New Darboux Transformation for Hirota-Satsuma coupled KdV System

A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlev\'{e} analysis and reduction of a binary Darboux transformation. By iteration of the Darboux transformation, the Grammian type solutions are found for the coupled KdV system.Comment: LaTeX 2.09, 10 page

Holographic Algorithm with Matchgates Is Universal for Planar #\#CSP Over Boolean Domain

We prove a complexity classification theorem that classifies all counting constraint satisfaction problems ($\#$CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) $\#$P-hard for general instances, but solvable in polynomial-time over planar graphs; and (3) $\#$P-hard over planar graphs. The classification applies to all sets of local, not necessarily symmetric, constraint functions on Boolean variables that take complex values. It is shown that Valiant's holographic algorithm with matchgates is a universal strategy for all problems in category (2).Comment: 94 page

Lensless high-resolution on-chip optofluidic microscopes for Caenorhabditis elegans and cell imaging

Low-cost and high-resolution on-chip microscopes are vital for reducing cost and improving efficiency for modern biomedicine and bioscience. Despite the needs, the conventional microscope design has proven difficult to miniaturize. Here, we report the implementation and application of two high-resolution (≈0.9 μm for the first and ≈0.8 μm for the second), lensless, and fully on-chip microscopes based on the optofluidic microscopy (OFM) method. These systems abandon the conventional microscope design, which requires expensive lenses and large space to magnify images, and instead utilizes microfluidic flow to deliver specimens across array(s) of micrometer-size apertures defined on a metal-coated CMOS sensor to generate direct projection images. The first system utilizes a gravity-driven microfluidic flow for sample scanning and is suited for imaging elongate objects, such as Caenorhabditis elegans; and the second system employs an electrokinetic drive for flow control and is suited for imaging cells and other spherical/ellipsoidal objects. As a demonstration of the OFM for bioscience research, we show that the prototypes can be used to perform automated phenotype characterization of different Caenorhabditis elegans mutant strains, and to image spores and single cellular entities. The optofluidic microscope design, readily fabricable with existing semiconductor and microfluidic technologies, offers low-cost and highly compact imaging solutions. More functionalities, such as on-chip phase and fluorescence imaging, can also be readily adapted into OFM systems. We anticipate that the OFM can significantly address a range of biomedical and bioscience needs, and engender new microscope applications

Towards a warped inflationary brane scanning

We present a detailed systematics for comparing warped brane inflation with the observations, incorporating the effects of both moduli stabilization and ultraviolet bulk physics. We explicitly construct an example of the inflaton potential governing the motion of a mobile D3 brane in the entire warped deformed conifold. This allows us to precisely identify the corresponding scales of the cosmic microwave background. The effects due to bulk fluxes or localized sources are parametrized using gauge/string duality. We next perform some sample scannings to explore the parameter space of the complete potential, and first demonstrate that without the bulk effects there can be large degenerate sets of parameters with observationally consistent predictions. When the bulk perturbations are included, however, the observational predictions are generally spoiled. For them to remain consistent, the magnitudes of the bulk effects need to be highly suppressed via fine tuning.Comment: (v1) 11 pages, 2 figures, 2 tables; (v2) more clarifications and references added; (v3) 12 pages, more discussions, to appear in Physical Review

Boundary effects to the entanglement entropy and two-site entanglement of the spin-1 valence-bond solid

We investigate the von Neumann entropy of a block of subsystem for the valence-bond solid (VBS) state with general open boundary conditions. We show that the effect of the boundary on the von Neumann entropy decays exponentially fast in the distance between the subsystem considered and the boundary sites. Further, we show that as the size of the subsystem increases, its von Neumann entropy exponentially approaches the summation of the von Neumann entropies of the two ends, the exponent being related to the size. In contrast to critical systems, where boundary effects to the von Neumann entropy decay slowly, the boundary effects in a VBS, a non-critical system, decay very quickly. We also study the entanglement between two spins. Curiously, while the boundary operators decrease the von Neumann entropy of L spins, they increase the entanglement between two spins.Comment: 4 pages, 2 figures. Physical Review B (in press

Atmospheric Dynamics of Hot Exoplanets

The characterization of exoplanetary atmospheres has come of age in the last decade, as astronomical techniques now allow for albedos, chemical abundances, temperature profiles and maps, rotation periods and even wind speeds to be measured. Atmospheric dynamics sets the background state of density, temperature and velocity that determines or influences the spectral and temporal appearance of an exoplanetary atmosphere. Hot exoplanets are most amenable to these characterization techniques; in the present review, we focus on highly-irradiated, large exoplanets (the "hot Jupiters"), as astronomical data begin to confront theoretical questions. We summarize the basic atmospheric quantities inferred from the astronomical observations. We review the state of the art by addressing a series of current questions and look towards the future by considering a separate set of exploratory questions. Attaining the next level of understanding will require a concerted effort of constructing multi-faceted, multi-wavelength datasets for benchmark objects. Understanding clouds presents a formidable obstacle, as they introduce degeneracies into the interpretation of spectra, yet their properties and existence are directly influenced by atmospheric dynamics. Confronting general circulation models with these multi-faceted, multi-wavelength datasets will help us understand these and other degeneracies. The coming decade will witness a decisive confrontation of theory and simulation by the next generation of astronomical data.Comment: Accepted by Annual Review of Earth and Planetary Sciences. 32 pages, 9 figures, 1 table. Posted with permission from the Annual Review of Earth and Planetary Sciences, Volume 43 by Annual Reviews, http://www.annualreviews.or

Entanglement-assisted local operations and classical communications conversion in the quantum critical systems

Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (eLOCC) are studied. We propose a new method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground state local convertibility in the one dimensional transverse field Ising model, XY model and XXZ model. It is found that the eLOCC convertibility sudden changes at the phase transition points. In transverse field Ising model the eLOCC convertibility between the first excited state and the ground state are also distinct for different phases. The relation between the order of quantum phase transitions and the local convertibility is discussed.Comment: 7 pages, 5 figures, 5 table

Null-stream veto for two co-located detectors: Implementation issues

Time-series data from multiple gravitational wave (GW) detectors can be linearly combined to form a null-stream, in which all GW information will be cancelled out. This null-stream can be used to distinguish between actual GW triggers and spurious noise transients in a search for GW bursts using a network of detectors. The biggest source of error in the null-stream analysis comes from the fact that the detector data are not perfectly calibrated. In this paper, we present an implementation of the null-stream veto in the simplest network of two co-located detectors. The detectors are assumed to have calibration uncertainties and correlated noise components. We estimate the effect of calibration uncertainties in the null-stream veto analysis and propose a new formulation to overcome this. This new formulation is demonstrated by doing software injections in Gaussian noise.Comment: Minor changes; To appear in Class. Quantum Grav. (Proc. GWDAW10