Instanton Theory of Burgers Shocks and Intermittency

A lagrangian approach to Burgers turbulence is carried out along the lines of the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics. We derive, from an analysis based on the hypothesis of unbroken galilean invariance, the asymptotic form of the probability distribution function of negative velocity-differences. The origin of Burgers intermittency is found to rely on the dynamical coupling between shocks, identified to instantons, and non-coherent background fluctuations, which, then, cannot be discarded in a consistent statistical description of the flow.Comment: 7 pages; LaTe

Lensing effect on polarization in microwave background: extracting convergence power spectrum

Matter inhomogeneities along the line of sight deflect the cosmic microwave background (CMB) photons originating at the last scattering surface at redshift $z \sim 1100$. These distortions modify the pattern of CMB polarization. We identify specific combinations of Stokes $Q$ and $U$ parameters that correspond to spin 0,$\pm 2$ variables and can be used to reconstruct the projected matter density. We compute the expected signal to noise as a function of detector sensitivity and angular resolution. With Planck satellite the detection would be at a few $\sigma$ level. Several times better detector sensitivity would be needed to measure the projected dark matter power spectrum over a wider range of scales, which could provide an independent confirmation of the projected matter power spectrum as measured from other methods.Comment: 17 pages, 5 figures, accepted for publication in PR

Recovery of the Shape of the Mass Power Spectrum from the Lyman-alpha Forest

We propose a method for recovering the shape of the mass power spectrum on large scales from the transmission fluctuations of the Lyman-alpha forest, which takes into account directly redshift-space distortions. The procedure, in discretized form, involves the inversion of a triangular matrix which projects the mass power spectrum in 3-D real-space to the transmission power spectrum in 1-D redshift-space. We illustrate the method by performing a linear calculation relating the two. A method that does not take into account redshift-space anisotropy tends to underestimate the steepness of the mass power spectrum, in the case of linear distortions. The issue of the effective bias-factor for the linear distortion kernel is discussed.Comment: 18 pages, 4 figures; minor revision

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time

Cosmic Complementarity: Joint Parameter Estimation from CMB Experiments and Redshift Surveys

We study the ability of future CMB anisotropy experiments and redshift surveys to constrain a thirteen-dimensional parameterization of the adiabatic cold dark matter model. Each alone is unable to determine all parameters to high accuracy. However, considered together, one data set resolves the difficulties of the other, allowing certain degenerate parameters to be determined with far greater precision. We treat in detail the degeneracies involving the classical cosmological parameters, massive neutrinos, tensor-scalar ratio, bias, and reionization optical depth as well as how redshift surveys can resolve them. We discuss the opportunities for internal and external consistency checks on these measurements. Previous papers on parameter estimation have generally treated smaller parameter spaces; in direct comparisons to these works, we tend to find weaker constraints and suggest numerical explanations for the discrepancies.Comment: Submitted to ApJ. LaTeX, 20 pages, emulateapj.sty and onecolfloat.sty. Minor errors in Table 8 corrected; reference adde

Weak Lensing of the CMB: A Harmonic Approach

Weak lensing of CMB anisotropies and polarization for the power spectra and higher order statistics can be handled directly in harmonic-space without recourse to real-space correlation functions. For the power spectra, this approach not only simplifies the calculations but is also readily generalized from the usual flat-sky approximation to the exact all-sky form by replacing Fourier harmonics with spherical harmonics. Counterintuitively, due to the nonlinear nature of the effect, errors in the flat-sky approximation do not improve on smaller scales. They remain at the 10% level through the acoustic regime and are sufficiently large to merit adoption of the all-sky formalism. For the bispectra, a cosmic variance limited detection of the correlation with secondary anisotropies has an order of magnitude greater signal-to-noise for combinations involving magnetic parity polarization than those involving the temperature alone. Detection of these bispectra will however be severely noise and foreground limited even with the Planck satellite, leaving room for improvement with higher sensitivity experiments. We also provide a general study of the correspondence between flat and all sky potentials, deflection angles, convergence and shear for the power spectra and bispectra.Comment: 17 pages, 5 figures, submitted to PR

Halo stochasticity in global clustering analysis

In the present work we study the statistics of haloes, which in the halo model determines the distribution of galaxies. Haloes are known to be biased tracer of dark matter, and at large scales it is usually assumed there is no intrinsic stochasticity between the two fields. Following the work of Seljak & Warren (2004), we explore how correct this assumption is and, moving a step further, we try to qualify the nature of stochasticity. We use Principal Component Analysis applied to the outputs of a cosmological N-body simulation to: (1) explore the behaviour of stochasticity in the correlation between haloes of different masses; (2) explore the behaviour of stochasticity in the correlation between haloes and dark matter. We show results obtained using a catalogue with 2.1 million haloes, from a PMFAST simulation with box size of 1000h^{-1}Mpc. In the relation between different populations of haloes we find that stochasticity is not-negligible even at large scales. In agreement with the conclusions of Tegmark & Bromley (1999) who studied the correlations of different galaxy populations, we found that the shot-noise subtracted stochasticity is qualitatively different from `enhanced' shot noise and, specifically, it is dominated by a single stochastic eigenvalue. We call this the `minimally stochastic' scenario, as opposed to shot noise which is `maximally stochastic'. In the correlation between haloes and dark matter, we find that stochasticity is minimized, as expected, near the dark matter peak (k ~ 0.02 h Mpc^{-1} for a LambdaCDM cosmology) and, even at large scales, it is of the order of 15 per cent above the shot noise. Moreover, we find that the reconstruction of the dark matter distribution is improved when we use eigenvectors as tracers of the bias. [Abridged]Comment: 9 pages, 12 figures. Submitted to MNRA

Reconstructing Projected Matter Density from Cosmic Microwave Background

Gravitational lensing distorts the cosmic microwave background (CMB) anisotropies and imprints a characteristic pattern onto it. The distortions depend on the projected matter density between today and redshift $z \sim 1100$. In this paper we develop a method for a direct reconstruction of the projected matter density from the CMB anisotropies. This reconstruction is obtained by averaging over quadratic combinations of the derivatives of CMB field. We test the method using simulations and show that it can successfully recover projected density profile of a cluster of galaxies if there are measurable anisotropies on scales smaller than the characteristic cluster size. In the absence of sufficient small scale power the reconstructed maps have low signal to noise on individual structures, but can give a positive detection of the power spectrum or when cross correlated with other maps of large scale structure. We develop an analytic method to reconstruct the power spectrum including the effects of noise and beam smoothing. Tests with Monte Carlo simulations show that we can recover the input power spectrum both on large and small scales, provided that we use maps with sufficiently low noise and high angular resolution.Comment: 21 pages, 9 figures, submitted to PR

The Sunyaev-Zeldovich effect in CMB-calibrated theories applied to the Cosmic Background Imager anisotropy power at l > 2000

We discuss the nature of the possible high-l excess in the Cosmic Microwave Background (CMB) anisotropy power spectrum observed by the Cosmic Background Imager (CBI). We probe the angular structure of the excess in the CBI deep fields and investigate whether it could be due to the scattering of CMB photons by hot electrons within clusters, the Sunyaev-Zeldovich (SZ) effect. We estimate the density fluctuation parameters for amplitude, sigma_8, and shape, Gamma, from CMB primary anisotropy data and other cosmological data. We use the results of two separate hydrodynamical codes for Lambda-CDM cosmologies, consistent with the allowed sigma_8 and Gamma values, to quantify the expected contribution from the SZ effect to the bandpowers of the CBI experiment and pass simulated SZ effect maps through our CBI analysis pipeline. The result is very sensitive to the value of sigma_8, and is roughly consistent with the observed power if sigma_8 ~ 1. We conclude that the CBI anomaly could be a result of the SZ effect for the class of Lambda-CDM concordance models if sigma_8 is in the upper range of values allowed by current CMB and Large Scale Structure (LSS) data.Comment: Accepted by The Astrophysical Journal; 17 pages including 12 color figures. v2 matches accepted version. Additional information at http://www.astro.caltech.edu/~tjp/CBI

Management of pain in Fabry disease in the UK clinical setting: consensus findings from an expert Delphi panel

Background: Fabry disease is a rare, X-linked inherited lysosomal storage disorder, that manifests as a heterogeneous disease with renal, cardiac and nervous system involvement. The most common pain experienced by people with Fabry disease are episodes of neuropathic pain reported in up to 80% of classical hemizygous male patients and up to 65% of heterozygous female patients. No clear consensus exists within UK clinical practice for the assessment and management of pain in Fabry disease based on agreed clinical practice and clinical experience. Here we describe a modified Delphi initiative to establish expert consensus on management of pain in Fabry disease in the UK clinical setting. Methods: Delphi panel members were identified based on their demonstrated expertise in managing adult or paediatric patients with Fabry disease in the UK and recruited by an independent third-party administrator. Ten expert panellists agreed to participate in two survey rounds, during which they remained anonymous to each other. Circulation of the questionnaires, and collection and processing of the panel’s responses were conducted between September 2021 and December 2021. All questions required an answer. Results: The Delphi panel reached a consensus on 21 out of 41 aspects of pain assessment and management of pain in Fabry disease. These encompassed steps in the care pathway from the goals of therapy through to holistic support, including the use of gabapentin and carbamazepine as first-line analgesic medications for the treatment of neuropathic pain in Fabry disease, as well as the proactive management of symptoms of anxiety and/or depression associated with Fabry pain. Conclusions: The consensus panel outcomes reported here have highlighted strengths in current UK clinical practice, along with unmet needs for further research and agreement. This consensus is intended to prompt the next steps towards developing clinical guidelines