Bifurcation of homoclinics

We show that homoclinic trajectories of nonautonomous vector fields parametrized by a circle bifurcate from the stationary solution when the asymptotic stable bundles of the linearization at plus and minus infinity are ``twisted' in different ways.

     

Eigenvalues and eigenfunctions of discontinuous Sturm--Liouville problems with eigenparameter-dependent boundary conditions

We extend some fundamental spectral properties of classic regular Sturm--Liouville problems to discontinuous boundary-value problems with eigenvalue-dependent boundary conditions. We suggest a new approach for investigation of such type discontinuous problems.     

Nonparametric estimation under length-biased sampling and Type I censoring: A moment based approach

Observation of lifetimes by means of cross-sectional surveys typically results in left-truncated, right-censored data. In some applications, it may be assumed that the truncation variable is uniformly distributed on some time interval, leading to the so-called length-biased sampling. This information is relevant, since it allows for more efficient estimation of survival and related parameters. In this work we introduce and analyze new empirical methods in the referred scenario, when the sampled lifetimes are at risk of Type I censoring from the right. We illustrate the method with real economic data. Work supported by the Grants PGIDIT02PXIA30003PR and BFM2002-03213.     

CFD analysis of a TG–DSC apparatus

A ThermoGravimetric analyser with differential scanning calorimetry (TG–DSC) has been studied during the fusion of an indium sample using both an experimental procedure and a CFD simulation. To do so, a CAD model of the real device was built and meshed in detail, in order to take into account the small scale processes which occur inside the crucibles. Several theoretical models, some previously existing in the CFD software used and others developed ad hoc, were applied to simulate the whole facility. Therefore, realistic boundary conditions and a PID-based control system already developed for previous studies had to be used. The validation of the CFD model was done by comparing the outcome of the resulting simulation to the results obtained by experimental procedure in a case where natural convection is the main heat and mass transfer mechanism. This comparison was made for two different heating rates inside the furnace. Typical characteristics of phase change process inside a TG-DSC as thermal lag, onset temperature or heat flow exchange during the fusion could be analysed. As well, a more detailed approach to physical phenomena taking place inside the furnace could be done, since CFD simulations allow to obtain data which is not achievable experimentally. Besides, a valid CFD model for a TG-DSC could be later used in further CFD simulations.     

Isobaric thermal expansivity behaviour against temperature and pressure of associating fluids

In order to study the influence of association on the isobaric thermal expansivity, this magnitude has been experimentally determined for a set of associating fluids within the temperature and pressure intervals (278.15 to 348.15) K and (5 to 55) MPa by means of calorimetric measurements. The 1-alcohol series, from methanol to 1-decanol, 2-pentanol, 3-pentanol, and 1-pentylamine were selected. With a view on checking the quality of the experimental data, they are compared with available literature values; good coherence was obtained for most of the studied liquids. The analysis of the experimental results reveals that the association capability presents a strong influence not only on the value of the isobaric thermal expansivity itself, but also on its behaviour against temperature and pressure.     

Excess molar properties for binary systems of alkylimidazolium-based ionic liquids + nitromethane. Experimental results and ERAS-model calculations

Density, isobaric molar heat capacity, and excess molar enthalpy were experimentally determined at atmospheric pressure for a set of binary systems ionic liquid + nitromethane. The studied ionic liquids were: 1-butyl-3-methylimidazolium tetrafluoroborate, 1-hexyl-3-methylimidazolium tetrafluoroborate, 1-butyl-3-methylpyridinium tetrafluoroborate, 1-ethyl-3-methylimidazolium ethylsulfate, 1-butyl-3-methylimidazolium methylsulfate, 1-ethyl-3-methylimidazolium trifluoromethanesulfonate, and 1-butyl-3-methylimidazolium trifluoromethanesulfonate. Density and heat capacity were obtained within the temperature range (293.15 to 318.15) K whereas excess molar enthalpy was measured at 303.15 K; excess molar volume and excess molar isobaric heat capacity were calculated from experimental data. The ERAS-model was applied in order to study the microscopic mechanisms involved in the mixing process. Although the studied compounds are not self-associated, ERAS-model describe adequately the experimental results if cross-association between both compounds is considered.     

An accurate calibration method for high pressure vibrating tube densimeters in the density interval (700 to 1600) kg · m−3

A calibration procedure of vibrating tube densimeters for density measurement of liquids in the intervals (700 to 1600) kg · m^?3, (283.15 to 323.15) K, and (0.1 to 60) MPa is presented. It is based on the modelization of the vibrating tube as a thick-tube clamped at one end (cantilever) whose stress and thermal behaviour follows the ideas proposed in the Forced Path Mechanical Calibration model (FPMC). Model parameters are determined using two calibration fluids with densities certified at atmospheric pressure (dodecane and tetracholoroethylene) and a third one with densities known as a function of pressure (water). It is applied to the Anton Paar 512P densimeter, obtaining density measurements with an expanded uncertainty less than 0.2 kg · m^?3 in the working intervals. This accuracy comes from the combination of several factors: densimeter behaves linearly in the working density interval, densities of both calibration fluids cover that interval and they have a very low uncertainty, and the mechanical behaviour of the tube is well characterized by the considered model. The main application of this method is the precise measurement of high density fluids for which most of the calibration procedures are inaccurate.     

A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples

In this paper, we discuss the estimation of a density function based on censored data by the kernel smoothing method when the survival and the censoring times form a stationary α-mixing sequence. A Berry-Esseen type bound is derived for the kernel density estimator at a fixed point x. For practical purposes, a randomly weighted estimator of the density function is also constructed and investigated.     

Nonparametric estimation of a conditional distribution from length-biased data

In this paper we consider the problem of estimating a conditional distribution function in a nonparametric way, when the response variable is nonnegative, and the observational procedure is length-biased. We propose a proper adaptation of the estimate to right-censoring provoked by limitation in following-up. Large sample analysis of the introduced estimator is given, including rates of convergence, limiting distribution, and efficiency results. We show that the length-bias model results in less variance in estimation, when compared to methods based on observed truncation times. Practical performance of the proposed estimator is explored through simulations. Application to unemployment data analysis is provided.