A hyperchaotic system without equilibrium

Abstract: This article introduces a new chaotic system of 4-D autonomous ordinary differential equations, which has no equilibrium. This system shows a hyper-chaotic attractor. There is no sink in this system as there is no equilibrium. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. There is little difference between this chaotic system and other chaotic systems with one or several equilibria shown by phase portraits, Lyapunov exponents and time series methods, but the Poincaré maps show this system is a chaotic system with more complicated dynamics. Moreover, the circuit realization is also presented

Long-Term <i>n</i>‑Caproic Acid Production from Yeast-Fermentation Beer in an Anaerobic Bioreactor with Continuous Product Extraction

Multifunctional reactor microbiomes can elongate short-chain carboxylic acids (SCCAs) to medium-chain carboxylic acids (MCCAs), such as <i>n</i>-caproic acid. However, it is unclear whether this microbiome biotechnology platform is stable enough during long operating periods to consistently produce MCCAs. During a period of 550 days, we improved the operating conditions of an anaerobic bioreactor for the conversion of complex yeast-fermentation beer from the corn kernel-to-ethanol industry into primarily <i>n</i>-caproic acid. We incorporated and improved in-line, membrane liquid–liquid extraction to prevent inhibition due to undissociated MCCAs at a pH of 5.5 and circumvented the addition of methanogenic inhibitors. The microbiome accomplished several functions, including hydrolysis and acidogenesis of complex organic compounds and sugars into SCCAs, subsequent chain elongation with undistilled ethanol in beer, and hydrogenotrophic methanogenesis. The methane yield was 2.40 ± 0.52% based on COD and was limited by the availability of carbon dioxide. We achieved an average <i>n-</i>caproate production rate of 3.38 ± 0.42 g L^–1 d^–1 (7.52 ± 0.94 g COD L^–1 d^–1) with an <i>n</i>-caproate yield of 70.3 ± 8.81% and an <i>n</i>-caproate/ethanol ratio of 1.19 ± 0.15 based on COD for a period of ∼55 days. The maximum production rate was achieved by increasing the organic loading rates in tandem with elevating the capacity of the extraction system and a change in the complex feedstock batch

200-fold lifetime extension of 2,6-dihydroxyanthraquinone during flow battery operation

We study the capacity fade rate of a flow battery utilizing 2,6-dihydroxyanthraquinone (DHAQ) and its dependence on hydroxide concentration, state of charge, cutoff voltages for the discharge step and for the electrochemical regeneration (oxidation of decomposition compounds back to active species) step, and period of performing the electrochemical regeneration events. Our observations confirm that the first decomposition product, 2,6-dihydroxyanthrone (DHA), is stable but after electro-oxidative dimerization, the anthrone dimer decomposes. We identify conditions for which there is little time after dimerization until the dimer is rapidly re-oxidized electrochemically to form DHAQ. Combining these approaches, we decrease the fade rate to 0.02%/day, which is 18 times lower than lowest rate reported previously of 0.38%/day, and over 200 times lower than the value under standard cycling conditions of 4.3%/day. The findings and their mechanistic interpretation are expected to extend the lifetime and enhance the effectiveness of in-situ electrochemical regeneration for other electroactive species with finite lifetimes

Microalgae Recovery from Water for Biofuel Production Using CO₂‑Switchable Crystalline Nanocellulose

There is a pressing need to develop efficient and sustainable approaches to harvesting microalgae for biofuel production and water treatment. CO₂-switchable crystalline nanocellulose (CNC) modified with 1-(3-aminopropyl)­imidazole (APIm) is proposed as a reversible coagulant for harvesting microalgae. Compared to native CNC, the positively charged APIm-modified CNC, which dispersed well in carbonated water, showed appreciable electrostatic interaction with negatively charged Chlorella vulgaris upon CO₂-treatment. The gelation between the modified CNC, triggered by subsequent air sparging, can also enmesh adjacent microalgae and/or microalgae-modified CNC aggregates, thereby further enhancing harvesting efficiencies. Moreover, the surface charges and dispersion/gelation of APIm-modified CNC could be reversibly adjusted by alternatively sparging CO₂/air. This CO₂-switchability would make the reusability of redispersed CNC for further harvesting possible. After harvesting, the supernatant following sedimentation can be reused for microalgal cultivation without detrimental effects on cell growth. The use of this approach for harvesting microalgae presents an advantage to other current methods available because all materials involved, including the cellulose, CO₂, and air, are natural and biocompatible without adverse effects on the downstream processing for biofuel production