Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices

By using the asymptotic theory of Pemantle and Wilson, exact asymptotic expansions of the free energy of the monomer-dimer model on rectangular $n \times \infty$ lattices in terms of dimer density are obtained for small values of $n$, at both high and low dimer density limits. In the high dimer density limit, the theoretical results confirm the dependence of the free energy on the parity of $n$, a result obtained previously by computational methods. In the low dimer density limit, the free energy on a cylinder $n \times \infty$ lattice strip has exactly the same first $n$ terms in the series expansion as that of infinite $\infty \times \infty$ lattice.Comment: 9 pages, 6 table

In an Attempt to Introduce Long-range Interactions into Small-world Networks

Distinguishing the long-range bonds with the regular ones, the critical temperature of the spin-lattice Guassian model built on two typical Small-world Networks (SWNs) is studied. The results show much difference from the classical case, and thus may induce some more accurate discussion on the critical properties of the spin-lattice systems combined with the SWNs.Comment: 4 pages, 3 figures, 18 referenc

Time-Periodic Solutions of the Einstein's Field Equations II

In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively. The singularities of these new time-periodic solutions are investigated and some new physical phenomena are found. The applications of these solutions in modern cosmology and general relativity can be expected.Comment: 10 pages, 1 figur

Induced Growth of Asymmetric Nanocantilever Arrays on Polar Surfaces

©2003 The American Physical Society. The electronic version of this article is the complete one and can be found online at: http://link.aps.org/doi/10.1103/PhysRevLett.91.185502DOI: 10.1103/PhysRevLett.91.185502We report that the Zn-terminated ZnO (0001) polar surface is chemically active and the oxygenterminated (0001) polar surface is inert in the growth of nanocantilever arrays. Longer and wider "comblike" nanocantilever arrays are grown from the (0001)-Zn surface, which is suggested to be a self-catalyzed process due to the enrichment of Zn at the growth front. The chemically inactive (0001)-O surface typically does not initiate any growth, but controlling experimental conditions could lead to the growth of shorter and narrower nanocantilevers from the intersections between (0001)-O with (0110) surfaces

The Montage Image Mosaic Service: Custom Image Mosaics On-Demand

The Montage software suite has proven extremely useful as a general engine for reprojecting, background matching, and mosaicking astronomical image data from a wide variety of sources. The processing algorithms support all common World Coordinate System (WCS) projections and have been shown to be both astrometrically accurate and flux conserving. The background ‘matching’ algorithm does not remove background flux but rather finds the best compromise background based on all the input and matches the individual images to that. The Infrared Science Archive (IRSA), part of the Infrared Processing and Analysis Center (IPAC) at Caltech, has now wrapped the Montage software as a CGI service and provided a compute and request management infrastructure capable of producing approximately 2 TBytes / day of image mosaic output (e.g. from 2MASS and SDSS data). Besides the basic Montage engine, this service makes use of a 16-node LINUX cluster (dual processor, dual core) and the ROME request management software developed by the National Virtual Observatory (NVO). ROME uses EJB/database technology to manage user requests, queue processing and load balance between users, and managing job monitoring and user notification. The Montage service will be extended to process userdefined data collections, including private data uploads

Nonplanar Chiral Metamaterials with Negative Index

We demonstrate experimentally and numerically that nonplanar chiral metamaterials give giant optical activity, circular dichroism, and negative refractive index. The transmission, reflection, and the retrieval results of the experiments agree pretty well with the simulations. This is an important step toward the design and fabrication of three-dimensional isotropic chiral metamaterials.Comment: 3 pages 4 figure

Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers.Comment: 4 pages, 2 figure

Continuous volumetric imaging via an optical phase-locked ultrasound lens

In vivo imaging at high spatiotemporal resolution is key to the understanding of complex biological systems. We integrated an optical phase-locked ultrasound lens into a two-photon fluorescence microscope and achieved microsecond-scale axial scanning, thus enabling volumetric imaging at tens of hertz. We applied this system to multicolor volumetric imaging of processes sensitive to motion artifacts, including calcium dynamics in behaving mouse brain and transient morphology changes and trafficking of immune cells