Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

The effect of behavior of wearing masks on epidemic dynamics

Nonlinear Dynamics - Recently, COVID-19 has attracted a lot of attention of researchers from different fields. Wearing masks is a frequently adopted precautionary measure. In this paper, we...     

Paradoxical reduction and the bifurcations of neuronal bursting activity modulated by positive self-feedback

Nonlinear Dynamics - Paradoxical enhancement rather than reduction in firing activity induced by inhibitory effect is very important for both nonlinear dynamics and neuroscience. In the present...     

Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model

Nonlinear Dynamics - In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined,...     

Feature extraction method based on NOFRFs and its application in faulty rotor system with slight misalignment

Nonlinear Dynamics - Fault features extraction method for slight misalignment of rotor systems is researched in this paper. When a rotor system with faults is excited by harmonic inputs, system...     

A colorimetric sensing strategy based on enzyme@metal-organic framework and oxidase-like IrO2/MnO2 nanocomposite for α-glucosidase inhibitor screening

Microchimica Acta - Testing gluten content in food, before it reaches the consumer, becomes a major challenge where cross-contamination during processing and transportation is a very common...     

Double-Shelled C@MoS2 Structures Preloaded with Sulfur: An Additive Reservoir for Stable Lithium Metal Anodes

The growth of Li dendrites hinders the practical application of lithium metal anodes (LMAs). In this work, a hollow nanostructure, based on hierarchical MoS₂ coated hollow carbon particles preloaded with sulfur (C@MoS₂/S), was designed to modify the LMA. The C@MoS₂ hollow nanostructures serve as a good scaffold for repeated Li plating/stripping. More importantly, the encapsulated sulfur could gradually release lithium polysulfides during the Li plating/stripping, acting as an effective additive to promote the formation of a mosaic solid electrolyte interphase layer embedded with crystalline hybrid lithium-based components. These two factors together effectively suppress the growth of Li dendrites. The as-modified LMA shows a high Coulombic efficiency of 98 % over 500 cycles at the current density of 1 mA cm⁻². When matched with a LiFePO₄ cathode, the assembled full cell displays a highly improved cycle life of 300 cycles, implying the feasibility of the proposed LMA.     

Kinetics of hydrogen peroxide decomposition catalyzed by Cu-buserite over a well-sealed and thermostated kinetics assembly

Herein a well-sealed and thermostated kinetics assembly is designed and built, which can run stirred at different reaction temperatures. With the reaction assembly above and the volumetric method together, the hydrogen peroxide (H₂O₂) decomposition reaction kinetics is systematically investigated under a variety of reaction conditions over a copper-doped buserite-type layer manganese oxide (referred to as Cu-buserite) as a heterogeneous catalyst. The overall second-order rate law is fitted out by the linear regression analysis, with the reaction orders with respect to both H₂O₂ and Cu-buserite determined to each be equal to 1, and then explicitly explained by the proposed Michaelis-Menten like mechanism. The apparent activation energy E_a is estimated as 33.5 ± 2.5 kJ mol⁻¹.     

Recent Advances in Iodine-Promoted C−S/N−S Bonds Formation

Sulfur-containing scaffold, as a ubiquitous structural motif, has been frequently used in natural products, bioactive chemicals and pharmaceuticals, particularly C−S/N−S bonds are indispensable in many biological important compounds and pharmaceuticals. Development of mild and general methods for C−S/N−S bonds formation has great significance in modern research. Iodine and its derivatives have been recognized as inexpensive, environmentally benign and easy-handled catalysts or reagents to promote the construction of C−S/N−S bonds under mild reaction conditions, with good regioselectivities and broad substrate scope. Especially based on this, several new strategies, such as oxidation relay strategy, have been greatly developed and accelerated the advancement of this field. This review focuses on recent advances in iodine and its derivatives promoted hybridized C−S/N−S bonds formation. The features and mechanisms of corresponding reactions are summarized and the results of some cases are compared with those of previous reports. In addition, the future of this domain is discussed.