Bayesian sequential reliability for Weibull and related distributions

Assume that the probability density function for the lifetime of a newly designed product has the form: [H(t)/Q()] exp{–H(t)/Q()}. The Exponential(), Rayleigh, WeibullW(, ) and Pareto pdf's are special cases.Q() will be assumed to have an inverse Gamma prior. Assume thatm independent products are to be tested with replacement. A Bayesian Sequential Reliability Demonstration Testing plan is used to eigher accept the product and start formal production, or reject the product for reengineering. The test criterion is the intersection of two goals, a minimal goal to begin production and a mature product goal. The exact values of various risks and the distribution of total number of failures are evaluated. Based on a result about a Poisson process, the expected stopping time for the exponential failure time is also found. Included in these risks and expected stopping times are frequentist versions, thereof, so that the results also provide frequentist answers for a class of interesting stopping rules.This research was supported by NSF grants DMS-8703620 and DMS-8923071, and forms part of the Ph.D. Thesis of the first author, the development of which was supported in part by a David Ross grant at Purdue University. The authors thank the editors and a referee for insightful comments and suggestions.     

On the measurement of electron tunnelling time

A suggestion to experimentally measure the electron tunnelling time by observing the tunnelling current cut-off as a function of the magnetic field intensity in semiconductor pn tunnel junctions, when they are placed in a crossed electric and magnetic field configuration, has been made in this paper. A simple and a rigorous quantum mechanical analysis to justify the above proposition have been presented. An order of agreement between the tunnelling time values derived from the published experimental data and our theoretical prediction has been noticed.     

Rheological Properties of Template Polymerization Polyacrylamide Aqueous Solutions

In this work, the aqueous solution rheology properties of both partially hydrolyzed polyacrylamide (HPAM) and the template copolymer (TPAM) synthesized from acrylic acid (AA) and acrylamide (AM) were investigated using an advanced rheometer and viscometer. The results were correlated with the corresponding molecular structures of HPAM and TPAM, which were characterized by high-resolution nuclear magnetic resonance. It was found that the thickening ability of TPAM is much stronger than that of HPAM due to its unique microblocky structure, while the viscosity of TPAM was more sensitive to shear rate. Furthermore, the effect of polymer concentration was also tested in an oscillation shear mode. It showed that the characteristic relaxation time of TPAM was much higher than that of HPAM at the high concentrations. The research on salt-resistance properties showed that the viscosity retention of TPAM was similar to HPAM at the same NaCl concentration. But, unexpectedly, at the same CaCl₂ concentration the viscosity retention of TPAM was much lower than that of HPAM, indicating a poor divalent salt-resistance property.     

Ignition delay times of methane and hydrogen highly diluted in carbon dioxide at high pressures up to 300 atm

The need for more efficient power cycles has attracted interest in super-critical CO₂ (sCO₂) cycles. However, the effects of high CO₂ dilution on auto-ignition at extremely high pressures has not been studied in depth. As part of the effort to understand oxy-fuel combustion with massive CO₂ dilution, we have measured shock tube ignition delay times (IDT) for methane/O₂/CO₂ mixtures and hydrogen/O₂/CO₂ mixtures using sidewall pressure and OH* emission near 306?nm. Ignition delay time was measured in two different facilities behind reflected shock waves over a range of temperatures, 1045–1578?K, in different pressures and mixture regimes, i.e., CH₄/O₂/CO₂ mixtures at 27–286 atm and H₂/O₂/CO₂ mixtures at 37–311 atm. The measured data were compared with the predictions of two recent kinetics models. Fair agreement was found between model and experiment over most of the operating conditions studied. For those conditions where kinetic models fail, the current ignition delay time measurements provide useful target data for development and validation of the mechanisms.     

Optimization of the slowly actively Q-switched laser

By taking into account turnoff time of the slowly active Q-switch, the coupled equations of a slowly actively Q-switched laser are given. These rate equations are solved numerically. The key parameters of an optimally coupled actively Q-switched laser with the turnoff time are determined, and a group of general curves are generated for the first time. These key parameters include the optimal normalized coupling parameter which maximizes the output energy, and the corresponding normalized energy, normalized peak power and normalized pulse width. The curves clearly show the dependence of the optimal key parameters on the parameters of the gain medium and the resonator. In addition, the importance of including turnoff time of the slowly active Q-switch is also shown. The optimal calculations for an actively Q-switched Nd:YVO₄ laser with acoustic–optic modulator are presented to demonstrate the use of the curves and the related formulas.     

Anwendung nuklearer Verfahren in der ungarischen Tonerdeindustrie

Der Beitrag gibt einen zusammenfassenden Überblick über die in der ungarischen Tonerdeindustric verwendeten nuklearen Versuchsmethoden.

Anhand von Beispielen werden die an Betriebsapparaturen durchgeführten Durchlauf- und Verteiungsmessungen sowie die unter Laborbedingungen vorgenommenen reaktionskinetischen Untersuchungen, die auf die Klärung verschiedener Prozesse der Tonerdeherstellung gerichlet waren, veranschaulicht.

Weiterhin werden analytische Anwendungen der Neutronenaktivierungs- und Röntgenfluoreszenzmethode sowie Meß- und Regelungseinrichtungen, die auf der Strahlenabsorption beruhen, bekanntgemacht.     

Non-equilibrium effects in chaperone-assisted translocation of a stiff polymer

Chaperone-assisted biopolymer translocation is the main model proposed for translocation in vivo. A dynamical Monte Carlo method is used to simulate the translocation of a stiff homopolymer through a nanopore driven by chaperones. Chaperones are proteins that bind to the polymer near the wall and prevent its backsliding through Cis side. The important parameters include binding energy, size and the local concentration of the chaperones. The profile of these local concentrations, build up the chaperones distribution. Here we investigate the effects of binding energy, size and the exponential distribution of chaperones in their equilibration in each step of the polymer translocation needed for stable translocation time. The simulation results show that in case of chaperones with the size of a monomer ($\lambda =1$) and/or positive effective binding energy and/or uniform distribution, the chaperones binding equilibration rate/frequency is less than 5 times per monomer. However, in some special cases in the exponential distribution of chaperones with size $\lambda >1$ and negative effective binding energy the equilibration rate will diverge to more than 20 times per monomer. We show that this non-equilibrium effect results in supper diffusion, seen before. Moreover, we confirm the equilibration process theoretically.     

Development of the fast arcing protection for ECRH system on the HL-2A tokamak

1 Introduction A series of engineering tests and physical experiments,including ECRH[1],was carried out on the HL-2A tokamak in 2005.A fast arcing protection system[2] was developed to ensure operating of ECRH facilities[3],especially the gyrotron,against arcing in the transmission line.     

Last Passage Time Statistics for Barrier-Crossing Processes

A concept of mean last passage time at the saddle point is proposed in order to compute both the lifetime and the escape rate of a particle in a metastable potential, where the backstreaming across the saddle point is taken into account. It is shown that the mean oscillating time around the saddle point is the longest one among all the time scales at high temperatures and the inverse of the mean last passage time at the saddle point is more close to the steady escape rate.     

Transmission time of a particle in the reflectionless Sech-squared potential: Quantum clock approach

We investigate the time for a particle to pass through the reflectionless Sech-squared potential. Using the Salecker-Wigner and Peres quantum clock an average transmission time of a Gaussian wave packet representing the particle is explicitly evaluated in terms of average momentum and travel distance. The average transmission time is shown to be shorter than the time of free-particle motion and very close to the classical time for wave packets with well-localized momentum states. Since the clock measures the duration of scattering process the average transmission time can be interpreted as the average dwell time.