Integral Equations with Hypersingular Kernels -- Theory and Applications to Fracture Mechanics

Hypersingular integrals of the type I_{\alpha}(T_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{T_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 and I_{\alpha}(U_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{U_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 are investigated for general integers $\alpha$ (positive) and $m$ (non-negative), where $T_n(s)$ and $U_n(s)$ are the Tchebyshev polynomials of the 1st and 2nd kinds, respectively. Exact formulas are derived for the cases $\alpha = 1, 2, 3, 4$ and $m = 0, 1, 2, 3$; most of them corresponding to new solutions derived in this paper. Moreover, a systematic approach for evaluating these integrals when $\alpha > 4$ and $m>3$ is provided. The integrals are also evaluated as $|r|>1$ in order to calculate stress intensity factors (SIFs). Examples involving crack problems are given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. The examples include classical linear elastic fracture mechanics (LEFM), functionally graded materials (FGM), and gradient elasticity theory. An appendix, with closed form solutions for a broad class of integrals, supplements the paper

Perverse Romanticism

Richard C. Sha’s revealing study considers how science shaped notions of sexuality, reproduction, and gender in the Romantic period. Through careful and imaginative readings of various scientific texts, the philosophy of Immanuel Kant and Longinus, and the works of such writers as William Blake, Percy Bysshe Shelley, Mary Wollstonecraft, and Lord Byron, Sha explores the influence of contemporary aesthetics and biology on literary Romanticism. Revealing that ideas of sexuality during the Romantic era were much more fluid and undecided than they are often characterized in the existing scholarship, Sha’s innovative study complicates received claims concerning the shift from perversity to perversion in the nineteenth century. He observes that the questions of perversity—or purposelessness—became simultaneously critical in Kantian aesthetics, biological functionalism, and Romantic ideas of private and public sexuality. The Romantics, then, sought to reconceptualize sexual pleasure as deriving from mutuality rather than from the biological purpose of reproduction.At the nexus of Kantian aesthetics, literary analysis, and the history of medicine, Perverse Romanticism makes an important contribution to the study of sexuality in the long eighteenth century

Imagination and Science in Romanticism

How did the idea of the imagination impact Romantic literature and science?2018 Winner, Jean-Pierre Barricelli Book Prize, The International Conference on RomanticismRichard C. Sha argues that scientific understandings of the imagination indelibly shaped literary Romanticism. Challenging the idea that the imagination found a home only on the side of the literary, as a mental vehicle for transcending the worldly materials of the sciences, Sha shows how imagination helped to operationalize both scientific and literary discovery. Essentially, the imagination forced writers to consider the difference between what was possible and impossible while thinking about how that difference could be known. Sha examines how the imagination functioned within physics and chemistry in Percy Bysshe Shelley's Prometheus Unbound, neurology in Blake's Vala, or The Four Zoas, physiology in Coleridge's Biographia Literaria, and obstetrics and embryology in Mary Shelley's Frankenstein. He also demonstrates how the imagination was called upon to do aesthetic and scientific work using primary examples taken from the work of scientists and philosophers Davy, Dalton, Faraday, Priestley, Kant, Mary Somerville, Oersted, Marcet, Smellie, Swedenborg, Blumenbach, Buffon, Erasmus Darwin, and Von Baer, among others. Sha concludes that both fields benefited from thinking about how imagination could cooperate with reason—but that this partnership was impossible unless imagination's penchant for fantasy could be contained

Sequential induction of NF-κB/Rel family proteins during B-cell terminal differentiation

The NF-kappa B/Rel family of at least five transcription factor polypeptides is thought to function both as a developmental regulator in B cells and as a rapid response system in all cells. To examine this notion in more detail, we determined the protein contents of both the inducible and constitutive NF-kappa B/Rel activities in a pre-B-cell line, 70Z/3, and a mature B-cell line, WEHI 231. NF-kappa B p50/p65 is the major inducible nuclear complex after lipopolysaccharide or phorbol myristate acetate treatment of 70Z/3 cells. The constitutive and inducible complexes in WEHI 231 cells are mainly composed of p50 and Rel. The constitutive or induced activities are all sensitive to I kappa B-alpha, but this inhibitor is very short-lived in WEHI 231 cells, suggesting that the balance between synthesis and degradation of I kappa B-alpha determines whether a particular cell lineage has constitutive activity. A patterned expression of the NF-kappa B/Rel activator proteins emerges from an analysis of other B-lineage cell lines and splenic B cells: mainly p50 and p65 in pre-B (and non-B) cells, a predominance of Rel and p50 in mature B cells, and expression of p52 and RelB in plasmacytoma lines. This ordered pattern of regulators may reflect the requirement for expression of different genes during terminal B-cell differentiation because different combinations of NF-kappa B/Rel family members preferentially activate distinct kappa B sites in reporter constructs

Exploring the Way to Approach the Efficiency Limit of Perovskite Solar Cells by Drift-Diffusion Model

Drift-diffusion model is an indispensable modeling tool to understand the carrier dynamics (transport, recombination, and collection) and simulate practical-efficiency of solar cells (SCs) through taking into account various carrier recombination losses existing in multilayered device structures. Exploring the way to predict and approach the SC efficiency limit by using the drift-diffusion model will enable us to gain more physical insights and design guidelines for emerging photovoltaics, particularly perovskite solar cells. Our work finds out that two procedures are the prerequisites for predicting and approaching the SC efficiency limit. Firstly, the intrinsic radiative recombination needs to be corrected after adopting optical designs which will significantly affect the open-circuit voltage at its Shockley-Queisser limit. Through considering a detailed balance between emission and absorption of semiconductor materials at the thermal equilibrium, and the Boltzmann statistics at the non-equilibrium, we offer a different approach to derive the accurate expression of intrinsic radiative recombination with the optical corrections for semiconductor materials. The new expression captures light trapping of the absorbed photons and angular restriction of the emitted photons simultaneously, which are ignored in the traditional Roosbroeck-Shockley expression. Secondly, the contact characteristics of the electrodes need to be carefully engineered to eliminate the charge accumulation and surface recombination at the electrodes. The selective contact or blocking layer incorporated nonselective contact that inhibits the surface recombination at the electrode is another important prerequisite. With the two procedures, the accurate prediction of efficiency limit and precise evaluation of efficiency degradation for perovskite solar cells are attainable by the drift-diffusion model.Comment: 32 pages, 11 figure

Nickel-Catalyzed Asymmetric Negishi Cross-Couplings of Racemic Secondary Allylic Chlorides with Alkylzincs

The transition metal-catalyzed enantioselective coupling of allylic electrophiles with carbon nucleophiles has been the focus of intense investigation.5 Salient examples include palladium-catalyzed couplings with enolates, nickel-catalyzed couplings with Grignard reagents, and copper-catalyzed couplings with Grignard and diorganozinc reagents.6 Despite impressive progress, the development of methods that have broader scope with respect to the nucleophile, as well as improved functional-group compatibility, persist as important challenges

Palladium-Catalyzed Alkyl-Alkyl Suzuki Cross-Couplings of Primary Alkyl Bromides at Room Temperature: (13-Chlorotridecyloxy)triethylsilane [Silane, [(13-chlorotridecyl)oxy]triethyl-]

A. 1-Bromo-8-chlorooctane (1). An oven-dried, 200-mL, two-necked, round-bottomed flask equipped with an argon inlet and a magnetic stirbar (octagonal, molded pivot ring, 25 mm length and 6 mm diameter) is purged with argon for 5 min and then charged through the open neck with CH2Cl2 (50 mL via syringe) (Note 1), imidazole (2.19 g, 32.1 mmol, 1.10 equiv) (Note 2), and dichlorotriphenylphosphorane (10.4 g, 31.2 mmol, 1.07 equiv) (Note 3). The open neck is capped with a rubber septum, and the stirred solution is cooled in an ice bath for 5 min. A solution of 8-bromo-1-octanol (5.0 mL, 6.11 g, 29.2 mmol, 1.00 equiv) (Note 4) in CH2Cl2 (10 mL) (Note 1) is added via syringe over 5 min. The reaction mixture is allowed to warm to rt, and the resulting heterogeneous solution (a white precipitate formed) is stirred for 4 h. The progress of the reaction is followed by TLC analysis on SiO2 (10% EtOAc/hexanes as the eluent; visualization with a KMnO4 stain; the alcohol starting material has an Rf = 0.2, and the chloride product has an Rf = 0.9) (Note 5). After the alcohol is consumed, the reaction is diluted with pentane (200 mL), and the mixture is filtered through a pad of SiO2 (7 cm diameter 6 cm height) in a sintered glass funnel. The SiO2 is washed with additional pentane (400 mL). The filtrate is concentrated by rotary evaporation (20 mmHg, 30 °C), which furnishes the desired product as a colorless oil (6.23–6.44 g, 94–97 % yield) (Note 6). The product is used in the next step without further purification