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.

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.

A Generalized Rate Model for Free Radical Copolymerization and Its Simulation

A generalized rate model for free radical copolymerization was proposed. It can be applied not only to the system with the participation of charge-transfer complex (CTC), but also to the system without the participation of CTC. The effects of equillbrlum constant, total monomer concentration, homc-propagation parameters and reactivity ratios on free monomer, CTC, overall rates, and the contribution of CTC were considered in thesimuiatlon. North equation of copolymerization rate as a special case can be derived from the generalized model.

Adsorption Rate Models for Multicomponent Adsorption Systems

Three adsorption rate models are derived for multicomponent adsorption systems under either pore diffusion or surface diffusion control. The linear driving force (LDF) model is obtained by assuming a parabolic intraparticle concentration profile. Models I and Ⅱ are obtained from the parabolic concentration layer approximation. Examples are presented to demonstrate the usage and accuracy of these models. It is shown that Model I is suitable for batch adsorption calculations and Model Ⅱ provides a good approximation in fixed-bed adsorption processes while the LDF model should not be used in batch adsorption and may be considered acceptable in fixed-bed adsorption where the parameter Ti is relatively large.

Fuel Burning Rate Model for Stratified Charge Engine

一个零维的单个地区的双曲线模型被介绍在成层的电荷引擎预言燃料燃烧速率，并且预言成层的电荷引擎的全面表演与 GT 力量是综合的。模型为在不同电荷地区计算燃料燃烧速率由二指数的功能组成。模型因素由一种非线性的曲线试穿技术的 redetermined，基于在中间、低的负担从 30cases 获得的试验性的数据。结果证明在测量并且计算的柱体压力之间的好同意，和在计算、测量的柱体压力之间的偏差是不到 5% 。零维的单个地区的双曲线模型在为成层的电荷引擎当模特儿的燃烧是成功的。

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.

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.

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.

Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.

Modeling the Failure Rate of a Standby Multi-Component System and Improving Reliability

Evaluating the reliability of a system requires knowledge of the failure modes to which it is subjected. Complex topology systems generally require a high level of availability, which is a function of the arrangement of elements (components) in the system. To avoid serious failures for such complex systems, recourse can be had to the redundancy techniques available in the literature. These techniques help to improve system reliability, without affecting the reliability of system components. This paper is interested in the proposal of a model for evaluating the failure rate of a standby multi-components system and in improving the reliability of mechanical systems, arranged in a topology (series, parallel, or mixed).

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

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 Aalen 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.

RETRACTED: Nuclear Structure Study of Odd-Odd Yttrium Nuclei within Interacting-Boson Fermi-Fermion Model (IBFFM)

Short Retraction NoticeThe paper does not meet the standards of "Journal of Applied Mathematics and Physics". This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.Editor guiding this retraction: Prof. Wen-Xiu Ma (EiC of JAMP)The full retraction notice in PDF is preceding the original paper, which is marked "RETRACTED".

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.

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.