174 research outputs found
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
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