Counting function for a sphere of anisotropic quartz

We calculate the leading Weyl term of the counting function for a mono-crystalline quartz sphere. In contrast to other studies of counting functions, the anisotropy of quartz is a crucial element in our investigation. Hence, we do not obtain a simple analytical form, but we carry out a numerical evaluation. To this end we employ the Radon transform representation of the Green's function. We compare our result to a previously measured unique data set of several tens of thousands of resonances.Comment: 16 pages, 11 figure

Periodic orbit analysis of an elastodynamic resonator using shape deformation

We report the first definitive experimental observation of periodic orbits (POs) in the spectral properties of an elastodynamic system. The Fourier transform of the density of flexural modes show peaks that correspond to stable and unstable POs of a clover shaped quartz plate. We change the shape of the plate and find that the peaks corresponding to the POs that hit only the unperturbed sides are unchanged proving the correspondence. However, an exact match to the length of the main POs could be made only after a small rescaling of the experimental results. Statistical analysis of the level dynamics also shows the effect of the stable POs.Comment: submitted to Europhysics Letter

Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos we consider elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors. Based on that we derive the correlation functions for amplitudes and intensities of elastic displacements. Comparison to numerics in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure

Electronic transport through ballistic chaotic cavities: reflection symmetry, direct processes, and symmetry breaking

We extend previous studies on transport through ballistic chaotic cavities with spatial left-right (LR) reflection symmetry to include the presence of direct processes. We first analyze fully LR-symmetric systems in the presence of direct processes and compare the distribution w(T) of the transmission coefficient T with that for an asymmetric cavity with the same "optical" S matrix. We then study the problem of "external mixing" of the symmetry caused by an asymmetric coupling of the cavity to the outside. We first consider the case where symmetry breaking arises because two symmetrically positioned waveguides are coupled to the cavity by means of asymmetric tunnel barriers. Although this system is asymmetric with respect to the LR operation, it has a striking memory of the symmetry of the cavity it was constructed from. Secondly, we break LR symmetry in the absence of direct proceses by asymmetrically positioning the two waveguides and compare the results with those for the completely asymmetric case.Comment: 15 pages, 8 Postscript figures, submitted to Phys. Rev.

Graph-based description of tertiary lymphoid organs at single-cell level

Our aim is to complement observer-dependent approaches of immune cell evaluation in microscopy images with reproducible measures for spatial composition of lymphocytic infiltrates. Analyzing such patterns of inflammation is becoming increasingly important for therapeutic decisions, for example in transplantation medicine or cancer immunology. We developed a graph-based assessment of lymphocyte clustering in full whole slide images. Based on cell coordinates detected in the full image, a Delaunay triangulation and distance criteria are used to build neighborhood graphs. The composition of nodes and edges are used for classification, e.g. using a support vector machine. We describe the variability of these infiltrates on CD3/CD20 duplex staining in renal biopsies of long-term functioning allografts, in breast cancer cases, and in lung tissue of cystic fibrosis patients. The assessment includes automated cell detection, identification of regions of interest, and classification of lymphocytic clusters according to their degree of organization. We propose a neighborhood feature which considers the occurrence of edges with a certain type in the graph to distinguish between phenotypically different immune infiltrates. Our work addresses a medical need and provides a scalable framework that can be easily adjusted to the requirements of different research questions

Directing Cluster Formation of Au Nanoparticles from Colloidal Solution

Discrete clusters of closely spaced Au nanoparticles can be utilized in devices from photovoltaics to molecular sensors because of the formation of strong local electromagnetic field enhancements when illuminated near their plasmon resonance. In this study, scalable, chemical self-organization methods are shown to produce Au nanoparticle clusters with uniform nanometer interparticle spacing. The performance of two different methods, namely electrophoresis and diffusion, for driving the attachment of Au nanoparticles using a chemical cross-linker on chemically patterned domains of polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) thin films are evaluated. Significantly, electrophoresis is found to produce similar surface coverage as diffusion in 1/6th of the processing time with an ~2-fold increase in the number of Au nanoparticles forming clusters. Furthermore, average interparticle spacing within Au nanoparticle clusters was found to decrease from 2-7 nm for diffusion deposition to approximately 1-2 nm for electrophoresis deposition, and the latter method exhibited better uniformity with most clusters appearing to have about 1 nm spacing between nanoparticles. The advantage of such fabrication capability is supported by calculations of local electric field enhancements using electromagnetic full-wave simulations from which we can estimate surface-enhanced Raman scattering (SERS) enhancements. In particular, full-wave results show that the maximum SERS enhancement, as estimated here as the fourth power of the local electric field, increases by a factor of 100 when the gap goes from 2 to 1 nm, reaching values as large as 10(10), strengthening the usage of electrophoresis versus diffusion for the development of molecular sensors