Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.     

On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions

Let X = X ₁ ... X _n and Y = Y ₁ ... Y _n be two binary sequences with length n. A common subsequence of X and Y is any subsequence of X that at the same time is a subsequence of Y; The common subsequence with maximal length is called the longest common subsequence (LCS) of X and Y. LCS is a common tool for measuring the closeness of X and Y. In this note, we consider the case when X and Y are both i.i.d. Bernoulli sequences with the parameters ϵ and 1 − ϵ, respectively. Hence, typically the sequences consist of large and short blocks of different colors. This gives an idea to the so-called block-by-block alignment, where the short blocks in one sequence are matched to the long blocks of the same color in another sequence. Such and alignment is not necessarily a LCS, but it is computationally easy to obtain and, therefore, of practical interest. We investigate the asymptotical properties of several block-by-block type of alignments. The paper ends with the simulation study, where the of block-by-block type of alignments are compared with the LCS.     

A new space–time discretization for the Swift–Hohenberg equation that strictly respects the Lyapunov functional

The Swift–Hohenberg equation is a central nonlinear model in modern physics. Originally derived to describe the onset and evolution of roll patterns in Rayleigh–Bénard convection, it has also been applied to study a variety of complex fluids and biological materials, including neural tissues. The Swift–Hohenberg equation may be derived from a Lyapunov functional using a variational argument. Here, we introduce a new fully-discrete algorithm for the Swift–Hohenberg equation which inherits the nonlinear stability property of the continuum equation irrespectively of the time step. We present several numerical examples that support our theoretical results and illustrate the efficiency, accuracy and stability of our new algorithm. We also compare our method to other existing schemes, showing that is feasible alternative to the available methods.     

On the structure of the Bochner–Martinelli residue currents

The paper presents a survey of the main results of I.M. Vinogradov.     

Organic‐acid mediated bulk polymerization of ε‐caprolactam and its copolymerization with ε‐caprolactone

Polyamides (PA) constitute one of the most important classes of polymeric materials and have gained strong position in different areas, such as textiles, fibers, and construction materials. Whereas most PA are synthesized by step‐growth polycondensation, PA 6 is synthesized by ring opening polymerization (ROP) of ε‐caprolactam (ε‐CLa). The most popular ROP methods involve the use of alkaline metal catalyst difficult to handle at large scale. In this article, we propose the use of organic acids for the ROP of ε‐CLa in bulk at 180 °C (below the polymer's melting point). Among evaluated organic acids, sulfonic acids were found to be the most effective for the polymerization of ε‐CLa , being the Brønsted acid ionic liquid: 1‐(4‐sulfobutyl)?3‐methylimidazolium hydrogen sulfate the most suitable due to its higher thermal stability. End‐group analysis by ¹H nuclear magnetic resonance and model reactions provided mechanistic insights and suggested that the catalytic activity of sulfonic acids was a function of not only the acid strength, but of the nucleophilic character of conjugate base as well. Finally, the ability of sulfonic acid to promote the copolymerization of ε‐CLa and ε‐caprolactone is demonstrated. As a result, poly(ε‐caprolactam‐co‐ε‐caprolactone) copolymers with considerably randomness are obtained. This benign route allows the synthesis of poly(ester amide)s with different thermal and mechanical properties. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2394–2402     

Crystal habit modifications of imatinib mesylate under various precipitation conditions

Abstract  

Crystals of the α-form of imatinib mesylate with various habits (e.g., polyhedral-like and plate-like) were prepared from various organic solvents (e.g., butyl lactate, 4-methyl-2-pentanone, 2-methyl-2-butanol, 2-isopropoxyethanol, propyl ether) by several precipitation methods. The methods provide imatinib mesylate in a non-needle-shaped crystalline α-form. The crystal modification was identified by hot-stage microscopy, scanning electron microscopy, differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FTIR), and X-ray powder diffraction (XRPD). The analyses by DSC, IR, and XRPD indicate that imatinib mesylate crystals with various habits have the same crystal structure. The plate-like habit has been also observed in the system where the organic solvent acts as a precipitant.