Probability Density Function Of Lifetime Research Articles

On the choice of proper average lifetime formula for an ensemble of emitters showing non-single exponential photoluminescence decay

In this paper, we investigate non-single exponential photoluminescence decays in various disordered condensed-matter systems. For such materials, two formulas for the average lifetime of system’s excited state are commonly used in the analysis of experimental data. In many cases, the choice of formula is arbitrary and lacks a clear physical justification. For this reason, our main goal is to show that the choice of correct mathematical formula should be based on the interpretation of measured photoluminescence decay curve. It is shown that depending on the investigated system, after appropriate normalization, photoluminescence decay curve can represent either a survival probability function or a probability density function of lifetime and for this reason two different formulas for the average lifetime are required. It is also shown that, depending on luminescence quantum yield, some information on the probability density function of lifetime can be lost in the process of measurement, which results in underestimated values of average lifetime. Finally, we provide an interpretation of total decay rate distributions which are frequently obtained by phenomenological modeling of non-single exponential photoluminescence decays.

Fatigue Failure Initiation Modeling in AA7075-T651 Using Microstructure-Sensitive Continuum Damage Mechanics

A continuum damage mechanics (CDM) model for high-cycle fatigue (HCF) is presented to study crack initiation in AA7075-T651. This study is based on the experimental observation of dependence of crack initiation life on microstructure of alloys. We investigate the effect of microstructural features such as grain size and grain orientation on crack initiation life. A crystal plasticity finite element model (CPFEM) is implemented in conjunction with CDM model to simulate damage evolution at grain scale. Finite element program ABAQUS has been used and the CPFEM–CDM model is written using a user material subroutine. Simulations are performed for constant amplitude, completely reversed loading. In order to provide a prediction for fatigue scatter, we consider different realizations of the microstructure as well as uncertainty in fatigue parameters. Given probability density function of damage parameters, we can transport it into a lifetime probability density function using simulations results. Good agreement is observed between simulations results and available experimental data. Further investigation is needed to develop the CPFEM–CDM model for HCF under variable loading conditions.

Probability density functions: From porosities to fatigue lifetime

This paper proposes a novel method to establish and identify a probability density function characterizing the fatigue lifetime. The method is initiated with a quantitative analysis of the microstructure of the material, which provides the initial probability distribution of defects. After identifying a given probability density function of defects, one can transport it into a lifetime probability density function using a growth law involving a measure of the loading over a cycle. Several parameters of the growth law are finally estimated from a given set of fatigue experiments on specimens and several techniques are discussed. The method is applied on real defect observations and lifetime data. The estimated lifetimes using the novel technique is of similar quality with standard estimation providing the probability density function of lifetime as an additional output. This output can be used directly as an input in a stress–strength interference method.

Analysis of Link Life Time in Vehicular Ad Hoc Networks for Free-Flow Traffic State

In this paper, we present analytical models for the probability density function (PDF) of link life time in vehicular ad hoc networks (VANETs), formed on both single lane as well as multi lane highways. Assuming free flow traffic state and Gaussian distributed vehicle speed, we extensively investigate the impact of vehicle mobility, vehicle density and transmission range on the link life time PDF and the mean link life time in VANETs. Our analytical and simulation results suggest that in the free-flow traffic state, exponential distribution with appropriate parametrization is a good approximation for the link life time PDF. We perform the Kolmogorov---Smirnov goodness-of-fit test to ascertain the validity of this claim.

Diffusion model in ion channel gating. Extension to agonist-activated ion channels

Previously, we described a model which treats ion channel gating as a discrete diffusion problem. In the case of agonist-activated channels at high agonist concentration, the model predicts that the closed lifetime probability density function from single channel recording approximates a power law with an exponent of -3/2 (Millhauser, G. L., E. E. Salpeter, and R. E. Oswald. 1988a. Proc. Natl. Acad. Sci. USA. 85: 1503-1507). This prediction is consistent with distributions derived from a number of ligand-gated channels at high agonist concentration (Millhauser, G. L., E. E. Salpeter, and R. E. Oswald. 1988b. Biophys. J. 54: 1165-1168.) but does not describe the behavior of ion channels at low activator concentrations. We examine here an extension of this model to include an agonist binding step. This extended model is consistent with the closed time distributions generated from the BC3H-1 nicotinic acetylcholine receptor for agonist concentrations varying over three orders of magnitude.

The lifetime probability density function for solute movement in the subsurface zone

The conceptual basis and physical significance of the solute lifetime probability density function (pdf) and its important special case, the travel time pdf, are discussed. The field-scale measurement and use of these two pdfs in characterizing solute mass transfer and solute concentrations in the subsurface zone are described along with their physical interpretation as lifetime or travel time “spectra”. The relation between the travel time pdf and mechanistic models of subsurface solute transport (e.g., the convection-dispersion equation) is illustrated with an application to three-dimensional reactive solute movement in a sand aquifer.

A Transfer Function Model of Solute Transport Through Soil: 1. Fundamental Concepts

The transfer function model (TFM) of solute transport through unsaturated soil initiated by W. A. Jury (1982) is generalized to describe the movement of a solute that may undergo physical, chemical, or biological transformations as it moves in a soil unit through which the water flow may vary in both space and time. The generalized TFM is shown to be related to the law of mass balance for a solute as interpreted in the context of probability theory. The principal conceptual entity in the TFM is the solute lifetime probability density function. Methodologies for determining this function experimentally are outlined and its relation to the solute travel time density function defined by Jury is shown. Since the generalized TFM is formulated independently of any particular mechanism of solute transport through soil, it is concluded that mechanistic models of solute movement consistent with the law of mass balance are also consistent with the TFM.