid AC into the hollow space below by the effect of gravity is considered. As a result, it is presented that the modeling shows reasonable information about the AC sublimation in a reactor, such as temperatures in a reactor, pressure of reactor, and flow rate of sublimated gas. However, it is also found that accurate prediction of spatial temperature distribution is challenging because it is related to the accurate prediction of the internal shape of AC and its collapse in a reactor.

Devising manufacturing techniques to control the process of zonal segregation in large steel ingots

A method of physical modeling was applied to study the effect of external actions on the processes of crystallization and the formation of the structure of ingots. A brief review of existing hypotheses about the evolution of physical, structural, and chemical heterogeneities in large steel ingots is given. The parameters of the structure and the two-phase zone have been determined, as well as the nature of the distribution of segregated materials along the cross-section of ingots, depending on the conditions of their curing. The decisive importance of convective and capillary mass transfer in the interdendritic channels of hardening ingots on the formation of a zonal heterogeneity at their cross-section has been proven. Experimentally, when crystallizing a model environment (camphene), it has been visually confirmed that the flow of segregated materials in interdendritic channels occurs when a certain amount of impurities accumulates in them. A clear dependence of the speed of this flow on the rate of melt crystallization has been established. With an increase of the hardened part of the melt, the rate of segregated material movement (Vl) increases while the rate of crystallization (R) decreases due to worsening heat release conditions. At a certain distance from the ingot’s surface, these rates become equal, and impurities are carried to the curing border, which is the main cause of the formation of zonal segregation. The results reported here show that the evolution of zonal segregation in ingots can be controlled using various techniques involving external influence on the hardening melt. This study has demonstrated that the adjustable intensity of heat removal from an ingot, as well as the addition of external excess pressure on the hardening melt, could be used as such tools. In the study, to obtain ingots with a minimum level of chemical heterogeneity, it would suffice to provide the following conditions for the curing of the alloy: a value of the alloy crystallization speeds at the level of Rcr ≥ 9·10–2 mm/s, or external pressure on the free surface of ingots Рext. ≥ 135 kPa. The industrial implementation of the reported results could make it possible to improve the technology of obtaining large blacksmith ingots, provide savings in materials and energy resources, increase the yield of a suitable metal, and improve its quality

Effect of Third-Stage Heat Treatments on Microstructure and Properties of Dual-Phase Titanium Alloy

Two-phase TC21 titanium alloy samples were solution-treated at 990 °C (β phase zone) and cooled by furnace cooling (FC), air cooling (AC), and water quenching (WQ), respectively. The second solution stage treatment was carried out at 900 °C (α + β phase zone), then aging treatment was performed at 590 °C. The influence of the size and quantity of the α phase on the properties of the sample were studied. The experimental results showed as the cooling rate increased after the first solution stage treatment, wherein the thickness of primary layer α gradually decreased, and the tensile strength and yield strength gradually increased. After the second solution stage treatment, the tensile properties of samples increased due to the quantity of layers α increased. The aging treatment promoted the precipitation of the dispersed α phase and further improved the tensile strength. After the third solution stage treatments, the FC samples with more β-phase had the best comprehensive mechanical properties.

Dynamic Softening Mechanisms and Microstructure Evolution of TB18 Titanium Alloy during Uniaxial Hot Deformation

In this study, isothermal compression tests of TB18 titanium alloy were conducted using a Gleeble 3800 thermomechanical simulator for temperatures ranging from 650 to 880 °C and strain rates ranging from 0.001 to 10 s−1, with a constant height reduction of 60%, to investigate the dynamic softening mechanisms and hot workability of TB18 alloy. The results showed that the flow stress significantly decreased with an increasing deformation temperature and decreasing strain rate, which was affected by the competition between work hardening and dynamic softening. The hyperbolic sine Arrhenius-type constitutive equation was established, and the deformation activation energy was calculated to be 303.91 kJ·mol−1 in the (α + β) phase zone and 212.813 kJ·mol−1 in the β phase zone. The processing map constructed at a true strain of 0.9 exhibited stability and instability regions under the tested deformation conditions. The microstructure characteristics demonstrated that in the stability region, the dominant restoration and flow-softening mechanisms were the dynamic recovery of β phase and dynamic globularization of α grains below transus temperature, as well as the dynamic recovery and continuous dynamic recrystallization of β grains above transus temperature. In the instability region, the dynamic softening mechanism was flow localization in the form of a shear band and a deformation band caused by adiabatic heating.