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

Anisotropic sub-Doppler laser cooling in dysprosium magneto-optical traps

Magneto-optical traps (MOTs) of Er and Dy have recently been shown to exhibit population-wide sub-Doppler cooling due to their near degeneracy of excited and ground state Lande g factors. We discuss here an additional, unusual intra-MOT sub-Doppler cooling mechanism that appears when the total Dy MOT cooling laser intensity and magnetic quadrupole gradient increase beyond critical values. Specifically, anisotropically sub-Doppler-cooled cores appear, and their orientation with respect to the quadrupole axis flips at a critical ratio of the MOT laser intensity along the quadrupole axis versus that in the plane of symmetry. This phenomenon can be traced to a loss of the velocity-selective resonance at zero velocity in the cooling force along directions in which the atomic polarization is oriented by the quadrupole field. We present data characterizing this anisotropic laser cooling phenomenon and discuss a qualitative model for its origin based on the extraordinarily large Dy magnetic moment and Dy's near degenerate g factors.Comment: 4 pages, 5 figure

Overexpression of Both Human Sodium Iodide Symporter (NIS) and BRG1-Bromodomain Synergistically Enhances Radioiodine Sensitivity by Stabilizing p53 through NPM1 Expression.

Improved therapeutic strategies are required to minimize side effects associated with radioiodine gene therapy to avoid unnecessary damage to normal cells and radiation-induced secondary malignancies. We previously reported that codon-optimized sodium iodide symporter (oNIS) enhances absorption of I-131 and that the brahma-associated gene 1 bromodomain (BRG1-BRD) causes inefficient DNA damage repair after high-energy X-ray therapy. To increase the therapeutic effect without applying excessive radiation, we considered the combination of oNIS and BRG1-BRD as gene therapy for the most effective radioiodine treatment. The antitumor effect of I-131 with oNIS or oNIS+BRD expression was examined by tumor xenograft models along with functional assays at the cellular level. The synergistic effect of both BRG1-BRD and oNIS gene overexpression resulted in more DNA double-strand breaks and led to reduced cell proliferation/survival rates after I-131 treatment, which was mediated by the p53/p21 pathway. We found increased p53, p21, and nucleophosmin 1 (NPM1) in oNIS- and BRD-expressing cells following I-131 treatment, even though the remaining levels of citrulline and protein arginine deiminase 4 (PAD4) were unchanged at the protein level

Spectroscopy of a narrow-line laser cooling transition in atomic dysprosium

The laser cooling and trapping of ultracold neutral dysprosium has been recently demonstrated using the broad, open 421-nm cycling transition. Narrow-line magneto-optical trapping of Dy on longer wavelength transitions would enable the preparation of ultracold Dy samples suitable for loading optical dipole traps and subsequent evaporative cooling. We have identified the closed 741-nm cycling transition as a candidate for the narrow-line cooling of Dy. We present experimental data on the isotope shifts, the hyperfine constants A and B, and the decay rate of the 741-nm transition. In addition, we report a measurement of the 421-nm transition's linewidth, which agrees with previous measurements. We summarize the laser cooling characteristics of these transitions as well as other narrow cycling transitions that may prove useful for cooling Dy.Comment: 6+ pages, 5 figures, 5 table

Symmetry-Breaking Motility

Locomotion of bacteria by actin polymerization, and in vitro motion of spherical beads coated with a protein catalyzing polymerization, are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.Comment: 4 pages, 2 figures, REVTeX; formatting of references correcte

Refinement of primary Si in hypereutectic Al-Si alloys by intensive melt shearing

Hypereutectic Al-Si based alloys are gaining popularity for applications where a combination of light weight and high wear resistance is required. The high wear resistance arising from the hard primary Si particles comes at the price of extremely poor machine tool life. To minimize machining problems while exploiting outstanding wear resistance, the primary Si particles must be controlled to a uniform small size and uniform spatial distribution. The current industrial means of refining primary Si chemically by the addition of phosphorous suffers from a number of problems. In the present paper an alternative, physical means of refining primary Si by intensive shearing of the melt prior to casting is investigated. Al-15wt%Si alloy has been solidified under varying casting conditions (cooling rate) and the resulting microstructures have been studied using microscopy and quantitative image analysis. Primary Si particles were finer, more compact in shape and more numerous with increasing cooling rate. Intensive melt shearing led to greater refinement and more enhanced nucleation of primary Si than was achieved by adding phosphorous. The mechanism of enhanced nucleation is discussed.EPSRC (grant EP/H026177/1)

Upper critical fields and thermally-activated transport of Nd(O_0.7F_0.3)FeAs single crystal

We present measurements of the resistivity and the upper critical field H_c2 of Nd(O_0.7F_0.3)FeAs single crystals in strong DC and pulsed magnetic fields up to 45 T and 60 T, respectively. We found that the field scale of H_c2 is comparable to ~100 T of high T_c cuprates. H_c2(T) parallel to the c-axis exhibits a pronounced upward curvature similar to what was extracted from earlier measurements on polycrystalline samples. Thus this behavior is indeed an intrinsic feature of oxypnictides, rather than manifestation of vortex lattice melting or granularity. The orientational dependence of H_c2 shows deviations from the one-band Ginzburg-Landau scaling. The mass anisotropy decreases as T decreases, from 9.2 at 44K to 5 at 34K. Spin dependent magnetoresistance and nonlinearities in the Hall coefficient suggest contribution to the conductivity from electron-electron interactions modified by disorder reminiscent that of diluted magnetic semiconductors. The Ohmic resistivity measured below T_c but above the irreversibility field exhibits a clear Arrhenius thermally activated behavior over 4-5 decades. The activation energy has very different field dependencies for H||ab and H\perp ab. We discuss to what extent different pairing scenarios can manifest themselves in the observed behavior of H_{c2}, using the two-band model of superconductivity. The results indicate the importance of paramagnetic effects on H_c2(T),which may significantly reduce H_c2(0) as compared toH_c2(0)~200-300 T based on extrapolations of H_c2(T) near T_c down to low temperatures.Comment: 11 pages, 16 figure

Selective conversion of CO into ethanol on Cu(511) surface reconstructed from Cu(pc): Operando studies by electrochemical scanning tunneling microscopy, mass spectrometry, quartz crystal nanobalance, and infrared spectroscopy

A polycrystalline copper, surface-terminated by a well-defined (511)-oriented facet, was electrochemically generated by a series of step-wise surface reconstruction and iterations of mild oxidative-reductive processes in 0.1 M KOH. The electrochemical reduction of CO on the resultant stepped surface was investigated by four surface-sensitive operando methodologies: electrochemical scanning tunneling microscopy (STM), electrochemical quartz crystal nanobalance (EQCN), differential electrochemical mass spectrometry (DEMS), and polarization-modulation infrared spectroscopy (PMIRS). The stepped surface catalyzed the facile conversion of CO into ethanol, the exclusive alcohol product at a low overpotential of −1.06 V (SHE) or − 0.3 V (RHE). The chemisorption of CO was found to be a necessary prelude to ethanol production; i.e. the surface coverages, rather than solution concentrations, of CO and its surface-bound intermediates primarily dictate the reaction rates (current densities). Contrary to the expected predominance of undercoordinated step-site reactivity over the coordination chemistry of vicinal surfaces, vibrational spectroscopic evidence reveals the involvement of terrace-bound CO adsorbates during the multi-atomic transformations associated with the production of ethanol

Reprint of "Selective conversion of CO into ethanol on Cu(511) surface reconstructed from Cu(pc): Operando studies by electrochemical scanning tunneling microscopy, mass spectrometry, quartz crystal nanobalance, and infrared spectroscopy"

A polycrystalline copper, surface-terminated by a well-defined (511)-oriented facet, was electrochemically generated by a series of step-wise surface reconstruction and iterations of mild oxidative-reductive processes in 0.1 M KOH. The electrochemical reduction of CO on the resultant stepped surface was investigated by four surface-sensitive operando methodologies: electrochemical scanning tunneling microscopy (STM), electrochemical quartz crystal nanobalance (EQCN), differential electrochemical mass spectrometry (DEMS), and polarization-modulation infrared spectroscopy (PMIRS). The stepped surface catalyzed the facile conversion of CO into ethanol, the exclusive alcohol product at a low overpotential of −1.06 V (SHE) or − 0.3 V (RHE). The chemisorption of CO was found to be a necessary prelude to ethanol production; i.e. the surface coverages, rather than solution concentrations, of CO and its surface-bound intermediates primarily dictate the reaction rates (current densities). Contrary to the expected predominance of undercoordinated step-site reactivity over the coordination chemistry of vicinal surfaces, vibrational spectroscopic evidence reveals the involvement of terrace-bound CO adsorbates during the multi-atomic transformations associated with the production of ethanol