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.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Determination of Natural Logarithm of Diffusion Coefficient and Activation Energy of Thin Layer Drying Process of Ginger Rhizome Slices

This study is an extension of the previous work done with ARS-680 Environmental Chamber. Drying is a complex operation that demands much energy and time. Drying is essentially important for preservation of ginger rhizome. Drying of ginger was modeled, and then the effective diffusion coefficient and activation energy were determined. For this purpose, the experiments were done at six levels of varied temperatures: 10°C, 20°C, 30°C, 40°C, 50°C and 60°C. The values of effective diffusion coefficients obtained in this work for the variously treated ginger rhizomes closely agreed with the average effective diffusion coefficients of other notable authors who determined the drying kinetics and convective heat transfer coefficients of ginger slices.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Time Dependent Chloride Diffusion Coefficient in Concrete

In order to study how to correctly apply the two different time dependencies to service life prediction models, the definition of parameters in the time dependent equation using the long-term test method and the short-term test method, and its relationship were discussed. The experimental results show that, as the two time dependencies have different meanings, they have different manners when handled in service life prediction models. Time dependency of chloride diffusion coefficients in concrete was obtained by fitting experimental data. A large number of accurate experimental data were required to fit the formula of time dependency to ensure the accuracy of service life prediction model.

Narrowband time delay estimation based on correlation coefficient

The problems of time delay estimation of narrowband signals are presented. The disadvantages of the existing algorithms are analyzed, and a new narrowband time delay estimating algorithm based on correlation coefficient is proposed. The original time delay information is transfered into the delay between the autocorrelation and cross-correlation function, and the precise estimating result by wave-comparison is given. The algorithm proposed here is also compared with other algorithms and its advantages over other algorithms are proved. The theoretical analysis and simulation show the effectiveness of the proposed algorithm.

Time effect and prediction of broken rock bulking coefficient on the base of particle discrete element method

Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.

Secondary settlement estimation in surcharge preload subject to time effect of secondary consolidation coefficient

In order to eliminate the settlement underestimation in surcharge preload engineering, a study based on Bjerrum's creep diagram and the tangent slope definition of secondary consolidation coefficient was carried out to analyze the time effect of secondary consolidation coefficient of over consolidated soil, and a time–growth model for it was formulated. As Bjerrum's creep diagram is an idealized model, oedometer tests were performed to improve the above time–growth model of secondary consolidation coefficient for the purpose of achieving a better agreement with the actual ground situations. It is found that secondary consolidation coefficient of over consolidated soil not only decreases with the ratio of historical maximum to current effective stress of soil(OCR), but also increases with the development time of secondary consolidation. No matter how large OCR is, the long-term time effect of secondary consolidation coefficient of over consolidated soil is all significant. Based on the above results, a model for settlement estimation was formulated and a case study to estimate it indicates that the settlement estimated by our method is 2–5 times larger than that estimated by the previous method. Moreover, the larger the OCR is as well as the longer the service life is, the larger the difference between our method and the previous method is. Thus, the post-construction secondary settlement in surcharge preload engineering will be underestimated when neglecting the time effect of secondary consolidation coefficient in over consolidated state.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Modelling of Time Dependency of Chloride Diffusion Coefficient in Cement Paste

A computer-based model and method was presented to predict the time dependency of chloride diffusion coefficients in cement paste. The HYMOSTRUC3D model was applied to generate a 3D representative elementary volume （REV） of cement paste. In the simulation of microstructure, both of cement hydration and chloride binding were considered. With the simulated microstructure of cement paste, the finite element method was applied to simulate the diffusion process of chloride through the saturated cement paste. Based on the Fick’s first law, the chloride diffusion coefficient can be calculated. In this method, the influences of age and w/c ratio on the chloride diffusion coefficient were evaluated. The simulated chloride diffusivities with various w/c at different time were compared to experimental data obtained from the literature. The experimental results indicate that the chloride diffusion coefficient decreases with the increase of time and the decrease of w/c ratio. The trend of simulated relationship （diffusion coefficient vs time, diffusion coefficient vs w/c ratio） fits very well with the experiments.

Coefficient of retardation time found out by polynomial fitting to predict creep behaviour of polystyrene

The universal creep function is successful in relating the creep （ε） to the ageing time （ta）, coefficient of retardation time （β）, and intrinsic time （t0）. The relation was used to treat the creep experimental data for polystyrene （PS） specimens at a given aged time and different stress levels. Comparing with “middle-point” method reported in the literatures, β is found out by another method “polynomial fitting” in this work. Then unified master lines were constructed with the treated data and curves according to the universal equation. The master lines can be used to predict the long-term creep behaviour and lifetime by extrapolating to a required ultimate strain.

A Simulation Study on Comparing General Class of Semiparametric Transformation Models for Survival Outcome with Time-Varying Coefficients and Covariates

The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametric transformation models. The aim of this article is to develop modified estimating equations under semiparametric transformation models of survival time with time-varying coefficient effect and time-varying continuous covariates. For this, it is important to organize the data in a counting process style and transform the time with standard transformation classes which shall be applied in this article. In the situation when the effect of coefficient and covariates change over time, the widely used maximum likelihood estimation method becomes more complex and burdensome in estimating consistent estimates. To overcome this problem, alternatively, the modified estimating equations were applied to estimate the unknown parameters and unspecified monotone transformation functions. The estimating equations were modified to incorporate the time-varying effect in both coefficient and covariates. The performance of the proposed methods is tested through a simulation study. To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models. Finally, the results have shown that the role of the time-varying covariate in the semiparametric transformation models was plausible and credible.

Variable Coefficient KdV Equation for Amplitude of Nonlinear Solitary Rossby Waves in a Sort of Time-Dependent Zonal Flow

On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

Histogram analysis of apparent diffusion coefficient predicts response to radiofrequency ablation in hepatocellular carcinoma

Objective: The aim of this study was to predict tumor progression in patients with hepatocellular carcinoma(HCC) treated with radiofrequency ablation(RFA) using histogram analysis of apparent diffusion coefficients(ADC).Methods: Breath-hold diffusion weighted imaging(DWI) was performed in 64 patients(33 progressive and 31 stable) with biopsy-proven HCC prior to RFA. All patients had pre-treatment magnetic resonance imaging(MRI)and follow-up computed tomography(CT) or MRI. The ADC values(ADC_(10), ADC_(30_, ADC_(median) and ADC_(max))were obtained from the histogram's 10 th, 30 th, 50 th and 100 th percentiles. The ratios of ADC_(10), ADC_(30_,ADCmedian and ADCmax to the mean non-lesion area-ADC(RADC_(10), RADC_(30_, RADC_(median), and RADC_(max)) were calculated. The two patient groups were compared. Key predictive factors for survival were determined using the univariate and multivariate analysis of the Cox model. The Kaplan-Meier survival analysis was performed, and pairs of survival curves based on the key factors were compared using the log-rank test.Results: The ADC_(30_, ADCmedian, ADCmax, RADC_(30_, RADC_(median), and RADC_(max) were significantly larger in the progressive group than in the stable group(P<0.05). The median progression-free survival(PFS) was 22.9 months for all patients. The mean PFS for the stable and progressive groups were 47.7±1.3 and 9.8±1.3 months,respectively. Univariate analysis indicated that RADC_(10), RADC_(30_, and RADC_(median) were significantly correlated with the PFS [hazard ratio(HR)=31.02, 43.84, and 44.29, respectively, P<0.05 for all]. Multivariate analysis showed that RADCmedian was the only independent predictor of tumor progression(P=0.04). And the cutoff value of RADC_(median) was 0.71.Conclusions: Pre-RFA ADC histogram analysis might serve as a useful biomarker for predicting tumor progression and survival in patients with HCC treated with RFA.

The Physical Significance of the Synthetic Running Correlation Coefficient and Its Applications in Oceanic and Atmospheric Studies

In order to study the temporal variations of correlations between two time series,a running correlation coefficient(RCC)could be used.An RCC is calculated for a given time window,and the window is then moved sequentially through time.The current calculation method for RCCs is based on the general definition of the Pearson product-moment correlation coefficient,calculated with the data within the time window,which we call the local running correlation coefficient(LRCC).The LRCC is calculated via the two anomalies corresponding to the two local means,meanwhile,the local means also vary.It is cleared up that the LRCC reflects only the correlation between the two anomalies within the time window but fails to exhibit the contributions of the two varying means.To address this problem,two unchanged means obtained from all available data are adopted to calculate an RCC,which is called the synthetic running correlation coefficient(SRCC).When the anomaly variations are dominant,the two RCCs are similar.However,when the variations of the means are dominant,the difference between the two RCCs becomes obvious.The SRCC reflects the correlations of both the anomaly variations and the variations of the means.Therefore,the SRCCs from different time points are intercomparable.A criterion for the superiority of the RCC algorithm is that the average value of the RCC should be close to the global correlation coefficient calculated using all data.The SRCC always meets this criterion,while the LRCC sometimes fails.Therefore,the SRCC is better than the LRCC for running correlations.We suggest using the SRCC to calculate the RCCs.

Study of road tunnel threshold zone lighting reduction coefficient

The luminance in the road tunnel threshold zone attracts broad attention due to its enormous energy consumption and direct influence on tunnel transportation security.Current lighting design methods in threshold zones mostly adopt the reduction coefficient method.However,the determination of reduction coefficient k simply considers tunnel design speed and flow rate,while excluding outside tunnel luminance and threshold zone color temperature and luminance,which have a major impact on driver visual adaptation.Existing problems in the determination of k value are analyzed;a visual performance experiment is utilized;and the reaction time of drivers in changeable outside tunnel luminance and threshold zone color temperature and luminance conditions is obtained;thus,the equations concerning reduction coefficient variation law are derived.In the end,a comparative analysis is made of the k values of the reduction coefficient stipulated by various norms under different color temperature conditions.

Mathematical Proof of the Synthetic Running Correlation Coefficient and Its Ability to Reflect Temporal Variations in Correlation

The running correlation coefficient(RCC)is useful for capturing temporal variations in correlations between two time series.The local running correlation coefficient(LRCC)is a widely used algorithm that directly applies the Pearson correlation to a time window.A new algorithm called synthetic running correlation coefficient(SRCC)was proposed in 2018 and proven to be rea-sonable and usable;however,this algorithm lacks a theoretical demonstration.In this paper,SRCC is proven theoretically.RCC is only meaningful when its values at different times can be compared.First,the global means are proven to be the unique standard quantities for comparison.SRCC is the only RCC that satisfies the comparability criterion.The relationship between LRCC and SRCC is derived using statistical methods,and SRCC is obtained by adding a constraint condition to the LRCC algorithm.Dividing the temporal fluctuations into high-and low-frequency signals reveals that LRCC only reflects the correlation of high-frequency signals;by contrast,SRCC reflects the correlations of high-and low-frequency signals simultaneously.Therefore,SRCC is the ap-propriate method for calculating RCCs.