Absorption of planar waves in a draining bathtub

We present an analysis of the absorption of acoustic waves by a black hole analogue in (2 + 1) dimensions generated by a fluid flow in a draining bathtub. We show that the low-frequency absorption length is equal to the acoustic hole circumference and that the high-frequency absorption length is 4 times the ergoregion radius. For intermediate values of the wave frequency, we compute the absorption length numerically and show that our results are in excellent agreement with the low-and high-frequency limits. We analyze the occurrence of superradiance, manifested as negative partial absorption lengths for corotating modes at low frequencies.

Moderately strong vorticity in a bathtub-type flow

Theoretical and numerical analysis is performed for an inviscid axisymmetric vortical bathtub-type flow. The level of vorticity is kept high so that the image of the flow on the radial-axial plane (r-z plane) is not potential. The most significant findings are: (1) the region of validity of the strong vortex approximation is separated from the drain by a buffer region, (2) the power-law asymptote of the stream function, specified by Delta Psi similar to r(4/3) Deltaz, appears near the axis when vorticity in the flow is sufficiently strong and (3) the local Rossby number in the region of the 4/3 power-law the initial vorticity level in the flow and the global Rossby number.

Strategy Lab Experiences: Bathtub Dynamics

As the world changes ever faster, managers increasingly recognize the complexity and turbulence of the business systems in which they are embedded. The management problems are dynamic, while the dynamic complexity comes frequently from few variables with circle and delays interrelations that introduce nonlinearities.The present paper describes a research conducted in Portugal with two different groups - one, academic; the other, professional - where we explored the subjects’ understanding of some basic systems thinking concepts such as stock-flow relationship, feedback processes and time delays.

Uncertainties in tidally adjusted estimates of sea level rise flooding (bathtub model) for the Greater London

Sea-level rise (SLR) from global warming may have severe consequences for coastal cities, particularly when combined with predicted increases in the strength of tidal surges. Predicting the regional impact of SLR flooding is strongly dependent on the modelling approach and accuracy of topographic data. Here, the areas under risk of sea water flooding for London boroughs were quantified based on the projected SLR scenarios reported in Intergovernmental Panel on Climate Change (IPCC) fifth assessment report (AR5) and UK climatic projections 2009 (UKCP09) using a tidally-adjusted bathtub modelling approach. Medium- to very high-resolution digital elevation models (DEMs) are used to evaluate inundation extents as well as uncertainties. Depending on the SLR scenario and DEMs used, it is estimated that 3%–8% of the area of Greater London could be inundated by 2100. The boroughs with the largest areas at risk of flooding are Newham, Southwark, and Greenwich. The differences in inundation areas estimated from a digital terrain model and a digital surface model are much greater than the root mean square error differences observed between the two data types, which may be attributed to processing levels. Flood models from SRTM data underestimate the inundation extent, so their results may not be reliable for constructing flood risk maps. This analysis provides a broad-scale estimate of the potential consequences of SLR and uncertainties in the DEM-based bathtub type flood inundation modelling for London boroughs.

Risk Factors for Intracranial Haemorrhage in Accidents Associated with the Shower or Bathtub

BACKGROUND There has been little research on bathroom accidents. It is unknown whether the shower or bathtub are connected with special dangers in different age groups or whether there are specific risk factors for adverse outcomes. METHODS This cross-sectional analysis included all direct admissions to the Emergency Department at the Inselspital Bern, Switzerland from 1 January 2000 to 28 February 2014 after accidents associated with the bathtub or shower. Time, age, location, mechanism and diagnosis were assessed and special risk factors were examined. Patient groups with and without intracranial bleeding were compared with the Mann-Whitney U test.The association of risk factors with intracranial bleeding was investigated using univariate analysis with Fisher's exact test or logistic regression. The effects of different variables on cerebral bleeding were analysed by multivariate logistic regression. RESULTS Two hundred and eighty (280) patients with accidents associated with the bathtub or shower were included in our study. Two hundred and thirty-five (235) patients suffered direct trauma by hitting an object (83.9%) and traumatic brain injury (TBI) was detected in 28 patients (10%). Eight (8) of the 27 patients with mild traumatic brain injuries (GCS 13-15), (29.6%) exhibited intracranial haemorrhage. All patients with intracranial haemorrhage were older than 48 years and needed in-hospital treatment. Patients with intracranial haemorrhage were significantly older and had higher haemoglobin levels than the control group with TBI but without intracranial bleeding (p<0.05 for both).In univariate analysis, we found that intracranial haemorrhage in patients with TBI was associated with direct trauma in general and with age (both p<0.05), but not with the mechanism of the fall, its location (shower or bathtub) or the gender of the patient. Multivariate logistic regression analysis identified only age as a risk factor for cerebral bleeding (p<0.05; OR 1.09 (CI 1.01;1.171)). CONCLUSION In patients with ED admissions associated with the bathtub or shower direct trauma and age are risk factors for intracranial haemorrhage. Additional effort in prevention should be considered, especially in the elderly.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

Influence diagnostics for polyhazard models in the presence of covariates

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.