On numerical approximation using differential equations with piecewise-constant arguments

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for stability and oscillation of a class of linear delay equations with continuous and piecewise constant arguments. This research was partially supported by Hungarian NFSR Grant No. T046929.     

Realization of an advanced nozzle concept for compact chemical oxygen iodine laser

Conventional supersonic chemical oxygen–iodine lasers (SCOIL) are not only low-pressure systems, with cavity pressure of 2–3 Torr and Mach number of approximately 1.5, but also are high-throughput systems with a typical laser power per unit evacuation capacity of nearly 1 J/l, thus demanding high capacity vacuum systems which mainly determine the compactness of the system. These conventional nozzle-based systems usually require a minimum of a two-stage ejector system for realization of atmospheric pressure recovery in a SCOIL. Typically for a 500 W class SCOIL, a first stage requires a motive gas flow (air) of 120 gm/s to entrain a laser gas flow of 3 g/s and is capable of achieving the pressure recovery in the range of 60–80 Torr. On the other hand, the second stage ejector requires 4.5 kg/s of motive gas (air) to achieve atmospheric pressure recovery. An advanced nozzle, also known as ejector nozzle, suitable for a 500 W-class SCOIL employing an active medium flow of nearly 12 g/s, has been developed and used instead of a conventional slit nozzle. The nozzle has been tested in both cold as well as hot run conditions of SCOIL, achieving a typical cavity pressure of nearly 10 Torr, stagnation pressure of approximately 85 Torr and a cavity Mach number of 2.5. The present study details the gas dynamic aspects of this ejector nozzle and highlights its potential as a SCOIL pressure recovery device. This nozzle in conjunction with a diffuser is capable of achieving pressure recovery equivalent to a more cumbersome first stage of the pressure recovery system used in the case of a conventional slit nozzle-based system. Thus, use of this nozzle in place of a conventional slit nozzle can achieve atmospheric discharge using a single stage ejector system, thereby making the pressure recovery system quite compact.     

Stability of Attractive Bose–Einstein Condensates

We propose the critical nonlinear Schrödinger equation with a harmonic potential as a model of attractive Bose–Einstein condensates. By an elaborate mathematical analysis we show that a sharp stability threshold exists with respect to the number of condensate particles. The value of the threshold agrees with the existing experimental data. Moreover with this threshold we prove that a ground state of the condensate exists and is orbital stable. We also evaluate the minimum of the condensate energy.     

Hybrid reactor based on combined cavitation and ozonation: From concept to practical reality

The present work gives an in depth discussion related to the development of a hybrid advanced oxidation reactor, which can be effectively used for the treatment of various types of water. The reactor is based on the principle of intensifying degradation/disinfection using a combination of hydrodynamic cavitation, acoustic cavitation, ozone injection and electrochemical oxidation/precipitation. Theoretical studies have been presented to highlight the uniform distribution of the cavitational activity and enhanced generation of hydroxyl radicals in the cavitation zone, as well as higher turbulence in the main reactor zone. The combination of these different oxidation technologies have been shown to result in enhanced water treatment ability, which can be attributed to the enhanced generation of hydroxyl radicals, enhanced contact of ozone and contaminants, and the elimination of mass transfer resistances during electrochemical oxidation/precipitation. Compared to the use of individual approaches, the hybrid reactor is expected to intensify the treatment process by 5–20 times, depending on the application in question, which can be confirmed based on the literature illustrations. Also, the use of Ozonix® has been successfully proven while processing recycled fluids at commercial sites on over 750 oil and natural gas wells during hydraulic operations around the United States. The superiority of the hybrid process over conventional chemical treatments in terms of bacteria and scale reduction as well as increased water flowability and better chemical compatibility, which is a key requirement for oil and gas applications, has been established.     

Analytical and numerical stability of partial differential equations with piecewise constant arguments

This article is concerned with the stability analysis of the analytic and numerical solutions of a partial differential equation with piecewise constant arguments of mixed type. First, by means of the similar technique in Wiener and Debnath [Int J Math Math Sci 15 (1992), 781–788], the sufficient conditions under which the analytic solutions asymptotically stable are obtained. Then, the θ‐methods are used to solve the above‐mentioned equation, the sufficient conditions for the asymptotic stability of numerical methods are derived. Finally, some numerical experiments are given to demonstrate the conclusions.Copyright © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1‐16, 2014     

EXISTENCE OF PERIODIC SOLUTIONS TO THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION

By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differential equation with deviating arguments are obtained.     

Photo oxidative degradation of azure-B by sono-photo-Fenton and photo-Fenton reagents

A model for the decomposition of azure-B by photo-Fenton reagent in the presence of ultrasound in homogeneous aqueous solution has been described. The photochemical decomposition rate of azure-B is markedly increased in the presence of ultrasound. It is a rather inexpensive reagent for wastewater treatment. The effect of different variables like the concentration of ferric ion, concentration of dye, hydrogen peroxide, pH, light intensity etc. on the reaction rate has been observed. The progress of the sono-photochemical degradation was monitored spectrophotometrically. The optimum sono-photochemical degradation conditions were experimentally determined. The results showed that the dye was completely oxidized and degraded into CO₂ and H₂O. A suitable tentative mechanism for sono-photochemical bleaching of azure-B by sono-photo-Fenton’s reaction has been proposed.     

Progress of Copper-based Nanocatalysts in Advanced Oxidation Degraded Organic Pollutants

To address global pollution caused by contaminants in water bodies, it is crucial to develop an efficient and environmentally friendly treatment process for wastewater from various industries. Advanced oxidation processes (AOPs) have proven to be highly effective in wastewater treatment due to their high oxidation efficacy and the absence of secondary pollutants. Different methods such as ozone, Fenton, electrochemical, photolysis, and sonolysis can be used in AOPs to degrade emerging pollutants that are resistant to conventional methods. In recent years, nanotechnology has emerged as a viable solution, with various nanomaterials being developed for wastewater treatment. Among them, copper-based nanocatalysts have shown great potential in AOPs. This review focuses on the progress and mechanisms of copper-based nanocatalysts in wastewater treatment via AOPs. It also discusses the challenges associated with oxidation, electrochemistry, Fenton, and photocatalysis in wastewater treatment processes. Copper-based nanocatalysts can be modified to enhance their catalytic activity, selectivity, and stability, leading to improved performance in wastewater treatment. They have shown promising results in degrading pollutants like pharmaceuticals, pesticides, and dyes. However, the practical application of these nanocatalysts still faces challenges, including the high cost of synthesis, potential nanoparticle toxicity, and scalability issues. More research is needed to address these challenges and improve the utilization of copper-based nanocatalysts in wastewater treatment. In addition, Cu-based catalysts with magnetic properties offer the advantage of easy recovery and reusability in wastewater treatment. They can also be incorporated into catalytic membranes, forming efficient systems for recycling. Heterogeneous catalysts with diverse structures, including ternary or quaternary systems, are widely used. However, challenges remain in identifying suitable coupling pairs and understanding the complex processes involved in constructing heterogeneous interfaces without generating defects. Therefore, a thorough understanding of the catalyst‘s band structure is crucial for developing efficient heterogeneous structures. Furthermore, cost implications of synthesis methods and raw materials should be considered in the preparation of transition metal catalysts, and relevant cost analysis data is needed for optimizing the degradation of pollutants. In conclusion, copper-based nanocatalysts hold great potential in AOPs for wastewater treatment. With their magnetic properties, Cu-based catalysts offer the advantage of easy recovery and reusability. However, challenges such as high synthesis costs, nanoparticle toxicity, and scalability issues need to be addressed. Further research is needed to overcome these challenges and optimize the utilization of copper-based nanocatalysts in wastewater treatment processes.