On the “viscous incompressible fluid + rigid body” system with Navier conditions

In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body's boundary. The whole system “viscous incompressible fluid + rigid body” is assumed to occupy the full space R³${\mathbb{R}}^3$. We start by proving the existence of global weak solutions to the Cauchy problem. Then, we exhibit several properties of these solutions. First, we show that the added-mass effect can be computed which yields better-than-expected regularity (in time) of the solid velocity-field. More precisely we prove that the solid translation and rotation velocities are in the Sobolev space H¹$H^1$. Second, we show that the case with the body fixed can be thought as the limit of infinite inertia of this system, that is when the solid density is multiplied by a factor converging to +∞. Finally we prove the convergence in the energy space of weak solutions “à la Leray” to smooth solutions of the system “inviscid incompressible fluid + rigid body” as the viscosity goes to zero, till the lifetime T   of the smooth solution of the inviscid system. Moreover we show that the rate of convergence is optimal with respect to the viscosity and that the solid translation and rotation velocities converge in H¹(0,T)$H^1(0,T)$.     

Effective learning hyper-heuristics for the course timetabling problem

Course timetabling is an important and recurring administrative activity in most educational institutions. This article combines a general modeling methodology with effective learning hyper-heuristics to solve this problem. The proposed hyper-heuristics are based on an iterated local search procedure that autonomously combines a set of move operators. Two types of learning for operator selection are contrasted: a static (offline) approach, with a clear distinction between training and execution phases; and a dynamic approach that learns on the fly. The resulting algorithms are tested over the set of real-world instances collected by the first and second International Timetabling competitions. The dynamic scheme statistically outperforms the static counterpart, and produces competitive results when compared to the state-of-the-art, even producing a new best-known solution. Importantly, our study illustrates that algorithms with increased autonomy and generality can outperform human designed problem-specific algorithms.     

Variational Solutions to Nonlinear Diffusion Equations with Singular Diffusivity

We provide existence results for nonlinear diffusion equations with multivalued time-dependent nonlinearities related to convex continuous not coercive potentials. The results in this paper, following a variational principle, state that a generalized solution of the nonlinear equation can be retrieved as a solution of an appropriate minimization problem for a convex functional involving the potential and its conjugate. In the not coercive case, this assertion is conditioned by the validity of a relation between the solution and the nonlinearity. A sufficient condition, under which this relation is true, is given. At the end, we present a discussion on the solution existence for a particular equation describing a self-organized criticality model.     

Zur Trennung der Metalle der dritten Analysengruppe

Ohne Zusammenfassung     

Cocrystal Formation through Mechanochemistry: from Neat and Liquid‐Assisted Grinding to Polymer‐Assisted Grinding

Mechanochemistry is an effective method for the preparation of multicomponent crystal systems. In the present work, we propose an alternative to the established liquid‐assisted grinding (LAG) approach. Polymer‐assisted grinding (POLAG) is demonstrated to provide a new class of catalysts for improving reaction rate and increasing product diversity during mechanochemical cocrystallization reactions. We demonstrate that POLAG provides advantages comparable to the conventional liquid‐assisted process, whilst eliminating the risk of unwanted solvate formation as well as enabling control of resulting particle size. It represents a new approach for the development of functional materials through mechanochemistry, and possibly opens new routes toward the understanding of the mechanisms and pathways of mechanochemical cocrystal formation.     

An integrated platform for gas-diffusion separation and electrochemical determination of ethanol on fermentation broths

An integrated platform was developed for point-of-use determination of ethanol in sugar cane fermentation broths. Such analysis is important because ethanol reduces its fuel production efficiency by altering the alcoholic fermentation step when in excess. The custom-designed platform integrates gas diffusion separation with voltammetric detection in a single analysis module. The detector relied on a Ni(OH)₂-modified electrode. It was stabilized by uniformly depositing cobalt and cadmium hydroxides as shown by XPS measurements. Such tests were in accordance with the hypothesis related to stabilization of the Ni(OH)₂ structure by insertion of Co²⁺ and Cd²⁺ ions in this structure. The separation step, in turn, was based on a hydrophobic PTFE membrane, which separates the sample from receptor solution (electrolyte) where the electrodes were placed. Parameters of limit of detection and analytical sensitivity were estimated to be 0.2% v/v and 2.90 μA % (v/v)⁻¹, respectively. Samples of fermentation broth were analyzed by both standard addition method and direct interpolation in saline medium based-analytical curve. In this case, the saline solution exhibited ionic strength similar to those of the samples intended to surpass the tonometry colligative effect of the samples over analyte concentration data by attributing the reduction in quantity of diffused ethanol vapor majorly to the electrolyte. The approach of analytical curve provided rapid, simple and accurate analysis, thus contributing for deployment of point-of-use technologies. All of the results were accurate with respect to those obtained by FTIR method at 95% confidence level.