A Covariant Information-Density Cutoff in Curved Space-Time

In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be completely equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.Comment: 4 pages, RevTe

Bayesian cosmic density field inference from redshift space dark matter maps

We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after cosmic evolution observed in redshift space. Previous works on density reconstruction did not self-consistently consider redshift space distortions or included an additional iterative distortion correction step. We present here the analytic solution of coherent flows within a Hamiltonian Monte Carlo posterior sampling of the primordial density field. We test our method within the Zel'dovich approximation, presenting also an analytic solution including tidal fields and spherical collapse on small scales using augmented Lagrangian perturbation theory. Our resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true one defined by our mock observations. Novel algorithmic implementations are introduced regarding the mass assignment kernels when defining the dark matter density field and optimization of the time step in the Hamiltonian equations of motions. Our algorithm, dubbed barcode, promises to be specially suited for analysis of the dark matter cosmic web down to scales of a few Megaparsecs. This large scale structure is implied by the observed spatial distribution of galaxy clusters --- such as obtained from X-ray, SZ or weak lensing surveys --- as well as that of the intergalactic medium sampled by the Lyman alpha forest or perhaps even by deep hydrogen intensity mapping. In these cases, virialized motions are negligible, and the tracers cannot be modeled as point-like objects. It could be used in all of these contexts as a baryon acoustic oscillation reconstruction algorithm.Comment: 34 pages, 25 figures, 1 table. Submitted to MNRAS. Accompanying code at https://github.com/egpbos/barcod

Wavelet-based density estimation for noise reduction in plasma simulations using particles

For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets that involve different levels of collisionality and interaction with external and self-consistent fields

Elastic properties of a tungsten-silver composite by reconstruction and computation

We statistically reconstruct a three-dimensional model of a tungsten-silver composite from an experimental two-dimensional image. The effective Young's modulus ($E$) of the model is computed in the temperature range 25-1060^o C using a finite element method. The results are in good agreement with experimental data. As a test case, we have reconstructed the microstructure and computed the moduli of the overlapping sphere model. The reconstructed and overlapping sphere models are examples of bi-continuous (non-particulate) media. The computed moduli of the models are not generally in good agreement with the predictions of the self-consistent method. We have also evaluated three-point variational bounds on the Young's moduli of the models using the results of Beran, Molyneux, Milton and Phan-Thien. The measured data were close to the upper bound if the properties of the two phases were similar ($1/6 < E_1 /E_2 < 6$).Comment: 23 Pages, 12 Figure

Bias deconstructed: Unravelling the scale dependence of halo bias using real space measurements

We explore the scale dependence of halo bias using real space cross-correlation measurements in N-body simulations and in Pinocchio, an algorithm based on Lagrangian Perturbation Theory. Recent work has shown how to interpret such real space measurements in terms of k-dependent bias in Fourier space, and how to remove the k-dependence to reconstruct the k-independent peak-background split halo bias parameters. We compare our reconstruction of the linear bias, which requires no free parameters, with previous estimates from N-body simulations which were obtained directly in Fourier space at large scales, and find very good agreement. Our reconstruction of the quadratic bias is similarly parameter-free, although in this case there are no previous Fourier space measurements to compare with. Our analysis of N-body simulations explicitly tests the predictions of the excursion set peaks (ESP) formalism of Paranjape et al. (2013) for the scale dependence of bias; we find that the ESP predictions accurately describe our measurements. In addition, our measurements in Pinocchio serve as a useful, successful consistency check between Pinocchio and N-body simulations that is not accessible to traditional measurements.Comment: 13 pages, 9 figures; v3 -- Matches published versio

Electronic charge reconstruction of doped Mott insulators in multilayered nanostructures

Dynamical mean-field theory is employed to calculate the electronic charge reconstruction of multilayered inhomogeneous devices composed of semi-infinite metallic lead layers sandwiching barrier planes of a strongly correlated material (that can be tuned through the metal-insulator Mott transition). The main focus is on barriers that are doped Mott insulators, and how the electronic charge reconstruction can create well-defined Mott insulating regions in a device whose thickness is governed by intrinsic materials properties, and hence may be able to be reproducibly made.Comment: 9 pages, 8 figure