Magnification Bias Estimators for Realistic Surveys: an Application to the BOSS Survey

In addition to the intrinsic clustering of galaxies themselves, the spatial distribution of galaxies observed in surveys is modulated by the presence of weak lensing due to matter in the foreground. This effect, known as magnification bias, is a significant contaminant to analyses of galaxy-lensing cross-correlations and must be carefully modelled. We present a method to estimate the magnification bias in spectroscopically confirmed galaxy samples based on finite differences of galaxy catalogues while marginalizing over errors due to finite step size. We use our estimator to measure the magnification biases of the CMASS and LOWZ samples in the SDSS BOSS galaxy survey, analytically taking into account the dependence on galaxy shape for fiber and PSF magnitudes, finding $\alpha_{\rm CMASS} = 2.71 \pm 0.02$ and $\alpha_{\rm LOWZ} = 2.45 \pm 0.02$ and quantify modelling uncertainties in these measurements. Finally, we quantify the redshift evolution of the magnification bias within the CMASS and LOWZ samples, finding a difference of up to a factor of three between the lower and upper redshift bounds for the former. We discuss how to account for this evolution in modelling and its interaction with commonly applied redshift-dependent weights. Our method should be readily-applicable to upcoming surveys and we make our code publicly available as part of this work.Comment: 14 pages, 9 figures, 3 tables, Accepted in MNRA

Magnetic flux dynamics in critical state of one-dimensional discrete superconductor

We give a theoretical description of avalanche-like dynamics of magnetic flux in the critical state of "hard" type-II superconductors using a model of a one-dimensional multijunction SQUID that well reproduces the main magnetic properties of these objects. We show that the system under consideration demonstrates the self-organized criticality. The avalanches of vortices manifest themselves as jumps of the total magnetic flux in the sample. The sizes of these jumps have a power-law distribution. Our results are in qualitative agreement with experiments.Comment: 7 pages, 5 figure

Prediction Model of End Mill Cutting Edge Based on Material Properties and Cutting Conditions

In machining, the cutting performance of the tool depends on the tool material, tool structure, tool geometry, properties of workpiece materials, and cutting conditions. If the user chooses an inappropriate cutting tool for the machining of the workpiece material, this will cause energy loss and severe tool wear. This study aims to investigate the influence of mechanical properties of workpiece material and cutting conditions on the tool geometry and to establish a polynomial network for the prediction of a reasonable normal relief angle and a normal wedge angle based on experimental data. Experimental results indicate that the cutting of high hardness and high strength workpiece materials requires a larger normal wedge angle to increase the cutting edge strength. In addition, the design of the normal relief angle is related to Young\u27s modulus and the toughness of the workpiece material, mainly to avoid material elastic recovery during the cutting process. In terms of cutting parameters, as the radial depth of cut increases, the contact area between the tool and the chip increases, which causes the heat to concentrate at the tip of the tool; hence, it is necessary to increase the normal wedge angle. In addition, the feed per tooth had a negligible effect on the normal wedge angle. Finally, the prediction model was verified by five untested workpiece materials. The results of the cutting tests showed that the flatness of the cutting edge was less than 15 μm, which indicates that a normal cutting phenomenon occurred on the flank

Duality Cascade in Brane Inflation

We show that brane inflation is very sensitive to tiny sharp features in extra dimensions, including those in the potential and in the warp factor. This can show up as observational signatures in the power spectrum and/or non-Gaussianities of the cosmic microwave background radiation (CMBR). One general example of such sharp features is a succession of small steps in a warped throat, caused by Seiberg duality cascade using gauge/gravity duality. We study the cosmological observational consequences of these steps in brane inflation. Since the steps come in a series, the prediction of other steps and their properties can be tested by future data and analysis. It is also possible that the steps are too close to be resolved in the power spectrum, in which case they may show up only in the non-Gaussianity of the CMB temperature fluctuations and/or EE polarization. We study two cases. In the slow-roll scenario where steps appear in the inflaton potential, the sensitivity of brane inflation to the height and width of the steps is increased by several orders of magnitude comparing to that in previously studied large field models. In the IR DBI scenario where steps appear in the warp factor, we find that the glitches in the power spectrum caused by these sharp features are generally small or even unobservable, but associated distinctive non-Gaussianity can be large. Together with its large negative running of the power spectrum index, this scenario clearly illustrates how rich and different a brane inflationary scenario can be when compared to generic slow-roll inflation. Such distinctive stringy features may provide a powerful probe of superstring theory.Comment: Corrections in Eq.(5.47), Eq (5.48), Eq(5.49) and Fig

Study of higher-order harmonics of complex ac susceptibility in YB2C3O7−δYB_2C_3O_{7-\delta} thin films by the mutual inductive method

We have applied the mutual inductive method to study higher-order harmonics of complex ac susceptibility $\chi_n=\chi'_n-i\chi"_n$ for $$YB_2C_3O_{7-\delta}$thin films as function of the temperature and the applied field. The experimental results were compared with analytical and numerical results obtained from the Ishida-Mazaki model and the solution of the integral equation for the current density, respectively. Both models allow us to reproduced the main experimental features, however, as$n$increases the numerical model shows notable discrepancies. This failure can be attributed to the current-voltage characteristics. Also this investigation yields the activation energy$U_c$and the critical current density$J_c$ for two samples both at T=0.Comment: 8 pages, 3 figure

Comparing Infrared Dirac-Born-Infeld Brane Inflation to Observations

We compare the Infrared Dirac-Born-Infeld (IR DBI) brane inflation model to observations using a Bayesian analysis. The current data cannot distinguish it from the \LambdaCDM model, but is able to give interesting constraints on various microscopic parameters including the mass of the brane moduli potential, the fundamental string scale, the charge or warp factor of throats, and the number of the mobile branes. We quantify some distinctive testable predictions with stringy signatures, such as the large non-Gaussianity, and the large, but regional, running of the spectral index. These results illustrate how we may be able to probe aspects of string theory using cosmological observations.Comment: 54 pages, 13 figures. v2: non-Gaussianity constraint has been applied to the model; parameter constraints have tightened significantly, conclusions unchanged. References added; v3, minor revision, PRD versio

A Consistency Relation for Power Law Inflation in DBI models

Brane inflation in string theory leads to a new realization of power law inflation which can give rise to significant non-gaussianity. This can happen for any throat geometry if the scalar potential is appropriate. This note presents a consistency relation connecting the running of the nonlinearity parameter characterizing the non-gaussianity and the scalar and tensor indices. The relationship is valid assuming that the throat geometry and scalar potential support power law inflation, regardless of the level of non-gaussianity.Comment: Added references, a couple of comments, fixed 3 typo

Universality in D-brane Inflation

We study the six-field dynamics of D3-brane inflation for a general scalar potential on the conifold, finding simple, universal behavior. We numerically evolve the equations of motion for an ensemble of more than 7 \times 10^7 realizations, drawing the coefficients in the scalar potential from statistical distributions whose detailed properties have demonstrably small effects on our results. When prolonged inflation occurs, it has a characteristic form: the D3-brane initially moves rapidly in the angular directions, spirals down to an inflection point in the potential, and settles into single-field inflation. The probability of N_{e} e-folds of inflation is a power law, P(N_{e}) \propto N_{e}^{-3}, and we derive the same exponent from a simple analytical model. The success of inflation is relatively insensitive to the initial conditions: we find attractor behavior in the angular directions, and the D3-brane can begin far above the inflection point without overshooting. In favorable regions of the parameter space, models yielding 60 e-folds of expansion arise approximately once in 10^3 trials. Realizations that are effectively single-field and give rise to a primordial spectrum of fluctuations consistent with WMAP, for which at least 120 e-folds are required, arise approximately once in 10^5 trials. The emergence of robust predictions from a six-field potential with hundreds of terms invites an analytic approach to multifield inflation.Comment: 28 pages, 9 figure