A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Research on fault time prediction method for high speed rail BTM unit based on multi method interactive validation

The Balise Transmission Module(BTM)unit of the on-board train control system is a crucial component.Due to its unique installation position and complex environment,this unit has a higher fault rate within the on-board train control system.To conduct fault prediction for the BTM unit based on actual fault data,this study proposes a prediction method combining reliability statistics and machine learning,and achieves the fusion of prediction results from different dimensions through multi-method interactive validation.Firstly,a method for predicting equipment fault time targeting batch equipment is introduced.This method utilizes reliability statistics to construct a model of the remaining faultless operating time distribution considering uncertainty,thereby predicting the remaining faultless operating probability of the BTM unit.Secondly,considering the complexity of the BTM unit’s fault mechanism,the small sample size of fault cases,and the potential presence of multiple fault features in fault text records,an individual-oriented fault prediction method based on Bayesian-optimized Gradient Boosting Regression Tree(Bayes-GBRT)is proposed.This method achieves better prediction results compared to linear regression algorithms and random forest regression algorithms,with an average absolute error of only 0.224 years for predicting the fault time of this type of equipment.Finally,a multi-method interactive validation approach is proposed,enabling the fusion and validation of multi-dimensional results.The results indicate that the predicted fault time and the actual fault time conform to a log-normal distribution,and the parameter estimation results are basically consistent,verifying the accuracy and effectiveness of the prediction results.The above research findings can provide technical support for the maintenance and modification of BTM units,effectively reducing maintenance costs and ensuring the safe operation of high-speed railway,thus having practical engineering value for preventive maintenance.

Effects of Standing Time during Pretreatment on the Nitrite Concentration Detected by Spectrophotometric Method

Food safety problems caused by excessive nitrite addition have been frequently reported and the detection of nitrite in food is particularly important. The standing time during the pretreatment of primary sample has a great influence on the concentration of nitrite tested by spectrophotometric method. In this context, three kinds of food samples are prepared, including canned mustard, canned fish and home-made pickled water. A series of standing times are placed during the sample pretreatments and the corresponding nitrite contents in these samples are detected by spectrophotometric method based on N-ethylenediamine dihydrochloride. This study aims to find out a reasonable standing time during the pretreatment of food sample, providing influence factor for precise detection of nitrite.

Variational Iteration Method for Solving Time Fractional Burgers Equation Using Maple

The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.

A Time Neighborhood Method for the Verification of Landfalling Typhoon Track Forecast

Landfalling typhoons can cause disasters over large regions.The government and emergency responders need to take measures to mitigate disasters according to the forecast of landfall position,while slight timing error can be ignored.The reliability of operational model forecasts of typhoon landfall position needs to be evaluated beforehand,according to the forecasts and observation of historical cases.In the evaluation of landfalling typhoon track,the traditional method based on point-to-point matching methods could be influenced by the predicted typhoon translation speed.Consequently,the traditional track evaluation method may result in a large track error even if the predicted landfall position is close to observation.The purpose of this paper is to address the above issue using a simple evaluation method of landfalling typhoon track forecast based on the time neighborhood approach.In this new method,the timing error was lessened to highlight the importance of the position error during the landfall of typhoon.The properties of the time neighborhood method are compared with the traditional method based on numerical forecast results of 12 landfalling typhoon cases.Results demonstrated that the new method is not sensitive to the sampling frequency,and that the difference between the time neighborhood and traditional method will be more obvious when the moving speed of typhoon is moderate(between 15−30 km h^(−1)).The time neighborhood concept can be easily extended to a broader context when one attempts to examine the position error more than the timing error.

Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic

A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the computation costs,the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations.The effectiveness of the proposed algorithm is verified by the first numerical example.The mass conservation property and stability statement are confirmed by two other numerical examples.

Generation of endurance time excitation functions using spectral representation method

In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its acceleration response spectrum in any desired time duration is compatible with a time-scaled predefined acceleration response spectrum.For this purpose,simulated stationary acceleration time series is multiplied by the time dependent linear modulation function,then using a simple iterative scheme,it is forced to match a target acceleration response spectrum.It is shown that the generated samples have excellent conformity in low frequency,which is useful for nonlinear endurance time analysis.In the second part of this study,it is shown that this procedure can be extended to generate a set of spatially correlated endurance time excitation functions.This makes it possible to assess the performance of long structures under multi-support seismic excitation using endurance time analysis.

A LOCAL DISCONTINUOUS GALERKIN METHOD FOR TIME-FRACTIONAL DIFFUSION EQUATIONS

In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finite difference method with an accuracy of order3-α,and the space discretization is based on the LDG method.For the finite difference method,we summarize and supplement some previous work by others,and apply it to the analysis of the convergence and stability of the proposed scheme.The optimal error estimate is obtained in the L2norm,indicating that the scheme has temporal(3-α)th-order accuracy and spatial(k+1)th-order accuracy,where k denotes the highest degree of a piecewise polynomial in discontinuous finite element space.The numerical results are also provided to verify the accuracy and efficiency of the considered scheme.

Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples.

Adomian Decomposition Method for Solving Time Fractional Burgers Equation Using Maple

In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program.

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

A spatiotemporal evolution model of a short-circuit arc to a secondary arc based on the improved charge simulation method

The initial shape of the secondary arc considerably influences its subsequent shape.To establish the model for the arcing time of the secondary arc and modify the single-phase reclosing sequence,theoretical and experimental analysis of the evolution process of the short-circuit arc to the secondary arc is critical.In this study,an improved charge simulation method was used to develop the internal-space electric-field model of the short-circuit arc.The intensity of the electric field was used as an independent variable to describe the initial shape of the secondary arc.A secondary arc evolution model was developed based on this model.Moreover,the accuracy of the model was evaluated by comparison with physical experimental results.When the secondary arc current increased,the arcing time and dispersion increased.There is an overall trend of increasing arc length with increasing arcing time.Nevertheless,there is a reduction in arc length during arc ignition due to short circuits between the arc columns.Furthermore,the arcing time decreased in the range of 0°-90°as the angle between the wind direction and the x-axis increased.This work investigated the method by which short-circuit arcs evolve into secondary arcs.The results can be used to develop the secondary arc evolution model and to provide both a technical and theoretical basis for secondary arc suppression.

Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

24重荧光real-time PCR技术在食物中毒快速检测中的应用

目的:应用24重荧光real-time PCR检测技术快速筛检食物中毒病原菌,结合国家标准中的培养法探讨24重荧光real-time PCR检测技术符合性和应用价值。方法:采用高灵敏度、高特异性的24重荧光real-time PCR检测技术作为中毒病原菌的初筛方法,国标方法进行细菌分离培养,并对分离出的病原菌进行生化鉴定。结果:5份食物中毒患者肛拭子在增菌前检出4份霍乱弧菌核酸(非O1/非O139群,24重荧光real-time PCR),9份患者肛拭子在增菌后检出5株霍乱弧菌(非O1/非O139群,国标培养法),其中包含4份PCR技术初筛阳性样品,两个方法的符合率为80%。所有样本均未检出沙门氏菌、志贺菌、副溶血性弧菌、致泻性大肠埃希菌以及金黄色葡萄球菌。结论:应用24重荧光real-time PCR检测技术同时检测24种常见致病病原菌,能高效锁定中毒病原菌。将其与国标培养法相结合,对临床治疗和食物中毒快速处置能起到积极作用,值得应用和推广。

DETERMINING CRITICAL TIME OF ROCK DYNAMIC FRACTURE BY DYNAMIC MOIRE METHOD

An effective Dynamic Moire method was presented to determine the critical time of crack instable propagation in rock dynamic fracture. Two pieces of grating were installed near the notch of Short Rod specimen to form the Moire fringes, then the COD versus time could be monitored from the movement of the Moire fringes, and finally the critical time could be determined from the velocity of COD. This method was also compared with another one.It could be concluded that the critical time determined by Dynamic Moire method corresponds with that of the Transmitted Wave method at the loading rates from 103 to 104 MPa·m(1/2)·S(-1).

Travel time and alternative configurations analysis for automated storage/retrieval systems based on geometrical method

In order to evaluate the efficiency of the automated storage/retrieval system(AS/RS)accurately,and compare different layouts of the AS/RS using mean travel time,under randomized storage conditions,an exact,geometry-based analytical model is presented.The model can be used to compute the expected single-command and dual-command travel time for a storage/retrieval(S/R)machine which can travel simultaneously horizontally and vertically as it moves along a storage aisle.The rack may be either square in time or non square in time.Additionally,the alternative layouts of the AS/RS and travel-time models are examined.Comparing with setting the I/O point at the left-lower corner of the rack,setting the I/O point at any point at the vertical edge can help enhance the efficiency of the AS/RS.

Effects of Storage Methods and Time on Content of Nutrients in Biogas Slurry of Straw

To study the effects of different storage methods and time on content of nutrients in biogas slurry of straw, two storage methods were carried out on biogas slurry between open storage and airtight storage conditions at normal atmospheric temperature. The contents of N, P, K, and organic matter in biogas slurry of straw were determined in different storage times. The results showed that： during the pro-cess of biogas slurry storage, little change occurred in the content of the organic matter while the total content of N, P, K significantly declined; up to 50 days, the total content of N, P, K reduced to nearly 80%-90%. Because the contents of N, P, K in biogas slurry reduced less in airtight storage conditions so that a better re-sult was found on airtight storage methods than open storage methods in fertilizer field of biogas slurry of straw.

Species distribution of polymeric aluminium ferrum——timed complexation colorimetric analysis method of Al-Fe-Ferron

The effects of the calorimetric buffer solutions were investigated while the two colorimetric reactions of AI-ferron complex and Fe-ferron complex occurred individually, and the effects of the testing wavelength and the pH of the solutions were also investigated. A timed complexatian colorimetric analysis method of Al-Fe-ferron in view of the total concentration of {AI + Fe} was then established to determine the species distribution of polymeric Al-Fe. The testing wavelength was recommended at 362 net and the testing pH value was 5. With a comparison of the ratios of n(Al)/n(Fe), the standard adsorption curves of the polymeric Al-Fe solutions were derived from the experimental results. Furthermore, the solutions' composition were carious in both the molar n(Al)/n(Fe) ratios, i.e. 0/0, 5/5, 9/1 and 0/10, and the concentrations associated with the total ( Al + Fe which ranged from 10(-5) to 10(-4) mol/L..

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.