Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.

Critical care nurses and their clinical reasoning for customizing monitor alarms:a mixed-method study

Objective:To explore the clinical rationale of critical care nurses for personalizing monitor alarms.One of the most crucial jobs assigned to critical care nurses is monitoring patients'physiological indicators and carrying out the necessary associated interventions.Successful use of equipment in the nursing practice environment will be improved by a thorough understanding of the nurse's approach to alarm configuration.Methods:A mixed-method design integrating quantitative and qualitative components was used.The sample of this study recruited a convenience sample of 60 nurses who have worked in critical care areas.This study took place at Lebanese American University Medical Center Rizk Hospital,utilizing a semi-structured interview with participants.Results:The study demonstrated the high incidence of nuisance alarms and the desensitization of critical care nurses to vital ones.According to the nurses,frequent false alarms and a shortage of staff are the 2 main causes of alarm desensitization.Age was significantly associated with the perception of Smart alarms,according to the data(P=0.03).Four interconnected themes and subcategories that reflect the clinical reasoning process for alarm customization were developed as a result of the study's qualitative component:(1)unit alarm environment;(2)nursing style;(3)motivation to customize;and(4)clinical and technological customization.Conclusions:According to this study,nurses believe that alarms are valuable.However,a qualitative analysis of the experiences revealed that customization has been severely limited since the healthcare team depends on nurses to complete these tasks independently.Additionally,a staffing shortage and lack of technical training at the start of placement have also hindered customization.

Solving Navier-Stokes equation by mixed interpolation method

The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Experimental study on secondary air mixing along the bed height in a circulating fluidized bed with a multitracer-gas method

A multitracer-gas method was proposed to study the secondary air(SA)mixing along the bed height in a circulating fluidized bed(CFB)using carbon monoxide(CO),oxygen(O_(2)),and carbon dioxide(CO_(2))as tracer gases.Experiments were carried out on a cold CFB test rig with a cross-section of 0.42 m×0.73 m and a height of 5.50 m.The effects of superficial velocity,SA ratio,bed inventory,and particle diameter on the SA mixing were investigated.The results indicate that there are some differences in the measurement results obtained using different tracer gases,wherein the deviation between CO and CO_(2) ranges from 42%to 66%and that between O_(2) and CO_(2) ranges from 45%to 71%in the lower part of the fluidized bed.However,these differences became less pronounced as the bed height increased.Besides,the high solid concentration and fine particle diameter in the CFB may weaken the difference.The measurement results of different tracer gases show the same trends under the variation of operating parameters.Increasing superficial velocity and SA ratio and decreasing particle diameter result in better mixing of the SA.The effect of bed inventory on SA mixing is not monotonic.

Error estimates of H^1-Galerkin mixed finite element method for Schrdinger equation

An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.

Synthesis and luminescent properties of Ce^(3+) doped LuAG nano-sized powders by mixed solvo-thermal method

Polycrystalline LuAG:Ce3+(cerium3+-doped lutetium aluminum garnet) powders were prepared by mixed solvo-thermal method.Fourier-transform IR spectroscopy(FTIR) and X-ray diffraction(XRD) measurements showed that the precursors were ethanol derivatives AlO(OH) crystal with hydroxyl and carbonate group.XRD results showed that phase of Lu2O3 disappeared with the precursors were annealed at 400 °C,cubic phase LuAG:Ce3+ appeared but only one diffraction peaks of LuAP(LuAlO3) at calcination temperature to 700 °C,a...

Numerical solutions to regularized long wave equation based on mixed covolume method

The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.

Application of the Modified nverse Design Method in the Optimization of the Runner Blade of a Mixed-Flow Pump

To improve the design speed and reduce the design cost for the previous blade design method, a modified inverse design method is presented. In the new method, after a series of physical and mathematical simplifications, a sail?like constrained area is proposed, which can be used to configure di erent runner blade shapes. Then, the new method is applied to redesign and optimize the runner blade of the scale core component of the 1400?MW canned nuclear coolant pump in an established multi?optimization system compromising the Computational Fluid Dynamics(CFD) analysis, the Response Surface Methodology(RSM) and the Non?dominated Sorting Genetic Algorithm?II(NSGA?II). After the execution of the optimization procedure, three optimal samples were ultimately obtained. Then, through comparative analysis using the target runner blade, it was found that the maximum e ciency improvement reached 1.6%, while the head improvement was about 10%. Overall, a promising runner blade inverse design method which will benefit the hydraulic design of the mixed?flow pump has been proposed.

Factors Related to Engaging in Physical Activity: A Mixed Methods Study of Female University Students

Objective: As a needs assessment for intervention, quantitative and qualitative methods were used to examine attitude, subjective norms, perceived behavioral control, intention, knowledge, and weight control status related to physical activity in female university students within the Theory of Planned Behavior (TPB). Methods: A two-phase mixed method design was used. In Phase I, 362 students participated in an online survey, and in Phase II, 33 students participated in five focus group discussions. Ages of participants ranged from 18 to 45 years old, with 18 - 25 year olds making up over 74% of the sample. Results: Attitude, subjective norms, and perceived behavioral control, along with weight control status of trying to lose weight, were found to be significant predictors of intention to follow physical activity recommendations, which in turn were the strongest predictor of physical activity. Knowledge was not found to be significant. Group discussions revealed barriers to meeting physical activity recommendations, which included lack of companionship and social support, lack of motivation, time and cost restrictions, and lack of privacy in the gym. Social norms exerted both positive and negative influences. Conclusion: The mixed method approach provided a deeper insight into the influential factors pertaining to physical activity among female students, and results could be used in further research to develop effective interventions.

MIXED FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS AND ITS ALTERNATING-DIRECTION ITERATIVE SCHEME

In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.

An H^1-Galerkin Expanded Mixed Element Method for Semi-linear Hyperbolic Wave Equation

An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.

AN ANALYTICAL METHOD FOR A MIXED BOUNDARY VALUE PROBLEM OF CIRCULAR PLATES UNDER ARBITRARY LATERAL LOADS

In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Synthesis of mesoporous cerium-zirconium mixed oxides by hydrothermal templating method

Mesoporous cerium-zirconium mixed oxides were prepared by hydrothermal method using cetyl trimethyl ammonium bromide (CTAB) as template. The effects of amount of template, pH value of solution and hydrothermal temperature on mesostructure of samples were systematically investigated. The final products were characterized by XRD, TEM, FT-IR, and BET. The results indicate that all the cerium-zirconium mixed oxides present a meso-structure. At molar ratio of n(CTAB)/n((Ce)+(Zr))= 0.15, pH value of 9, and hydrothermal temperature of 120 ℃, the samples obtained possess a specific surface area of 207.9 m2/g with pore diameter of 3.70 nm and pore volume of 0.19 cm3/g.

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅱ)——THE DISCRETE-TIME CASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete_time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.

Mixed H_2/H_∞ State Feedback Attitude Control of Microsatellite Based on Extended LMI Method

For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.

Mixed time discontinuous space-time finite element method for convection diffusion equations

A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.

Comparative structural and electrochemical properties of mixed P2/O′3-layered sodium nickel manganese oxide prepared by sol-gel and electrospinning methods:Effect of Na-excess content

The effect of Na-excess content in the precursor on the structural and electrochemical performances of sodium nickel manganese oxide(NNMO)prepared by sol-gel and electrospinning methods is investigated in this paper.X-ray diffraction results of the prepared NNMO without adding Na-excess content indicate sodium loss,while the mixed phase of P2/O′3-type layered NNMO presented after adding Na-excess content.Compared with the sol-gel method,the secondary phase of NiO is more suppressed by using the electrospinning method,which is further confirmed by field emission scanning electron microscope images.N_(2) adsorption-desorption isotherms show no remarkably difference in specific surface areas between different preparation methods and Na-excess contents.The analysis of X-ray absorption near edge structure indicates that the oxidation states of Ni and Mn are+2 and+4,respectively.For the electrochemical properties,superior electrochemical performance is observed in the NNMO electrode with a low Na-excess content of 5wt%.The highest specific capacitance is 36.07 F·g^(-1)at0.1 A·g^(-1)in the NNMO electrode prepared by using the sol-gel method.By contrast,the NNMO electrode prepared using the electrospinning method with decreased Na-excess content shows excellent cycling stability of 100%after charge-discharge measurements for 300 cycles.Therefore,controlling the Na excess in the precursor together with the preparation method is important for improving the electrochemical performance of Na-based electrode materials in supercapacitors.

On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.