Conformal Symmetry on the Instanton Moduli Space

The conformal symmetry on the instanton moduli space is discussed using the ADHM construction, where a viewpoint of "homogeneous coordinates" for both the spacetime and the moduli space turns out to be useful. It is shown that the conformal algebra closes only up to global gauge transformations, which generalizes the earlier discussion by Jackiw et al. An interesting 5-dimensional interpretation of the SU(2) single-instanton is also mentioned.Comment: 7 pages, LaTeX, version to appear in J. Phys. A: Math. Ge

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Silver Nanoparticle Aggregates as Highly Efficient Plasmonic Antennas for Fluorescence Enhancement

The enhanced local fields around plasmonic structures can lead to enhancement of the excitation and modification of the emission quantum yield of fluorophores. So far, high enhancement of fluorescence intensity from dye molecules was demonstrated using bow-tie gap antenna made by e-beam lithography. However, the high manufacturing cost and the fact that currently there are no effective ways to place fluorophores only at the gap prevent the use of these structures for enhancing fluorescence-based biochemical assays. We report on the simultaneous modification of fluorescence intensity and lifetime of dye-labeled DNA in the presence of aggregated silver nanoparticles. The nanoparticle aggregates act as efficient plasmonic antennas, leading to more than 2 orders of magnitude enhancement of the average fluorescence. This is comparable to the best-reported fluorescence enhancement for a single molecule but here applies to the average signal detected from all fluorophores in the system. This highlights the remarkable efficiency of this system for surface-enhanced fluorescence. Moreover, we show that the fluorescence intensity enhancement varies with the plasmon resonance position and measure a significant reduction (300×) of the fluorescence lifetime. Both observations are shown to be in agreement with the electromagnetic model of surface-enhanced fluorescence

Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

The phase transition of Reissner-Nordstr\"om black holes in $(n+1)$-dimensional anti-de Sitter spacetime is studied in details using the thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid gas system. We first investigate critical phenomena of the RN-AdS black hole. The critical exponents of relevant thermodynamical quantities are evaluated. We find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas system. This suggests a possible universality in the phase transitions of these systems. We finally study the thermodynamic behavior using the equilibrium thermodynamic state space geometry and find that the scalar curvature diverges exactly at the van der Waals-like critical point where the heat capacity at constant charge of the black hole diverges.Comment: 18 pages, 5 figure

A compactness theorem for complete Ricci shrinkers

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the Euler characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.Comment: 28 pages, final version, to appear in GAF

The generic mapping tools version 6

The Generic Mapping Tools (GMT) software is ubiquitous in the Earth and ocean sciences. As a cross-platform tool producing high-quality maps and figures, it is used by tens of thousands of scientists around the world. The basic syntax of GMT scripts has evolved very slowly since the 1990s, despite the fact that GMT is generally perceived to have a steep learning curve with many pitfalls for beginners and experienced users alike. Reducing these pitfalls means changing the interface, which would break compatibility with thousands of existing scripts. With the latest GMT version 6, we solve this conundrum by introducing a new "modern mode" to complement the interface used in previous versions, which GMT 6 now calls "classic mode." GMT 6 defaults to classic mode and thus is a recommended upgrade for all GMT 5 users. Nonetheless, new users should take advantage of modern mode to make shorter scripts, quickly access commonly used global data sets, and take full advantage of the new tools to draw subplots, place insets, and create animations.Funding Agency National Science Foundation (NSF) Appeared in article as U.S. National Science Foundation MSU Geological Sciences Endowmentinfo:eu-repo/semantics/publishedVersio

Charged and spin-excitation gaps in half-filled strongly correlated electron systems: A rigorous result

By exploiting the particle-hole symmetries of the Hubbard model, the periodic Anderson model and the Kondo lattice model at half-filling and applying a generalized version of Lieb's spin-reflection positivity method, we show that the charged gaps of these models are always larger than their spin excitation gaps. This theorem confirms the previous results derived by either the variational approach or the density renormalization group approach.Comment: 20 pages, no figur

Closed orbit correction at synchrotrons for symmetric and near-symmetric lattices

This contribution compiles the benefits of lattice symmetry in the context of closed orbit correction. A symmetric arrangement of BPMs and correctors results in structured orbit response matrices of Circulant or block Circulant type. These forms of matrices provide favorable properties in terms of computational complexity, information compression and interpretation of mathematical vector spaces of BPMs and correctors. For broken symmetries, a nearest-Circulant approximation is introduced and the practical advantages of symmetry exploitation are demonstrated with the help of simulations and experiments in the context of FAIR synchrotrons

Nonlinear Modes of Liquid Drops as Solitary Waves

The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such ``rotons'' were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to drop-like systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.Comment: 11 pages RevTex, 1 figure p