Coupled bending-torsion vibration of a homogeneous beam with a single delamination subjected to axial loads and static end moments

Delaminations in structures may significantly reduce the stiffness and strength of the structures and may affect their vibration characteristics. As structural components, beams have been used for various purposes, in many of which beams are often subjected to axial loads and static end moments. In the present study, an analytical solution is developed to study the coupled bending-torsion vibration of a homogeneous beam with a single delamination subjected to axial loads and static end moments. Euler–Bernoulli beam theory and the "free mode" assumption in delamination vibration are adopted. This is the first study of the influences of static end moments upon the effects of delaminations on natural frequencies, critical buckling loads and critical moments for lateral instability. The results show that the effects of delamination on reducing natural frequencies, critical buckling load and critical moment for lateral instability are aggravated by the presence of static end moment. In turn, the effects of static end moments on vibration and instability characteristics are affected by the presence of delamination. The analytical results of this study can serve as a benchmark for finite element method and other numerical solutions.     

From the margin to the center: A framework for rehumanizing mathematics education for students with dis/abilities

Mathematics education for students with dis/abilities has a legacy of exclusion; its scholarship has been dominated by ableist perspective: a focus on rote mathematics facts, procedural instruction, and a narrow range of mathematics content. Grounded in critical pedagogy and critical disabilities studies, we argue for a shift in the focus away from the student as the site of defect and intervention to recognize the complex embodiment of dis/ability as a process produced within historical, political, social, and material contexts. The theoretical assumptions and guiding principles for a framework of culturally responsive and relational understanding of dis/ability will be shared together with a case of such an approach in classroom practice. The paper advances efforts to support all learners in robust mathematics learning communities and to situate research from perspectives that acknowledge the situated, interactional nature of ability, identity, and achievement.     

Exploring the relevance of thiophene rings as bridge unit in acceptor‐bridge‐donor dyes on self‐aggregation and performance in DSSCs

The possibility of dye charge recombination in DSSCs remains a challenge for the field. This consists of: (a) back‐transfer from the TiO₂ to the oxidized dye and (b) intermolecular electron transfer between dyes. The latter is attributed to dye aggregation due to dimeric conformations. This leads to poor electron injection which decreases the photocurrent conversion efficiency. Most organic sensitizers are characterized by an Acceptor‐Bridge‐Donor ( A ‐Bridge‐ D ) arrangement that is commonly employed to provide charge separation and, therefore, lowering the unwanted back‐transfer. Here, we address the intermolecular electron transfer by studying the dimerization and photovoltaic performance of a group of A ‐Bridge‐ D structured dyes. Specifically, eight famous sulfur containing π‐bridges were analyzed ( A and D remained fixed). Through quantum mechanical and molecular dynamics approaches, it was found that the formation of weakly stabilized dimers is allowed. The dyes with covalently bonded and fused thiophene rings as Bridges, 6d and 7d as well as 8d with a fluorene, would present high aggregation and, therefore, high probability of recombination processes. Conversely, using TiO₂ cluster and surface models, delineated the shortest bridges to improve the adsorption energy and the stability of the system. Finally, the elongation of the bridge up to 2 and 3 units and their photovoltaic parameters were studied. These results showed that all the sensitizers are able to provide similar photocurrent outcomes, regardless of whether the bridge is elongated. © 2017 Wiley Periodicals, Inc.     

Judiciously 3‐partitioning 3‐uniform hypergraphs

Bollobás, Reed, and Thomason proved every 3‐uniform hypergraph ? with m edges has a vertex‐partition V()=V₁?V₂?V₃ such that each part meets at least edges, later improved to 0.6m by Halsegrave and improved asymptotically to 0.65m+o(m) by Ma and Yu. We improve this asymptotic bound to , which is best possible up to the error term, resolving a special case of a conjecture of Bollobás and Scott.     

Solvent Effects in the Homogeneous Catalytic Reduction of Propionaldehyde with Aluminium Isopropoxide Catalyst: New Insights from PFG NMR and NMR Relaxation Studies

Solvent effects in homogeneous catalysis are known to affect catalytic activity. Whilst these effects are often described using qualitative features, such as Kamlet-Taft parameters, experimental tools able to quantify and reveal in more depth such effects have remained unexplored. In this work, PFG NMR diffusion and T₁ relaxation measurements have been carried out to probe solvent effects in the homogeneous catalytic reduction of propionaldehyde to 1-propanol in the presence of aluminium isopropoxide catalyst. Using data on diffusion coefficients it was possible to estimate trends in aggregation of different solvents. The results show that solvents with a high hydrogen-bond accepting ability, such as ethers, tend to form larger aggregates, which slow down the molecular dynamics of aldehyde molecules, as also suggested by T₁ measurements, and preventing their access to the catalytic sites, which results in the observed decrease of catalytic activity. Conversely, weakly interacting solvents, such as alkanes, do not lead to the formation of such aggregates, hence allowing easy access of the aldehyde molecules to the catalytic sites, resulting in higher catalytic activity. The work reported here is a clear example on how combining traditional catalyst screening in homogeneous catalysis with NMR diffusion and relaxation time measurements can lead to new physico-chemical insights into such systems by providing data able to quantify aggregation phenomena and molecular dynamics.     

Spin switch effect in multiply connected superconductor-ferromagnet hybrid geometry

We consider a superconducting spin valve in multiply connected superconductor-ferromagnet hybrid geometry such as a superconducting ring enclosed a ferromagnetic metal, in the framework of linearized Usadel equations. We simplify our model by considering the presence of the exchange field in the superconducting ring which allows us to manipulate magnetization orientations in parallel or antiparallel configurations by switching the weaker exchange field. In such geometry the superconducting ground state is activated to higher orbital states characterized by the nonvanishing vorticity parameters L which will be the energetically favorable superconducting state in some ranges of the proximity superconductor-ferromagnet region. The competing effects caused by the exchange interactions and the orbital effect, are analyzed through the nonmonotonic dependence of the superconducting critical temperature $T_c$ on the radius $d_f$ of the ferromagnetic core. The analytic $T_c(d_f)$ formula is obtained within the single mode approach and the analysis of the spin switch effect is given.     

Molecular chaperone-like properties of sodium caseinate to suppress the pressure-induced aggregation of β-lactoglobulin

ABSTRACT

The objective of this study was to determine whether sodium caseinate can inhibit the aggregation of whey protein induced by pressure treatment. Solutions of β-lactoglobulin (β-Lg, 0.2%, w/v) and mixtures containing 0.2% (w/v) β-Lg and 0–0.5% (w/v) sodium caseinate (NaCas) were pressurized at 400–800?MPa. NaCas suppressed the aggregation of β-Lg induced by pressure treatment, and this function was dependent on the concentration of NaCas. Furthermore, NaCas altered the aggregation process of β-Lg by suppressing the transition of the aggregate from the soluble phase to the insoluble phase and, as a result, the fraction of insoluble aggregates was decreased. During this process, NaCas formed stable complexes with the denatured β-Lg, and the formation of complexes prevented further aggregation of β-Lg. These results indicate that NaCas exhibits a chaperone-like activity under high pressure.     

Ill-posedness of the Camassa–Holm and related equations in the critical space

We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space $H^{3/2}$ and even in the Besov space $B_{p,r}^{1+1/p}$ for $p\in [1,\infty ],r\in (1,\infty ]$. Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5], [14], [16]).