Strongly stable bases for adaptively refined multilevel spline spaces

The problem of constructing a normalized hierarchical basis for adaptively refined spline spaces is addressed. Multilevel representations are defined in terms of a hierarchy of basis functions, reflecting different levels of refinement. When the hierarchical model is constructed by considering an underlying sequence of bases $\{\Gamma ^{\ell }\}_{\ell =0,\ldots ,N-1}$ with properties analogous to classical tensor-product B-splines, we can define a set of locally supported basis functions that form a partition of unity and possess the property of coefficient preservation, i.e., they preserve the coefficients of functions represented with respect to one of the bases $\Gamma ^{\ell }$ . Our construction relies on a certain truncation procedure, which eliminates the contributions of functions from finer levels in the hierarchy to coarser level ones. Consequently, the support of the original basis functions defined on coarse grids is possibly reduced according to finer levels in the hierarchy. This truncation mechanism not only decreases the overlapping of basis supports, but it also guarantees strong stability of the construction. In addition to presenting the theory for the general framework, we apply it to hierarchically refined tensor-product spline spaces, under certain reasonable assumptions on the given knot configuration.     

Statistical Inference for Ergodic Algorithmic Model (EAM), Applied to Hydrophobic Hydration Processes

The thermodynamic properties of hydrophobic hydration processes can be represented in probability space by a Dual-Structure Partition Function {DS-PF} = {M-PF} · {T-PF}, which is the product of a Motive Partition Function {M-PF} multiplied by a Thermal Partition Function {T-PF}. By development of {DS-PF}, parabolic binding potential functions α) RlnK_dual = (−ΔG°_dual/T) ={f(1/T)*g(T)} and β) RTlnK_dual = (−ΔG°_dual) = {f(T)*g(lnT)} have been calculated. The resulting binding functions are “convoluted” functions dependent on the reciprocal interactions between the primary function f(1/T) or f(T) with the secondary function g(T) or g(lnT), respectively. The binding potential functions carry the essential thermodynamic information elements of each system. The analysis of the binding potential functions experimentally determined at different temperatures by means of the Thermal Equivalent Dilution (TED) principle has made possible the evaluation, for each compound, of the pseudo-stoichiometric coefficient ±ξ_w, from the curvature of the binding potential functions. The positive value indicates convex binding functions (Class A), whereas the negative value indicates concave binding function (Class B). All the information elements concern sets of compounds that are very different from one set to another, in molecular dimension, in chemical function, and in aggregation state. Notwithstanding the differences between, surprising equal unitary values of niche (cavity) formation in Class A <Δh_for>_A = −22.7 ± 0.7 kJ·mol⁻¹ ·ξ_w⁻¹ sets with standard deviation σ = ±3.1% and <Δs_for>_A = −445 ± 3J·K⁻¹·mol⁻¹·ξ_w⁻¹J·K⁻¹·mol⁻¹·ξ_w⁻¹ with standard deviation σ = ±0.7%. Other surprising similarities have been found, demonstrating that all the data analyzed belong to the same normal statistical population. The Ergodic Algorithmic Model (EAM) has been applied to the analysis of important classes of reactions, such as thermal and chemical denaturation, denaturation of proteins, iceberg formation or reduction, hydrophobic bonding, and null thermal free energy. The statistical analysis of errors has shown that EAM has a general validity, well beyond the limits of our experiments. Specifically, the properties of hydrophobic hydration processes as biphasic systems generating convoluted binding potential functions, with water as the implicit solvent, hold for all biochemical and biological solutions, on the ground that they also are necessarily diluted solutions, statistically validated.     

Surface Dynamics of A Vanadyl Pyrophosphate Catalyst for n‐Butane Oxidation to Maleic Anhydride: An In Situ Raman and Reactivity Study of the Effect of the P/V Atomic Ratio

This work focused on investigating the effect of the P/V atomic ratio in vanadyl pyrophosphate, catalyst for n‐butane oxidation to maleic anhydride, on the nature of the catalytically active phase. Structural transformations occurring on the catalyst surface were investigated by means of in situ Raman spectroscopy in a non‐reactive atmosphere, as well as by means of steady‐state and non‐steady‐state reactivity tests, in response to changes in the reaction temperature. It was found that the nature of the catalyst surface is affected by the P/V atomic ratio even in the case of small changes in this parameter. With the catalyst having P/V equal to the stoichiometric value, a surface layer made of α_I‐VOPO₄ developed in the temperature interval 340–400 °C in the presence of air; this catalyst gave a very low selectivity to maleic anhydride in the intermediate T range (340–400 °C). However, at 400–440 °C δ‐VOPO₄ overlayers formed; at these conditions, the catalyst was moderately active but selective to maleic anhydride. With the catalyst containing a slight excess of P, the ratio offering the optimal catalytic performance, δ‐VOPO₄ was the prevailing species over the entire temperature range investigated (340–440 °C). Analogies and differences between the two samples were also confirmed by reactivity tests carried out after in situ removal and reintegration of P. These facts explain why the industrial catalyst for n‐butane oxidation holds a slight excess of P; they also explain discrepancies registered in the literature about the nature of the active layer in vanadyl pyrophosphate.     

Neutral substituted carbonyl clusters of iridium. Synthesis and X-ray characterization of tri-μ3-carbonyl-μ-carbonylheptacarbonylpentakis(trimethylphosphite)-octahedro-hexairidium

The reaction of Ir₆(CO)₁₆ with P(OMe)₃ in toluene yields Ir₆(CO)₁₁ [P(OMe)₃]₅ which has been shown by X-ray diffraction to contain an octahedral cluster of iridium atoms bearing five terminal trimethylphosphite ligands, three face-bridging, one edge-bridging and seven terminal carbonyl groups.     

Unusual behavior of the aqueous solutions of gemini bispyridinium surfactants: apparent and partial molar enthalpies of the dimethanesulfonates

Apparent and partial molar enthalpies at 298 K of the aqueous solutions of cationic gemini surfactants 1,1'-didodecyl-2,2'-dimethylenebispyridinium dimethanesulfonate (12-Py(2)-2-(2)Py-12 MS); 1,1'-didodecyl-2,2'-trimethylenebispyridinium dimethanesulfonate (12-Py(2)-3-(2)Py-12 MS); 1,1'-didodecyl-2,2'-tetramethylenebispyridinium dimethanesulfonate (12-Py(2)-4-(2)Py-12 MS); 1,1'-didodecyl-2,2'-octamethylenebispyridinium dimethanesulfonate (12-Py(2)-8-(2)Py-12 MS); 1,1'-didodecyl-2,2'-dodecamethylenebispyridinium dimethanesulfonate (12-Py(2)-12-(2)Py-12 MS) were measured as a function of concentration and are here reported for the first time. They show a very peculiar behavior as a function of the spacer length, not allowing for the determination of a -CH 2- group contribution when this group is added to the spacer. The curve of the compound with a four-carbon-atom-long spacer lies between those of the compound with a spacer of 2 and 3 carbon atoms, instead of that below the latter, as expected. This surprising behavior, never found before in the literature and different from that found for the more popular m- s- m-type bisquaternary ammonium gemini surfactants, could be explained by a conformation change of the molecule, caused by stacking interactions between the two pyridinium rings, mediated by the counterion and appearing at an optimum length of the spacer. The hypothesis is also supported by the data obtained from the surface tension vs log c curves, showing that A min, the minimum area taken at the air-water interface by the molecule, is significantly lower for 12-Py(2)-4-(2)Py-12 MS than that of the other compounds of the same homologous series, and that the same compound has a greater tendency to form micelles instead of adsorbing at the air/water interface. The evaluation of the micellization enthalpies, by means of a pseudophase transition model, agrees with the exposed trends. These results confirm the great crop of information that can be derived from the study of the solution thermodynamics of aggregate systems and in particular from the curves of apparent and molar enthalpies vs concentration.     

Synthesis of mesoporous carbons and reduced graphene oxide and their influence on the cycling performance of rechargeable Li-O<Subscript>2</Subscript> batteries

In the lithium-oxygen (Li-O₂) cell, the porous structure of the cathode is an important issue as well as challenge for its task of accommodating discharge products and providing free paths for oxygen. Clogging of pores and degradation of materials at the cathode affect the discharge rates and cycling performance of Li-O₂ cell. Based on the study of five synthesized nanostructured porous carbons, namely, 2-D ordered mesoporous carbon C-15, 3-D ordered mesoporous carbons C-16 and C-16B with larger pores, hollow core mesoporous shell carbon (HCMSC), and reduced graphene oxide (rGO), we found that the type and pore structure of the carbon significantly affect the electrochemical performance of the cell. Both C-15 and rGO cathodes demonstrate good cell cycleability, while the HCMSC, with its interesting bimodal pore system, is not favorable for further improving cycling performance. The C-16B has similar morphology and electrolyte wettability of C-16. However, the former possesses larger pores, and such porosity significantly improves the cell cycleability up to 44 cycles, corresponding to an extended operation life of 850 h.

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Dual confinement of sulphur with rGO-wrapped microporous carbon from β-cyclodextrin nanosponges as a cathode material for Li–S batteries

A novel approach is developed to synthesize microporous carbon spheres with pore size ranges from 5 to 11 Å from hyper-cross-linked polymer β-cyclodextrin. Sulphur is incorporated in the micropores by solution impregnation followed by melt infusion. The resultant carbon sulphur (C/S) composite is wrapped in reduced graphene oxide (rGO) to provide conductive pathways to access the sulphur in micropores and to protect the surface-adhered sulphur. The cathode material obtained from rGO wrapping delivers initial discharge capacity of 1103 mA h g^?1 at 0.1 C, maintaining a capacity of 626 mA h g^?1 at 0.2 C with capacity loss of 0.2% per cycle for more than 100 cycles. In another cell configuration using carbon paper as an interlayer, discharge capacity has raised to 850 mA h g^?1 at 0.2 C and maintained 86% of its capacity for 100 cycles with excellent rate capability and high Coulombic efficiency. The good performance may be referred to excellent conductive networks, porous architecture of carbon spheres and adsorption of catholyte by fibrous interlayer that can effectively reduce the polysulfide shuttling.     

Some research perspectives in galloping phenomena: critical conditions and post-critical behavior

This paper gives an overview of wind-induced galloping phenomena, describing its manifold features and the many advances that have taken place in this field. Starting from a quasi-steady model of aeroelastic forces exerted by the wind on a rigid cylinder with three degree-of-freedom, two translations and a rotation in the plane of the model cross section, the fluid–structure interaction forces are described in simple terms, yet suitable with complexity of mechanical systems, both in the linear and in the nonlinear field, thus allowing investigation of a wide range of structural typologies and their dynamic behavior. The paper is driven by some key concerns. A great effort is made in underlying strengths and weaknesses of the classic quasi-steady theory as well as of the simplistic assumptions that are introduced in order to investigate such complex phenomena through simple engineering models. A second aspect, which is crucial to the authors’ approach, is to take into account and harmonize the engineering, physical and mathematical perspectives in an interdisciplinary way—something which does not happen often. The authors underline that the quasi-steady approach is an irreplaceable tool, tough approximate and simple, for performing engineering analyses; at the same time, the study of this phenomenon gives origin to numerous problems that make the application of high-level mathematical solutions particularly attractive. Finally, the paper discusses a wide range of features of the galloping theory and its practical use which deserve further attention and refinements, pointing to the great potential represented by new fields of application and advanced analysis tools.     

A high-capacity cathode based on silicates material for advanced lithium batteries

Silicate materials have been proposed as alternative cathodes for Li-ion battery applications. A novel mixture of silicates, labelled Li₆MnSi₅, based on the molar ratio among the Li/Mn/Si precursors, with promising electrochemical properties as positive electrode material is synthesized through a solid-state reaction. The results indicate the proposed synthetic method as effective for preparation of nanostructured silicate powders with average particle diameter of 30 nm. Structural morphology of the samples was determined using X-ray powder diffraction (XRPD), XPS and FESEM analysis. A joint analysis by XRPD data and by density functional theory (DFT) identified LiHMn₄Si₅O₁₅, Li₂Mn₄Si₅O₁₅, Li₂Si₂O₅ and Li_0.125Mn_0.875SiO₄ as components of Li₆MnSi₅ mixture. The electrochemical performance of Li₆MnSi₅ was evaluated by charge/discharge testing at constant current mode. Li₆MnSi₅ discharge behaviour is characterized by high capacity value of 480 mA h g^?1, although such capacity fades gradually on cycling. Ex situ XPS studies carried out on the electrode in both full charged and discharged states pointed out that Li₂Si₂O₅ is decisive for achieving such high capacity. The discharge/charge plateau is most probably related to the change in the oxidation state of silicon at the surface of the silica material.