Worldline algorithms for Casimir configurations

We present improved worldline numerical algorithms for high-precision calculations of Casimir interaction energies induced by scalar-field fluctuations with Dirichlet boundary conditions for various Casimir geometries. Significant reduction of numerical cost is gained by exploiting the symmetries of the worldline ensemble in combination with those of the configurations. This facilitates high-precision calculations on standard PCs or small clusters. We illustrate our strategies using the experimentally most relevant sphere-plate and cylinder-plate configuration. We compute Casimir curvature effects for a wide parameter range, revealing the tight validity bounds of the commonly used proximity force approximation (PFA). We conclude that data analysis of future experiments aiming at a precision of 0.1% must no longer be based on the PFA. Revisiting the parallel-plate configuration, we find a mapping between the D-dimensional Casimir energy and properties of a random-chain polymer ensemble.Comment: 23 pages, 9 figure

Solution of the Holstein polaron anisotropy problem

We study Holstein polarons in three-dimensional anisotropic materials. Using a variational exact diagonalization technique we provide highly accurate results for the polaron mass and polaron radius. With these data we discuss the differences between polaron formation in dimension one and three, and at small and large phonon frequency. Varying the anisotropy we demonstrate how a polaron evolves from a one-dimensional to a three-dimensional quasiparticle. We thereby resolve the issue of polaron stability in quasi-one-dimensional substances and clarify to what extent such polarons can be described as one-dimensional objects. We finally show that even the local Holstein interaction leads to an enhancement of anisotropy in charge carrier motion.Comment: 6 pages, 7 figures; extended version accepted for publication in Phys. Rev.

CD8 T-cell induction against vascular endothelial growth factor receptor 2 by Salmonella for vaccination purposes against a murine melanoma.

The Salmonella type III secretion system (T3SS) efficiently translocates heterologous proteins into the cytosol of eukaryotic cells. This leads to an antigen-specific CD8 T-cell induction in mice orally immunized with recombinant Salmonella. Recently, we have used Salmonella's T3SS as a prophylactic and therapeutic intervention against a murine fibrosarcoma. In this study, we constructed a recombinant Salmonella strain translocating the immunogenic H-2D(b)-specific CD8 T-cell epitope VILTNPISM (KDR2) from the murine vascular endothelial growth factor receptor 2 (VEGFR2). VEGFR2 is a member of the tyrosine protein kinase family and is upregulated on proliferating endothelial cells of the tumor vasculature. After single orogastric vaccination, we detected significant numbers of KDR2-tetramer-positive CD8 T cells in the spleens of immunized mice. The efficacy of these cytotoxic T cells was evaluated in a prophylactic setting to protect mice from challenges with B16F10 melanoma cells in a flank tumor model, and to reduce dissemination of spontaneous pulmonary melanoma metastases. Vaccinated mice revealed a reduction of angiogenesis by 62% in the solid tumor and consequently a significant decrease of tumor growth as compared to non-immunized mice. Moreover, in the lung metastasis model, immunization with recombinant Salmonella resulted in a reduction of the metastatic melanoma burden by approximately 60%

Zooming from Global to Local: A Multiscale RBF Approach

Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and finer scales. It also makes sense eventually to seek fine scale features locally, rather than globally. In the present work, we start with a global multiscale radial basis function (RBF) approximation, based on a sequence of point sets with decreasing mesh norm, and a sequence of (spherical) radial basis functions with proportionally decreasing scale centered at the points. We then prove that we can "zoom in" on a region of particular interest, by carrying out further stages of multiscale refinement on a local region. The proof combines multiscale techniques for the sphere from Le Gia, Sloan and Wendland, SIAM J. Numer. Anal. 48 (2010) and Applied Comp. Harm. Anal. 32 (2012), with those for a bounded region in $\mathbb{R}^d$ from Wendland, Numer. Math. 116 (2012). The zooming in process can be continued indefinitely, since the condition numbers of matrices at the different scales remain bounded. A numerical example illustrates the process