Compressive sensing adaptation for polynomial chaos expansions

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.Comment: Submitted to Journal of Computational Physic

Vida Verde. Barcelona

International audienceWe demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differential equation. The objective function and constraints of the optimization problem are then efficiently framed as non-parametric conditional expectations. Different spatial resolutions of a large-eddy simulation filter are used to explore the robustness of the model to the training dataset and to gain insight into the significance of spatial resolution on optimal design

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

Studies and researchers concerning grenade launcher with high-low pressure chambers

In this paper are presented some aspects concerning grenade launcher with high-low pressure chambers. On the bases of mathematical model of firing phenomenon for this ballistic system was elaborated interior ballistics software. With the aid of this software were studied the variation of gases pressure and grenade velocity versus time and displacement, as well as the influence of different parameters on main ballistic magnitudes. For an extant such ballistic system, the theoretical results obtained with the aid of interior ballistics software and experimental data are compared

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