Modelling of turbulent jets and wall layers: extensions of Lighthill's acoustic analogy with application to computational aeroacoustics

Two extensions to Lighthill’s aeroacoustic analogy are presented. First, equivalent sources due to initial conditions are derived that supplement those due to boundary conditions, as given by Ffowcs Williams & Hawkings. The resulting exact inhomogeneous wave equation is then reformulated with pressure rather than density as the wave variable, and the right-hand side is rearranged using the energy equation with no additional assumptions. Applications to computational aeroacoustics are discussed, and illustrated with examples based on 2D and 3D simulations

Focused Ion Beam Milling Strategies of Photonic Crystal Structures in Silicon

We report on optimisation of the side wall angle of focused ion beam (FIB) fabricated submicron diameter holes in silicon. Two optimisation steps were performed. First, we compare two different FIB scanning procedures and show the advantages of using a spiral scanning method for the definition of holes in photonic crystal slab structures. Secondly, we investigate the effect on the geometry, of parameters for reducing the tapering effect. Furthermore, we report on the initial results regarding effects of $Ga^{+}$ ion implantation during FIB milling on optical losses, both before and after an annealing step, showing over a decade reduction of optical loss

Observational constraints on Cosmic Reionization

Recent observations have set the first constraints on the epoch of reionization (EoR), corresponding to the formation epoch of the first luminous objects. Studies of Gunn-Peterson (GP) absorption, and related phenomena, suggest a qualitative change in the state of the intergalactic medium (IGM) at $z \sim 6$, indicating a rapid increase in the neutral fraction of the IGM, from $x_{HI} 10^{-3}$, perhaps up to 0.1, at $z \ge 6$. Conversely, transmission spikes in the GP trough, and the evolution of the \lya galaxy luminosity function indicate $x_{HI} < 0.5$ at $z\sim 6.5$, while the large scale polarization of the cosmic microwave background (CMB) implies a significant ionization fraction extending to higher redshifts, $z \sim 11 \pm 3$. The results suggest that reionization is less an event than a process, with the process beginning as early as $z \sim 14$, and with the 'percolation', or 'overlap' phase ending at $z \sim 6$. The data are consistent with low luminosity star forming galaxies as being the dominant sources of reionizing photons. Low frequency radio telescopes currently under construction should be able to make the first direct measurements of HI 21cm emission from the neutral IGM during the EoR, and upcoming measurements of secondary CMB temperature anisotropy will provide fine details of the dynamics of the reionized IGM.Comment: to appear in ARAA 2006, vol 44, page 415-462; latex. 84 pages. 15 fi

Entangled Husimi distribution and Complex Wavelet transformation

Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.Comment: 7 page

Gravitational lensing as a contaminant of the gravity wave signal in CMB

Gravity waves (GW) in the early universe generate B-type polarization in the cosmic microwave background (CMB), which can be used as a direct way to measure the energy scale of inflation. Gravitational lensing contaminates the GW signal by converting the dominant E polarization into B polarization. By reconstructing the lensing potential from CMB itself one can decontaminate the B mode induced by lensing. We present results of numerical simulations of B mode delensing using quadratic and iterative maximum-likelihood lensing reconstruction methods as a function of detector noise and beam. In our simulations we find the quadratic method can reduce the lensing B noise power by up to a factor of 7, close to the no noise limit. In contrast, the iterative method shows significant improvements even at the lowest noise levels we tested. We demonstrate explicitly that with this method at least a factor of 40 noise power reduction in lensing induced B power is possible, suggesting that T/S=10^-6 may be achievable in the absence of sky cuts, foregrounds, and instrumental systematics. While we do not find any fundamental lower limit due to lensing, we find that for high-sensitivity detectors residual lensing noise dominates over the detector noise.Comment: 6 pages, 2 figures, submitted to PR

Cross-Correlation Studies with CMB Polarization Maps

The free-electron population during the reionized epoch rescatters CMB temperature quadrupole and generates a now well-known polarization signal at large angular scales. While this contribution has been detected in the temperature-polarization cross power spectrum measured with WMAP data, due to the large cosmic variance associated with anisotropy measurements at tens of degree angular scales only limited information related to reionization, such as the optical depth to electron scattering, can be extracted. The inhomogeneities in the free-electron population lead to an additional secondary polarization anisotropy contribution at arcminute scales. While the fluctuation amplitude, relative to dominant primordial fluctuations, is small, we suggest that a cross-correlation between arcminute scale CMB polarization data and a tracer field of the high redshift universe, such as through fluctuations captured by the 21 cm neutral Hydrogen background or those in the infrared background related to first proto-galaxies, may allow one to study additional details related to reionization. For this purpose, we discuss an optimized higher order correlation measurement, in the form of a three-point function, including information from large angular scale CMB temperature anisotropies in addition to arcminute scale polarization signal related to inhomogeneous reionization. We suggest that the proposed bispectrum can be measured with a substantial signal-to-noise ratio and does not require all-sky maps of CMB polarization or that of the tracer field. A measurement such as the one proposed may allow one to establish the epoch when CMB polarization related to reionization is generated and to address if the universe was reionized once or twice.Comment: 13 pages, 7 figures; Version in press with Phys. Rev.

A circular polarimeter for the Cosmic Microwave Background

A primordial degree of circular polarization of the Cosmic Microwave Background is not observationally excluded. The hypothesis of primordial dichroism can be quantitatively falsified if the plasma is magnetized prior to photon decoupling since the initial V-mode polarization affects the evolution of the temperature fluctuations as well as the equations for the linear polarization. The observed values of the temperature and polarization angular power spectra are used to infer constraints on the amplitude and on the spectral slope of the primordial V-mode. Prior to photon decoupling magnetic fields play the role of polarimeters insofar as they unveil the circular dichroism by coupling the V-mode power spectrum to the remaining brightness perturbations. Conversely, for angular scales ranging between 4 deg and 10 deg the joined bounds on the magnitude of circular polarization and on the magnetic field intensity suggest that direct limits on the V-mode power spectrum in the range of 0.01 mK could directly rule out pre-decoupling magnetic fields in the range of 10-100 nG. The frequency dependence of the signal is located, for the present purposes, in the GHz range.Comment: 28 pages, 12 included figures

CMB B-polarization to map the Large-scale Structures of the Universe

We explore the possibility of using the B-type polarization of the CMB to map the large-scale structures of the Universe taking advantage of the lens effects on the CMB polarization. The functional relation between the B component with the primordial CMB polarization and the line-of-sight mass distribution is explicited. Noting that a sizeable fraction (at least 40%) of the dark halo population which is responsible of this effect can also be detected in galaxy weak lensing survey, we present statistical quantities that should exhibit a strong sensitivity to this overlapping. We stress that it would be a sound test of the gravitational instability picture, independent on many systematic effects that may hamper lensing detection in CMB or galaxy survey alone. Moreover we estimate the intrinsic cosmic variance of the amplitude of this effect to be less than 8% for a 100, deg^2 survey with a 10' CMB beam. Its measurement would then provide us with an original mean for constraining the cosmological parameters, more particularly, as it turns out, the cosmological constant Lambda.Comment: Latex2e with REVTEX ; 14 pages, 8 figure

Percolation on two- and three-dimensional lattices

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent and critical concentration are obtained for the square, simple cubic, HCP and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.Comment: 15 pages, 6 figures, 3 table

CMBfit: Rapid WMAP likelihood calculations with normal parameters

We present a method for ultra-fast confrontation of the WMAP cosmic microwave background observations with theoretical models, implemented as a publicly available software package called CMBfit, useful for anyone wishing to measure cosmological parameters by combining WMAP with other observations. The method takes advantage of the underlying physics by transforming into a set of parameters where the WMAP likelihood surface is accurately fit by the exponential of a quartic or sextic polynomial. Building on previous physics based approximations by Hu et.al., Kosowsky et.al. and Chu et.al., it combines their speed with precision cosmology grade accuracy. A Fortran code for computing the WMAP likelihood for a given set of parameters is provided, pre-calibrated against CMBfast, accurate to Delta lnL ~ 0.05 over the entire 2sigma region of the parameter space for 6 parameter ``vanilla'' Lambda CDM models. We also provide 7-parameter fits including spatial curvature, gravitational waves and a running spectral index.Comment: 14 pages, 8 figures, References added, accepted for publication in Phys.Rev.D., a Fortran code can be downloaded from http://space.mit.edu/home/tegmark/cmbfit