On the interaction of vortices with mixing layers

We describe the perturbations introduced by two counter-rotating vortices - in a two-dimensional configuration - or by a vortex ring - in an axisymmetric configuration - to the mixing layer between two counterflowing gaseous fuel and air streams of the same density. The analysis is confined to the near stagnation point region, where the strain rate of the unperturbed velocity field, A0, is uniform. We restrict our attention to cases where the typical distance 2r0 between the vortices - or the characteristic vortex ring radius r0 - is large compared to both the thickness, δv, of the vorticity core and the thickness, δm∼(ν/A0)1/2, of the mixing layer. In addition, we consider that the ratio, Γ/ν, of the vortex circulation, Γ, to the kinematic viscosity, ν, is large compared to unity. Then, during the interaction time, A0,-1, the viscous and diffusion effects are confined to the thin vorticity core and the thin mixing layer, which, when seen with the scale r0, appears as a passive interface between the two counterflowing streams when they have the same density. In this case, the analysis provides a simple procedure to describe the displacement and distortion of the interface, as well as the time evolution of the strain rate imposed on the mixing layer, which are needed to calculate the inner structure of the reacting mixing layer as well as the conditions for diffusion flame extinction and edge-flame propagation along the mixing layer. Although in the reacting case variable density effects due to heat release play an important role inside the mixing layer, in this paper the analysis of the inner structure is carried out using the constant density model, which provides good qualitative understanding of the mixing layer response

An integrated view of theiInfluence of temperature, pressure, and humidity on the stability of trimorphic cysteamine hydrochloride

Understanding the phase behavior of pharmaceuticals is important for dosage form development and regulatory requirements, in particular after the incident with ritonavir. In the present paper, a comprehensive study of the solid-state phase behavior of cysteamine hydrochloride used in the treatment of nephropathic cystinosis and recently granted orphan designation by the European Commission is presented employing (high-pressure) calorimetry, water vapor sorption, and X-ray diffraction as a function of temperature. A new crystal form (I2/a, form III) has been discovered, and its structure has been solved by X-ray powder diffraction, while two other crystalline forms are already known. The relative thermodynamic stabilities of the commercial form I and of the newly discovered form III have been established; they possess an overall enantiotropic phase relationship, with form I stable at room temperature and form III stable above 37 degrees C. Its melting temperature was found at 67.3 +/- 0.5 degrees C. Cysteamine hydrochloride is hygroscopic and immediately forms a concentrated saturated solution in water with a surprisingly high concentration of 47.5 mol % above a relative humidity of 35%. No hydrate has been observed. A temperature composition phase diagram is presented that has been obtained with the unary pressure temperature phase diagram, measurements, and calculations. For development, form I would be the best form to use in any solid dosage form, which should be thoroughly protected against humidity.Postprint (author's final draft

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models

Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia

A mathematical model, coupling the dynamics of short-term stem-like cells and mature leukocytes in leukemia with that of the immune system, is investigated. The model is described by a system of seven delay differential equations with seven delays. Three equilibrium points E0, E1, E2 are highlighted. The stability and the existence of the Hopf bifurcation for the equilibrium points are investigated. In the analysis of the model, the rate of asymmetric division and the rate of symmetric division are very important

Hull girder ultimate strength assessment according to rules requirements

Residual ultimate strength of hull girder is rather important in naval vessel design, being a fundamental driver and a specific project requirement. In this paper, an applicable approach facing such challenge in pre-liminary naval vessel design is presented in the form of a benchmark study. Two typical case-studies were defined and three damaged positions along the hull length were analysed at different transverse section heights as required by class rules. First case aims at comparing notation requirements provided by Lloyd’s Register and RINA Naval Ship Rules using the same input threat. Second application focuses on results ob-tained by different class support software using damage extent and load conditions defined by Lloyd’s Regis-ter Rules as a baseline. Results of residual ultimate strength analysis of damaged hull girder in all considered cases are outlined and compared, also including results of direct, residual strength, elastoplastic analyses performed by finite element software