A new Ignition-Growth reaction rate model for shock initiation

Accurately predicting reactive flow is a challenge when characterizing an explosive under external shock stimuli as the shock initiation time is on the order of a microsecond.The present study constructs a new Ignition-Growth reaction rate model,which can describe the shock initiation processes of explosives with different initial densities,particle sizes and loading pressures by only one set of model parameters.Compared with the Lee-Tarver reaction rate model,the new Ignition-Growth reaction rate model describes better the shock initiation process of explosives and requires fewer model parameters.Moreover,the shock initiation of a 2,4-Dinitroanisole(DNAN)-based melt-cast explosive RDA-2(DNAN/HMX(octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine)/aluminum)are investigated both experimentally and numerically.A series of shock initiation experiments is performed with manganin piezoresistive pressure gauges and corresponding numerical simulations are carried out with the new Ignition-Growth reaction rate model.The RDA-2 explosive is found to have higher critical initiation pressure and lower shock sensitivity than traditional explosives(such as the Comp.B explosive).The calibrated reaction rate model parameters of RDA-2 could provide numerical basis for its further application.

Pricing Stochastic Barrier Options under Hull-White Interest Rate Model

A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.

A melt-cast Duan-Zhang-Kim mesoscopic reaction rate model and experiment for shock initiation of melt-cast explosives

A melt-cast Duan-Zhang-Kim(DZK)mesoscopic reaction rate model is developed for the shock initiation of melt-cast explosives based on the pore collapse hot-spot ignition mechanism.A series of shock initiation experiments was performed for the Comp B melt-cast explosive to estimate effects of the loading pressure and the particle size of granular explosive component,and the mesoscopic model is validated against the experimental data.Further numerical simulations indicate that the initial density and formula proportion greatly affect the hot-spot ignition of melt-cast explosives.

Adsorption and Step Elution of Urokinase Using Affinity Chromatography-Comparison of Data with Rate Model Simulation

A non-equilibrium chromatographic rate model was employed to simulate the affinity chromatography of urokinase. The chromatography process was developed to a yield of high purity product of urokinase from crude materials. The affinity gel used in the process was prepared by an epichlorohydrin-activation method using epichlorohydrin activated Sepharose 4B as a matrix and p-aminobenzamidine as a ligand. The chromatographic process were numerically simulated and analyzed with the aid of VERSE-LC computer simulator. Considering the basic principles, rate model with the back mixing in column inlet was utilized in simulating and studying the effect of the column inlet pattern on other parameters. Comparison of the simulation results with the experimental data showed that the rate model can be used to describe the affinity chromatography of urokinase in a fixed bed column with satisfactory accuracy.

A Software Reliability Model for OSS Including Various Fault Data Based on Proportional Hazard-Rate Model

The software reliability model is the stochastic model to measure the software reliability quantitatively. A Hazard-Rate Model is the well-known one as the typical software reliability model. We propose Hazard-Rate Models Considering Fault Severity Levels (CFSL) for Open Source Software (OSS). The purpose of this research is to make the Hazard-Rate Model considering CFSL adapt to baseline hazard function and 2 kinds of faults data in Bug Tracking System (BTS), i.e., we use the covariate vectors in Cox proportional Hazard-Rate Model. Also, we show the numerical examples by evaluating the performance of our proposed model. As the result, we compare the performance of our model with the Hazard-Rate Model CFSL.

Fuel Burning Rate Model for Stratified Charge Engine

A zero-dimensional single-zone double-curve model is presented to predict fuel burning rate in stratified charge engines, and it is integrated with GT-Power to predict the overall performance of the stratified charge engines. The model consists of two exponential functions for calculating the fuel burning rate in different charge zones. The model factors are determined by a non-linear curve fitting technique, based on the experimental data obtained from 30 cases in middle and low loads. The results show good agreement between the measured and calculated cylinder pressures, and the deviation between calculated and measured cylinder pressures is less than 5%. The zerodimensional single-zone double-curve model is successful in the combustion modeling for stratified charge engines.

Application of transient burning rate model of solid propellant in electrothermal-chemical launch simulation

A 30 mm electrothermal-chemical(ETC) gun experimental system is employed to research the burning rate characteristics of 4/7 high-nitrogen solid propellant. Enhanced gas generation rates(EGGR) of propellants during and after electrical discharges are verified in the experiments. A modified 0D internal ballistic model is established to simulate the ETC launch. According to the measured pressure and electrical parameters, a transient burning rate law including the influence of EGGR coefficient by electric power and pressure gradient(dp/dt) is added into the model. The EGGR coefficient of 4/7 high-nitrogen solid propellant is equal to 0.005 MW-1. Both simulated breech pressure and projectile muzzle velocity accord with the experimental results well. Compared with Woodley's modified burning rate law, the breech pressure curves acquired by the transient burning rate law are more consistent with test results. Based on the parameters calculated in the model, the relationship among propellant burning rate, pressure gradient(dp/dt) and electric power is analyzed. Depending on the transient burning rate law and experimental data, the burning of solid propellant under the condition of plasma is described more accurately.

Leakage Rate Model of Urban Water Supply Networks Using Principal Component Regression Analysis

To analyze the factors affecting the leakage rate of water distribution system, we built a macroscopic "leakage rate–leakage factors"(LRLF) model. In this model, we consider the pipe attributes(quality, diameter,age), maintenance cost, valve replacement cost, and annual average pressure. Based on variable selection and principal component analysis results, we extracted three main principle components—the pipe attribute principal component(PAPC), operation management principal component, and water pressure principal component. Of these, we found PAPC to have the most influence. Using principal component regression, we established an LRLF model with no detectable serial correlations. The adjusted R2 and RMSE values of the model were 0.717 and 2.067, respectively.This model represents a potentially useful tool for controlling leakage rate from the macroscopic viewpoint.

STATISTICAL INFERENCE OF WEIBULL DISTRIBUTION FOR TAMPERED FAILURE RATE MODEL IN PROGRESSIVE STRESS ACCELERATED LIFE TESTING

In this note,the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time.For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull,maximum likelihood estimation is investigated.

A class of transformation rate models for recurrent event data

Recurrent event data frequently occur in longitudinal studies, and it is often of interest to estimate the effects of covariates on the recurrent event rate. This paper considers a class of semiparametric transformation rate models for recurrent event data, which uses an additive AMen model as its covariate dependent baseline. The new models are flexible in that they allow for both additive and multiplicative covariate effects, and some covariate effects are allowed to be nonparametric and time-varying. An estimating procedure is proposed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. Simulation studies and a real data analysis demonstrate that the proposed method performs well and is appropriate for practical use.

Additive Rate Model With Auxiliary Covariates

In this paper, we consider an inference method for recurrent event data in which the primary exposure covariate is assessed only in a validation set, while as an auxiliary covariate for the main exposure is available for the full cohort. Additive rate model is considered. The existing estimating equations in the absence of primary exposure are corrected by taking use of the validation data and auxiliary information, which yield consistent and asymptotically normal estimators of the regression parameters. The estimated baseline mean process is shown to converge weakly to a zero-mean Gaussian process. Extensive simulations are conducted to evaluate finite sample performance.

Partially Time-varying Coefficient Linear Rate Model for the Recurrent Event Data

In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this paper, rate function of the recurrent event is modeled by a semipaxametric partially linear function which can include the time-varying effects. We propose the method of generalized estimating equations to make inferences about both the time-varying effects and time-independent effects. The large sample properties are established, while extensive simulation studies are carried out to examine the proposed procedures. At last, we apply the procedures to the well-known bladder cancer study.

Modified landfill gas generation rate model of first-order kinetics and two-stage reaction

This investigation was carried out to establish a new domestic landfill gas(LFG)generation rate model that takes into account the impact of leachate recirculation.The first-order kinetics and two-stage reaction(FKTSR)model of the LFG generation rate includes mechanisms of the nutrient balance for biochemical reaction in two main stages.In this study,the FKTSR model was modified by the introduction of the outflow function and the organic acid conversion coefficient in order to represent the in-situ condition of nutrient loss through leachate.Laboratory experiments were carried out to simulate the impact of leachate recirculation and verify the modified FKTSR model.The model calibration was then calculated by using the experimental data.The results suggested that the new model was in line with the experimental data.The main parameters of the modified FKTSR model,including the LFG production potential(L0),the reaction rate constant in the first stage(K1),and the reaction rate constant in the second stage(K2)of 64.746 L,0.202 d^(–1),and 0.338 d^(–1),respectively,were comparable to the old ones of 42.069 L,0.231 d^(–1),and 0.231 d^(–1).The new model is better able to explain the mechanisms involved in LFG generation.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates (da/dN) of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-ΔK relations, the confidence-based da/dN-ΔK relations, and the probabilistic- and confidence-based da/dN-ΔK relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

A Dynamic Knowledge Model for Design of Suitable Sowing Date and Sowing Rate in Winter Wheat

Based on research concerning dynamic relationships of winter wheat growth to environments and production conditions, a winter wheat model for selecting suitable sowing date, population density and sowing rate under different varieties, spatial and temporal environments was developed. Case studies on sowing date with the data sets of five different eco-sites, three climatic years and soil fertility levels, and on population density and sowing rate with the data sets of two different variety types, three different soil types, soil fertility levels, sowing dates and grain yield levels indicate a good model performance for decision-making.

Experimental and modeling study of kinetics for methane hydrate formation in a crude oil-in-water emulsion

A low-viscosity emulsion of crude oil in water can be believed to be the bulk of a flow regime in a pipeline.To differentiate which crude oil would and which would not counter the blockage of flow due to gas hydrate formation in flow channels,varying amount of crude oil in water emulsion without any other extraneous additives has undergone methane gas hydrate formation in an autoclave cell.Crude oil was able to thermodynamically inhibit the gas hydrate formation as observed from its hydrate stability zone.The normalized rate of hydrate formation in the emulsion has been calculated from an illustrative chemical affinity model,which showed a decrease in the methane consumption（decreased normalized rate constant） with an increase in the oil content in the emulsion.Fourier transform infrared spectroscopy（FTIR） of the emulsion and characteristic properties of the crude oil have been used to find the chemical component that could be pivotal in selfinhibitory characteristic of the crude oil collected from Ankleshwar,India,against a situation of clogged flow due to formation of gas hydrate and establish flow assurance.

Application of thermodynamics-based rate-dependent constitutive models of concrete in the seismic analysis of concrete dams

This paper discusses the seismic analysis of concrete dams with consideration of material nonlinearity. Based on a consistent rate-dependent model and two thermodynamics-based models, two thermodynamics-based rate-dependent constitutive models were developed with consideration of the influence of the strain rate. They can describe the dynamic behavior of concrete and be applied to nonlinear seismic analysis of concrete dams taking into account the rate sensitivity of concrete. With the two models, a nonlinear analysis of the seismic response of the Koyna Gravity Dam and the Dagangshan Arch Dam was conducted. The results were compared with those of a linear elastic model and two rate-independent thermodynamics-based constitutive models, and the influences of constitutive models and strain rate on the seismic response of concrete dams were discussed. It can be concluded from the analysis that, during seismic response, the tensile stress is the control stress in the design and seismic safety evaluation of concrete dams. In different models, the plastic strain and plastic strain rate of concrete dams show a similar distribution. When the influence of the strain rate is considered, the maximum plastic strain and plastic strain rate decrease.

Investigation on resist development rate model for synchrotron radiation X-ray lithography

Since the synchrotron radiation X-ray lithography (SRXRL) was put forward, it hascaught many people’s attention day after day. It has much benefit, such as high-structuralresolution, large process window, high throughput. It is generally thought a very goodlithography technique when dimensions shrink to 0.25μm and below. Because of the im-

STUDY ON GREY FORECASTING MODEL OF COPPER EXTRACTION RATE WITH BIOLEACHING OF PRIMARY SULFIDE ORE

A model GM （grey model） （1,1） for forecasting the rate of copper extraction during the bioleaching of primary sulphide ore was established on the basis of the mathematical theory and the modeling process of grey system theory. It was used for forecasting the rate of copper extraction from the primary sulfide ore during a laboratory microbial column leaching experiment. The precision of the forecasted results were examined and modified via ＂posterior variance examination＂. The results show that the forecasted values coincide with the experimental values. GM （1,1） model has high forecast accuracy; and it is suitable for simulation control and prediction analysis of the original data series of the processes that have grey characteristics, such as mining, metallurgical and mineral processing, etc. The leaching rate of such copper sulphide ore is low. The grey forecasting result indicates that the rate of copper extraction is approximately 20% even after leaching for six months.

Prediction of leaching rate in heap leaching process by grey dynamic model GDM(1,1)

The method of developing GM（1,1） model is extended on the basis of grey system theory. Conditions for the transfer function that improve smoothness of original data sequence and decrease the revert error are given. The grey dynamic model is first combined with the transfer function to predict the leaching rate in heap leaching process. The results show that high prediction accuracy can be expected by using the proposed method. This provides a new approach to realize prediction and control of the future behavior of leaching kinetics.