Low-temperature and low-pressure effective fluorescence lifetimes and spectra of gaseous anisole and toluene

Fluorescence spectra and lifetimes of anisole and toluene vapor in nitrogen have been measured at conditions below ambient (257–293 K and 100–2000 mbar) upon excitation with 266-nm laser light to expand the applicable range of anisole and toluene laser-induced fluorescence (LIF) for conditions below room temperature that occur in expanding flows and cases with strong evaporative cooling. Anisole fluorescence spectra broaden with decreasing pressure while fluorescence lifetimes decrease simultaneously. This is consistent with a more pronounced effect of internal vibrational redistribution on the overall fluorescence signal and can be explained by significantly reduced collision rates. In the case of toluene, the transition from photo-induced heating to photo-induced cooling was observed for the first time for 266 nm. The data confirm predictions of earlier work and is particularly important for the advancement of the available photo-physical (step-ladder) models: since those transitions mark points where the molecules are already thermalized after excitation (i.e., no vibrational relaxation occurs during deactivation), they are important support points for fitting empirical parameters and allow analytical determination of the ground state energy transferred to the excited state. The data enable temperature and/or pressure sensing, e.g., in accelerating cold flows using laser-induced fluorescence of both tracers.

EXISTENCE AND UNIQUENESS OF CHAIN LADDER SOLUTIONS

The cross-classified chain ladder has a number of versions, depending on the distribution to which observations are subject. The simplest case is that of Poisson distributed observations, and then maximum likelihood estimates of parameters are explicit. Most other cases, however, including Bayesian chain ladder models, lead to implicit MAP (Bayesian) or MLE (non-Bayesian) solutions for these parameter estimates, raising questions as to their existence and uniqueness. The present paper investigates these questions in the case where observations are distributed according to some member of the exponential dispersion family.

Maxwell–Voigt and Maxwell Ladder Models for Multi-Degree-of-Freedom Elastomeric Isolation Systems

This paper presents a model for an elastomeric isolation system consisting of a three degree-of-freedom (DOF) rigid body assembled to a frame through multiple isolators. Each elastomeric isolator is either represented by a Maxwell–Voigt (MV) model consisting of two Maxwell elements or by a Maxwell ladder (ML) model consisting of three Maxwell elements. The MV models and the ML models are characterized by using experimental data that are collected at multiple excitation frequencies. The characterized models are evaluated and used to simulate the performance of the isolation system. The models developed in this paper are capable of representing frequency-dependent behavior that is exhibited by elastomeric isolators and the overall isolation system. Furthermore, the proposed model is capable of directly associating the behavior of the isolation system with physical and geometrical properties of each isolator. The proposed model is expected to be a useful tool for the analysis and design optimization of elastomeric isolation systems. Most of the isolation systems in practical applications exhibit multiple DOF, this model will be particularly useful in such applications since it does not constrain motion to translation only. This is a shortcoming of the models in the current literature that the proposed model attempts to overcome.