Logarithmic corrections to twisted indices from the quantum entropy function

We compute logarithmic corrections to the twisted index B-6(g) in four-dimensional N = 4 and N = 8 string theories using the framework of the Quantum Entropy Function. We find that these vanish, matching perfectly with the large-charge expansion of the corresponding microscopic expressions.

Heat kernels on the AdS(2) cone and logarithmic corrections to extremal black hole entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over ZN orbifolds of higher-dimensional spheres and hyperboloids.

Development of a global inundation map at high spatial resolution from topographic downscaling of coarse-scale remote sensing data

Large-scale estimates of the area of terrestrial surface waters have greatly improved over time, in particular through the development of multi-satellite methodologies, but the generally coarse spatial resolution (tens of kms) of global observations is still inadequate for many ecological applications. The goal of this study is to introduce a new, globally applicable downscaling method and to demonstrate its applicability to derive fine resolution results from coarse global inundation estimates. The downscaling procedure predicts the location of surface water cover with an inundation probability map that was generated by bagged derision trees using globally available topographic and hydrographic information from the SRTM-derived HydroSHEDS database and trained on the wetland extent of the GLC2000 global land cover map. We applied the downscaling technique to the Global Inundation Extent from Multi-Satellites (GIEMS) dataset to produce a new high-resolution inundation map at a pixel size of 15 arc-seconds, termed GIEMS-D15. GIEMS-D15 represents three states of land surface inundation extents: mean annual minimum (total area, 6.5 x 10(6) km(2)), mean annual maximum (12.1 x 10(6) km(2)), and long-term maximum (173 x 10(6) km(2)); the latter depicts the largest surface water area of any global map to date. While the accuracy of GIEMS-D15 reflects distribution errors introduced by the downscaling process as well as errors from the original satellite estimates, overall accuracy is good yet spatially variable. A comparison against regional wetland cover maps generated by independent observations shows that the results adequately represent large floodplains and wetlands. GIEMS-D15 offers a higher resolution delineation of inundated areas than previously available for the assessment of global freshwater resources and the study of large floodplain and wetland ecosystems. The technique of applying inundation probabilities also allows for coupling with coarse-scale hydro-climatological model simulations. (C) 2014 Elsevier Inc All rights reserved.

Comments on hydrographic and topographic LIDAR acquisition and merging with multibeam sounding data acquired in the Olympic Coast National Marine Sanctuary

In April 2005, a SHOALS 1000T LIDAR system was used as an efficient alternative for safely acquiring data to describe the existing conditions of nearshore bathymetry and the intertidal zone over an approximately 40.7 km2 (11.8 nm2) portion of hazardous coastline within the Olympic Coast National Marine Sanctuary (OCNMS). Data were logged from 1,593 km (860 nm) of track lines in just over 21 hours of flight time. Several islands and offshore rocks were also surveyed, and over 24,000 geo-referenced digital still photos were captured to assist with data cleaning and QA/QC. The 1 kHz bathymetry laser obtained a maximum water depth of 22.2 meters. Floating kelp beds, breaking surf lines and turbid water were all challenges to the survey. Although sea state was favorable for this time of the year, recent heavy rainfall and a persistent low-lying layer of fog reduced acquisition productivity. The existence of a completed VDatum model covering this same geographic region permitted the LIDAR data to be vertically transformed and merged with existing shallow water multibeam data and referenced to the mean lower low water (MLLW) tidal datum. Analysis of a multibeam bathymetry-LIDAR difference surface containing over 44,000 samples indicated surface deviations from –24.3 to 8.48 meters, with a mean difference of –0.967 meters, and standard deviation of 1.762 meters. Errors in data cleaning and false detections due to interference from surf, kelp, and turbidity likely account for the larger surface separations, while the remaining general surface difference trend could partially be attributed to a more dense data set, and shoal-biased cleaning, binning and gridding associated with the multibeam data for maintaining conservative least depths important for charting dangers to navigation. (PDF contains 27 pages.)

Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

Corrections to the paraxial approximation of an arbitrary free-propagation beam

A relatively simple transform from an arbitrary solution of the paraxial wave equation to the corresponding exact solution of the Helmholtz wave equation is derived in the condition that the evanescent waves are ignored and is used to study the corrections to the paraxial approximation of an arbitrary free-propagation beam. Specifically, the general lowest-order correction field is given in a very simple form and is proved to be exactly consistent with the perturbation method developed by Lax et nl. [Phys. Rev. A 11, 1365 (1975)]. Some special examples, such as the lowest-order correction to the paraxial approximation of a fundamental Gaussian beam whose waist plane has a parallel shin from the z = 0 plane, are presented. (C) 1998 Optical Society of America.

Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

On-line topographic analysis in the SEM

A novel method for on-line topographic analysis of rough surfaces in the SEM has been investigated. It utilises a digital minicomputer configured to act as a programmable scan generator and automatic focusing unit. The computer is coupled to the microscope through digital-to-analogue converters which enable it to generate ramp waveforms allowing the beam to be scanned over a small sub-region of the field under program control. A further digital-to-analogue converter regulates the current supply to the objective lens of the microscope. The video signal is sampled by means of an analogue-to-digital converter and the resultant binary code stored in the computer's memory as an array of numbers describing relative image intensity. Computations based on the intensity gradient of the image allow the objective lens current to be found for the in-focus condition, which may be related to the working distance through a previous calibration experiment. The sensitivity of the method for detecting small height changes is theoretically of the order of 1 μm. In practice the operator specifies features of interest by means of a mobile spot cursor injected into the SEM display screen, or he may scan the specimen at sub-regions corresponding to pre-determined points on a regular grid defined by him. The operation then proceeds under program control. | A novel method for on-line topographic analysis of rough surfaces in the SEM has been investigated. It utilizes a digital minicomputer configured to act as a programmable scan generator and automatic focusing unit. A further digital-to-analog converter regulates the current supply to the objective lens of the microscope. The video signal is sampled by means of an analog-to-digital converter and the resultant binary code stored in the computer's memory as an array of numbers describing relative image intensity. The sensitivity of the method for detecting small height changes is theroretically of the order of 1 mu m.