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

Orbital magnetism in the half-metallic Heusler alloys

Using the fully-relativistic screened Korringa-Kohn-Rostoker method I study the orbital magnetism in the half-metallic Heusler alloys. Orbital moments are almost completely quenched and they are negligible with respect to the spin moments. The change in the atomic-resolved orbital moments can be easily explained in terms of the spin-orbit strength and hybridization effects. Finally I discuss the orbital and spin moments derived from X-ray magnetic circular dichroism experiments

Low-velocity anisotropic Dirac fermions on the side surface of topological insulators

We report anisotropic Dirac-cone surface bands on a side-surface geometry of the topological insulator Bi$_2$Se$_3$ revealed by first-principles density-functional calculations. We find that the electron velocity in the side-surface Dirac cone is anisotropically reduced from that in the (111)-surface Dirac cone, and the velocity is not in parallel with the wave vector {\bf k} except for {\bf k} in high-symmetry directions. The size of the electron spin depends on the direction of {\bf k} due to anisotropic variation of the noncollinearity of the electron state. Low-energy effective Hamiltonian is proposed for side-surface Dirac fermions, and its implications are presented including refractive transport phenomena occurring at the edges of tological insulators where different surfaces meet.Comment: 4 pages, 2 columns, 4 figure

Host cell protein control via CHO genome engineering

Chinese hamster ovary (CHO) cells, a major mammalian platform in biomanufacturing, produce and secret recombinant proteins along with host cell proteins (HCPs). Because residual HCPs in the final drug product can adversely affect (1) patients by causing immune responses, (2) drug efficacy, and (3) product stability, the effective removal of HCPs is necessary. Unfortunately, many studies have reported that many HCPs can be difficult to remove through downstream purification processes because they share similar biophysical properties to biopharmaceuticals. In this study we employed a genome engineering approach using clustered regularly interspaced short palindromic repeats and associated protein 9 (CRISPR/Cas9) system-mediated knockout to address difficult-to-remove HCP problems. Three HCPs (Cathepsin D, Nidogen-1, and Prosaposin) that are known to be difficult to remove were selected, and respective knockout clones were isolated without using selective reagents or reporter genes. Clones for each HCP were characterized using various analysis methods. Taken together, we demonstrate the applicability of the CRISPR/Cas9 system to eliminate difficult-to-remove HCP expression in an industry-relevant setting