Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws

Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (Ann Math 170(3):1417–1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical schemes need not converge to an entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. We advocate entropy measure-valued solutions, first proposed by DiPerna, as the appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure which constructs stable approximations to entropy measure-valued solutions, and provide sufficient conditions that guarantee that these approximations converge to an entropy measure-valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed paradigm are presented and are utilized to examine several interesting properties of the computed entropy measure-valued solutions.     

Phase transition at 233 K in [(CH3)4N]2cdI4

Abstract

[(CH₃)₄N]₂cdI₄ exhibits a phase transition at 233 K from Pnma to P2 1/c as shown by single-crystal X-ray measurements and differential scanning calorimetry. The observed entropy change amounts to approximately 8.4 J.mole^?1 K^?1 and the spontaneous strain is about – 18.10^?3. The symmetry change can be interpreted in the framework of the Landau theory.     

The Katona cycle proof of the Erdős–Ko–Rado theorem and its possibilities

In this paper we give a framework for applying Katona’s cycle proof of the Erd?s–Ko–Rado theorem to other objects. We also show how this method can be realized as a result using homomorphisms of graphs.     

Aza-Michael reaction: selective mono- versus bis-addition under environmentally-friendly conditions

Aza-Michael reactions between primary amines and methyl propenoate have been investigated under environmentally-friendly solventless heterogeneous catalysis in order to obtain the mono- or the bis-adduct. The reaction conditions can be altered so as to maximise the yields of the required product with high selectivity.     

Novel Tripod Amphiphiles for Membrane Protein Analysis

Integral membrane proteins play central roles in controlling the flow of information and molecules across membranes. Our understanding of membrane protein structures and functions, however, is seriously limited, mainly due to difficulties in handling and analysing these proteins in aqueous solution. The use of a detergent or other amphipathic agents is required to overcome the intrinsic incompatibility between the large lipophilic surfaces displayed by the membrane proteins in their native forms and the polar solvent molecules. Here, we introduce new tripod amphiphiles displaying favourable behaviours toward several membrane protein systems, leading to an enhanced protein solubilisation and stabilisation compared to both conventional detergents and previously described tripod amphiphiles.     

Voltammetry coupled to mass spectrometry in the presence of isotope O labeled water for the prediction of oxidative transformation pathways of activated aromatic ethers: Acebutolol

The coupling between an electrochemical cell (EC) and a mass spectrometer (MS) is a useful screening tool (EC-MS) to study the oxidative transformation pathways of various electroactive species. For that purpose, we showed that the EC-MS method, carried out in the presence and absence of isotope ¹⁸O labeled water leads not only to a fast identification of oxidation products but also leads to a fast elucidation of the mechanism pathway reaction. We examined herein the case of the electrochemical hydrolysis of activated aromatic ether. Acebutolol (β-blockers) was selected herein as model of activated aromatic ether, and its electrochemical oxidation was examined in both the presence and absence of isotope ¹⁸O labeled water. To elucidate electrochemical hydrolysis pathway reaction: O-dealkylation or O-dealkoxylation, our approach was used to prove its applicability. The electrochemical oxidation mechanism was then elucidated showing an O-dealkoxylation reaction. In addition, density functional theory (DFT) calculations fully support the experimental conclusions.     

Network ensemble clustering using latent roles

We present a clustering method for collections of graphs based on the assumptions that graphs in the same cluster have a similar role structure and that the respective roles can be founded on implicit vertex types. Given a network ensemble (a collection of attributed graphs with some substantive commonality), we start by partitioning the set of all vertices based on attribute similarity. Projection of each graph onto the resulting vertex types yields feature vectors of equal dimensionality, irrespective of the original graph sizes. These feature vectors are then subjected to standard clustering methods. This approach is motivated by social network concepts, and we demonstrate its utility on an ensemble of personal networks of migrants, where we extract structurally similar groups and show their resemblance to predicted acculturation strategies.     

Dielectric properties of thin-film ZrO<Subscript>2</Subscript> up to 50 GHz for RF MEMS switches

The dielectric properties of zirconium dioxide (ZrO₂) ceramic thin films were characterized up to 50 GHz using coplanar waveguides (CPWs) and metal–insulator–metal (MIM) capacitors with top circular electrodes. The ZrO₂ films were deposited using a chemical solution onto high-resistivity Si wafers and metal layers. The real part of the dielectric constant of approximately 22 and 26 was extracted at 50 GHz for CPW and MIM structures, respectively, and the loss tangent was approximately 0.09 at 50 GHz. C–V and I–V measurements were carried out to determine low-frequency and DC dielectric properties. The measurement results indicate that ZrO₂ is a promising material to be used as a dielectric layer for radio-frequency (RF) microelectromechanical systems (MEMS) capacitive switches.