Analytical results for a Bessel function times Legendre polynomials class integrals

When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make unnecessary numerical quadrature techniques or localized approximations. The solution is presented using the properties of the Bessel and associated Legendre functions.Comment: 4 page

Discrete Fracture Model with Anisotropic Load Sharing

A two-dimensional fracture model where the interaction among elements is modeled by an anisotropic stress-transfer function is presented. The influence of anisotropy on the macroscopic properties of the samples is clarified, by interpolating between several limiting cases of load sharing. Furthermore, the critical stress and the distribution of failure avalanches are obtained numerically for different values of the anisotropy parameter $\alpha$ and as a function of the interaction exponent $\gamma$. From numerical results, one can certainly conclude that the anisotropy does not change the crossover point $\gamma_c=2$ in 2D. Hence, in the limit of infinite system size, the crossover value $\gamma_c=2$ between local and global load sharing is the same as the one obtained in the isotropic case. In the case of finite systems, however, for $\gamma\le2$, the global load sharing behavior is approached very slowly

The Luminosity Function of Low-Redshift Abell Galaxy Clusters

We present the results from a survey of 57 low-redshift Abell galaxy clusters to study the radial dependence of the luminosity function (LF). The dynamical radius of each cluster, r200, was estimated from the photometric measurement of cluster richness, Bgc. The shape of the LFs are found to correlate with radius such that the faint-end slope, alpha, is generally steeper on the cluster outskirts. The sum of two Schechter functions provides a more adequate fit to the composite LFs than a single Schechter function. LFs based on the selection of red and blue galaxies are bimodal in appearance. The red LFs are generally flat for -22 < M_Rc < -18, with a radius-dependent steepening of alpha for M_Rc > -18. The blue LFs contain a larger contribution from faint galaxies than the red LFs. The blue LFs have a rising faint-end component (alpha ~ -1.7) for M_Rc > -21, with a weaker dependence on radius than the red LFs. The dispersion of M* was determined to be 0.31 mag, which is comparable to the median measurement uncertainty of 0.38 mag. This suggests that the bright-end of the LF is universal in shape at the 0.3 mag level. We find that M* is not correlated with cluster richness when using a common dynamical radius. Also, we find that M* is weakly correlated with BM-type such that later BM-type clusters have a brighter M*. A correlation between M* and radius was found for the red and blue galaxies such that M* fades towards the cluster center.Comment: Accepted for publication in ApJ, 16 pages, 4 tables, 24 figure

A new improved optimization of perturbation theory: applications to the oscillator energy levels and Bose-Einstein critical temperature

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.Comment: 9 pages, no figures. v2: minor wording changes in title/abstract, to appear in Phys.Rev.

Spectroscopy of 50^{50}Sc and ab initio calculations of B(M3)B(M3) strengths

The GRIFFIN spectrometer at TRIUMF-ISAC has been used to study excited states and transitions in $^{50}$Sc following the $\beta$-decay of $^{50}$Ca. Branching ratios were determined from the measured $\gamma$-ray intensities, and angular correlations of $\gamma$ rays have been used to firmly assign the spins of excited states. The presence of an isomeric state that decays by an $M3$ transition with a $B(M3)$ strength of 13.6(7)\,W.u. has been confirmed. We compare with the first {\it ab initio} calculations of $B(M3$) strengths in light and medium-mass nuclei from the valence-space in-medium similarity renormalization group approach, using consistently derived effective Hamiltonians and $M3$ operator. The experimental data are well reproduced for isoscalar $M3$ transitions when using bare $g$-factors, but the strength of isovector $M3$ transitions are found to be underestimated by an order of magnitude

Plasmid Injection and Application of Electric Pulses Alter Endogenous mRNA and Protein Expression in B16.F10 Mouse Melanomas

The application of electric pulses to tissues causes cell membrane destabilization, allowing exogenous molecules to enter the cells. This delivery technique can be used for plasmid gene therapy. Reporter gene expression after plasmid delivery with eight representative published protocols was compared in B16.F10 mouse melanoma tumors. This expression varied significantly based on the pulse parameters utilized for delivery. To observe the possible influence of plasmid injection and/or pulse application on endogenous gene expression, levels of stress-related mRNAs 4 and 24 h after delivery were determined by PCR array. Increases in mRNA levels for several inflammatory chemokines and cytokines were observed in response to plasmid injection, electric pulses alone or the combination. This upregulation was confirmed by individual real-time reverse transcription TaqMan PCR assays. Proteins were extracted at the same time points from identically treated tumors and inflammatory protein levels were assayed by enzyme-linked immunosorbent assay and by a custom multiplex bead array. Increases in inflammatory protein levels generally paralleled mRNA levels. Some differences were observed, which may have been due to differing expression kinetics. The observed upregulated expression of these cytokines and chemokines may aid or inhibit the therapeutic effectiveness of immune-based cancer gene therapies

Robust Ferroelectric State in Multiferroic Mn1−x_{1-x}Znx_xWO4_4

We report the remarkably robust ferroelectric state in the multiferroic compound Mn$_{1-x}$Zn$_x$WO$_4$. The substitution of the magnetic Mn$^{2+}$ with nonmagnetic Zn$^{2+}$ reduces the magnetic exchange and provides control of the various magnetic and multiferroic states of MnWO$_4$. Only 5 % of Zn substitution results in a complete suppression of the frustrated collinear (paraelectric) low temperature phase. The helical magnetic and ferroelectric phase develops as the ground state. The multiferroic state is stable up to a high level of substitution of more than 50 %. The magnetic, thermodynamic, and dielectric properties as well as the ferroelectric polarization of single crystals of Mn$_{1-x}$Zn$_x$WO$_4$ are studied for different substitutions up to x=0.5. The magnetic phases have been identified in single crystal neutron scattering experiments. The ferroelectric polarization scales with the neutron intensity of the incommensurate peak of the helical phase.Comment: 6 pages, 8 figure