Fractional Analysis of Dynamical Novel COVID-19 by Semi-Analytical Technique

This study employs a semi-analytical approach,called Optimal Homotopy Asymptotic Method(OHAM),to analyze a coronavirus(COVID-19)transmission model of fractional order.The proposed method employs Caputo’s fractional derivatives and Reimann-Liouville fractional integral sense to solve the underlying model.To the best of our knowledge,this work presents the first application of an optimal homotopy asymptotic scheme for better estimation of the future dynamics of the COVID-19 pandemic.Our proposed fractional-order scheme for the parameterized model is based on the available number of infected cases from January 21 to January 28,2020,in Wuhan City of China.For the considered real-time data,the basic reproduction number is R0≈2.48293 that is quite high.The proposed fractional-order scheme for solving the COVID-19 fractional-order model possesses some salient features like producing closed-form semi-analytical solutions,fast convergence and non-dependence on the discretization of the domain.Several graphical presentations have demonstrated the dynamical behaviors of subpopulations involved in the underlying fractional COVID-19 model.The successful application of the scheme presented in this work reveals new horizons of its application to several other fractional-order epidemiological models.

Fractional S-transform-part 2:Application to reservoir prediction and fluid identification

The fractional S-transform （FRST） has good time-frequency focusing ability. The FRST can identify geological features by rotating the fractional Fourier transform frequency （FRFTfr） axis. Different seismic signals have different optimal fractional parameters which is not conducive to multichannel seismic data processing. Thus, we first decompose the common-frequency sections by the FRST and then we analyze the low-frequency shadow. Second, the combination of the FRST and blind-source separation is used to obtain the independent spectra of the various geological features. The seismic data interpretation improves without requiring to estimating the optimal fractional parameters. The top and bottom of a limestone reservoir can be clearly recognized on the common-frequency section, thus enhancing the vertical resolution of the analysis of the low-frequency shadows compared with traditional ST. Simulations suggest that the proposed method separates the independent frequency information in the time-fractional-frequency domain. We used field seismic and well data to verify the proposed method.

Reliability analysis based on a novel density estimation method for structures with correlations

Estimating the Probability Density Function（PDF） of the performance function is a direct way for structural reliability analysis,and the failure probability can be easily obtained by integration in the failure domain.However,efficiently estimating the PDF is still an urgent problem to be solved.The existing fractional moment based maximum entropy has provided a very advanced method for the PDF estimation,whereas the main shortcoming is that it limits the application of the reliability analysis method only to structures with independent inputs.While in fact,structures with correlated inputs always exist in engineering,thus this paper improves the maximum entropy method,and applies the Unscented Transformation（UT） technique to compute the fractional moments of the performance function for structures with correlations,which is a very efficient moment estimation method for models with any inputs.The proposed method can precisely estimate the probability distributions of performance functions for structures with correlations.Besides,the number of function evaluations of the proposed method in reliability analysis,which is determined by UT,is really small.Several examples are employed to illustrate the accuracy and advantages of the proposed method.

High throughput online sequential extraction of natural rare earth elements and determination by mass spectrometry

At the beginning of rare earth industry,several days are normally required for characterization of rare earth elements(REEs)fractionation in ore samples.Herein,rapid fractionation analysis of 15 REEs and accompanied metal(Fe,Mn,etc.)in ore samples has been achieved within 1 h using ICP-MS with a homemade device for online sequential solvent extraction.As a result,five fractionations for REEs occurrences,i.e.,water soluble,exchangeable,reducible,oxidizable and crystalline,have been identified,offering chemical insights which not only reveal the formation mechanism of REEs ores but also show great implications for guiding the exploitation and separation of REEs.In comparison with conventional methods,the present approach significantly shortened the analysis time(1 h vs.~80 h)and reduced the sample consumption(1.0 mg vs.5.0 g)with high recovery(>95%),providing a useful platform for the rapid quantitative fractionation analysis of REEs in complexed samples such as ore and fossils.

A model for expansion ratio in liquid-solid fluidized beds

Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.