Search

The mathematical concept of chaos was introduced by Edward Lorenz in the early 1960s while attempting to represent atmospheric convection through a two-dimensional fluid flow with an imposed temperature difference in the vertical direction. Since then, chaotic dynamical systems are accepted as the foundation of the meteorological sciences and represent an indispensable testbed for weather and climate forecasting tools. Operational weather forecasting platforms rely on costly partial differential equations (PDE)-based models that run continuously on high performance computing architectures. Machine learning (ML)-based low-dimensional surrogate models can be viewed as a cost-effective solution for such high-fidelity simulation platforms. In this work, we propose an ML method based on Reservoir Computing - Echo State Neural Network (RC-ESN) to accurately predict evolutionary states of chaotic systems. We start with the baseline Lorenz-63 and 96 systems and show that RC-ESN is extremely effective in consistently predicting time series using Pearson’s cross correlation similarity measure. RC-ESN can accurately forecast Lorenz systems for many Lyapunov time units into the future. In a practical numerical example, we applied RC-ESN combined with space-only proper orthogonal decomposition (POD) to build a reduced order model (ROM) that produces sequential short-term forecasts of pollution dispersion over the continental USA region. We use GEOS-CF simulated data to assess our RC-ESN ROM. Numerical experiments show reasonable results for such a highly complex atmospheric pollution system.

The Higgs effective potential becomes unstable at approximately $10^{11}$ GeV, and if only standard model interactions are considered, the lifetime $\tau$ of the electroweak vacuum turns out to be much larger than the age of the Universe $T_U$. It is well known, however, that $\tau$ is extremely sensitive to the presence of unknown new physics: the latter can enormously lower $\tau$. This poses a serious problem for the stability of our Universe, demanding for a physical mechanism that protects it from a disastrous decay. We have found that there exists a universal stabilizing mechanism that naturally originates from the nonminimal coupling between gravity and the Higgs boson. As this Higgs-gravity interaction necessarily arises from the quantum dynamics of the Higgs field in a gravitational background, this stabilizing mechanism is certainly present. It is not related to any specific model, being rather natural and universal as it comes from fundamental pillars of our physical world: gravity, the Higgs field, the quantum nature of physical laws., Comment: 5 pages, 4 figures

I investigate the suitability of the Scheduled-Relaxation-Jacobi method as a smoother within a geometric multilevel (ML) solver. Its performance in the solution of a linear elliptic equation is measured, based on two metrics: absolute performance (measured by the residual reduction in a fixed number of iterations), and parallel scalability. I discuss the theoretical expectations on the effect of this hybrid scheme on the solution iterate and, especially, the solution error, and confirm them numerically.

Despite its continued observational successes, there is a persistent (and growing) interest in extending cosmology beyond the standard model, ΛCDM. This is motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm. In this paper, we summarize the current status of ΛCDM as a physical theory, and review investigations into possible alternatives along a number of different lines, with a particular focus on highlighting the most promising directions. While the fundamental problems are proving reluctant to yield, the study of alternative cosmologies has led to considerable progress, with much more to come if hopes about forthcoming high-precision observations and new theoretical ideas are fulfilled.

It has been recently shown that, contrary to an intuitive decoupling argument, the presence of new physics at very large energy scales (say around the Planck scale) can have a strong impact on the electroweak vacuum lifetime. In particular, the vacuum could be totally destabilized. This study was performed in a flat spacetime background, and it is important to extend the analysis to curved spacetime since these are Planckian-physics effects. It is generally expected that under these extreme conditions gravity should totally quench the formation of true vacuum bubbles, thus washing out the destabilizing effect of new physics. In this work we extend the analysis to curved spacetime and show that, although gravity pushes toward stabilization, the destabilizing effect of new physics is still (by far) the dominating one. In order to get model independent results, high energy new physics is parametrized in two different independent ways: as higher order operators in the Higgs field, or introducing new particles with very large masses. The destabilizing effect is observed in both cases, hinting at a general mechanism that does not depend on the parametrization details for new physics, thus maintaining the results obtained from the analysis performed in flat spacetime., 22 pages, 11 figures

The applications of numerical relativity to cosmology are on the rise, contributing insight into such cosmological problems as structure formation, primordial phase transitions, gravitational-wave generation, and inflation. In this paper, I present the infrastructure for the computation of inhomogeneous dust cosmologies which was used recently to measure the effect of nonlinear inhomogeneity on the cosmic expansion rate. I illustrate the code's architecture, provide evidence for its correctness in a number of familiar cosmological settings, and evaluate its parallel performance for grids of up to several billion points. The code, which is available as free software, is based on the Einstein Toolkit infrastructure, and in particular leverages the automated-code-generation capabilities provided by its component Kranc., Comment: 11 pages, 6 figures

We construct a three-dimensional, fully relativistic numerical model of a universe filled with an inhomogeneous pressureless fluid, starting from initial data that represent a perturbation of the Einstein-de Sitter model. We then measure the departure of the average expansion rate with respect to this homogeneous and isotropic reference model, comparing local quantities to the predictions of linear perturbation theory. We find that collapsing perturbations reach the turnaround point much earlier than expected from the reference spherical top-hat collapse model and that the local deviation of the expansion rate from the homogeneous one can be as high as $28\%$ at an underdensity, for an initial density contrast of $10^{-2}$. We then study, for the first time, the exact behavior of the backreaction term ${\cal Q}_{\cal D}$. We find that, for small values of the initial perturbations, this term exhibits a $1/a$ scaling, and that it is negative with a linearly growing absolute value for larger perturbation amplitudes, thereby contributing to an overall deceleration of the expansion. Its magnitude, on the other hand, remains very small even for relatively large perturbations., Comment: Version updated to match published article

We discuss the possibility of a dimensional reduction of the Einstein equations in S3 black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotational and reflection Symmetry (LDRRS) can be carried out via a system of ODEs along these curves. However, 3+1 Numerical Relativity computations demonstrate that this is not the case, and we show analytically that this is due to the presence of a tensorial quantity which is not suppressed by the symmetry. We calculate the term analytically, and verify numerically for an 8-black-hole lattice that it fully accounts for the anomalous results, and thus quantify its magnitude in this specific case. The presence of this term prevents the exact evolution of these spaces via previously-reported methods which do not involve a full 3+1 integration of Einstein's equation., Comment: 18 pages, 4 figures

The apparent properties of distant objects encode information about the way the light they emit propagates to an observer, and therefore about the curvature of the underlying spacetime. Measuring the relationship between the redshift $z$ and the luminosity distance $D_{\rm L}$ of a standard candle, for example, yields information on the Universe's matter content. In practice, however, in order to decode this information the observer needs to make an assumption about the functional form of the $D_{\rm L}(z)$ relation; in other words, a cosmological model needs to be assumed. In this work, we use numerical-relativity simulations, equipped with a new ray-tracing module, to numerically obtain this relation for a few black-hole--lattice cosmologies and compare it to the well-known Friedmann-Lema\^itre-Robertson-Walker case, as well as to other relevant cosmologies and to the Empty-Beam Approximation. We find that the latter provides the best estimate of the luminosity distance and formulate a simple argument to account for this agreement. We also find that a Friedmann-Lema\^itre-Robertson-Walker model can reproduce this observable exactly, as long as a time-dependent cosmological constant is included in the fit. Finally, the dependence of these results on the lattice mass-to-spacing ratio $\mu$ is discussed: we discover that, unlike the expansion rate, the $D_{\rm L}(z)$ relation in a black-hole lattice does not tend to that measured in the corresponding continuum spacetime as $\mu \to 0$., Comment: 32 pages, 10 figures, matches published version

The construction of black-hole lattices, first attempted by Richard Lindquist and John Wheeler in 1957, has recently been tackled with renewed interest, as a test bed for studying the behavior of inhomogeneities in the context of the backreaction problem. In this contribution, I discuss how black-hole lattices can help shed light on two important issues, and illustrate the conclusions reached so far in the study of these systems., 4 pages, 2 figures. Contribution to the Proceedings of the 2012 Spanish Relativity Meeting

We present the numerical evolution of a family of conformally-flat, infinite, expanding cubic black-hole lattices. We solve for the initial data using an initial-data prescription presented recently, along with a new multigrid solver developed for this purpose. We then apply the standard tools of numerical relativity to calculate the time development of this initial dataset and derive quantities of cosmological relevance, such as the scaling of proper lengths. Similarly to the case of S3 lattices, we find that the length scaling remains close to the analytical solution for Friedmann-Lemaitre-Robertson-Walker cosmologies throughout our simulations, which span a window of about one order of magnitude in the growth of the scale factor. We highlight, however, a number of important departures from the Friedmann-Lemaitre-Robertson-Walker class., 20 pages, 15 figures. A few minor corrections

The idea of black-hole lattices as models for the large-scale structure of the universe has been under scrutiny for several decades, and some of the properties of these systems have been elucidated recently in the context of the problem of cosmological backreaction. The complete, three-dimensional and fully relativistic evolution of these system has, however, never been tackled. We explicitly construct the first of these solutions by numerically integrating Einstein's equation in the case of an eight-black-hole lattice with the topology of S3., 21 pages, 13 figures. Corrected and clarified discussion

We describe the Einstein Toolkit, a community-driven, freely accessible computational infrastructure intended for use in numerical relativity, relativistic astrophysics, and other applications. The Toolkit, developed by a collaboration involving researchers from multiple institutions around the world, combines a core set of components needed to simulate astrophysical objects such as black holes, compact objects, and collapsing stars, as well as a full suite of analysis tools. The Einstein Toolkit is currently based on the Cactus Framework for high-performance computing and the Carpet adaptive mesh refinement driver. It implements spacetime evolution via the BSSN evolution system and general-relativistic hydrodynamics in a finite-volume discretization. The toolkit is under continuous development and contains many new code components that have been publicly released for the first time and are described in this article. We discuss the motivation behind the release of the toolkit, the philosophy underlying its development, and the goals of the project. A summary of the implemented numerical techniques is included, as are results of numerical test covering a variety of sample astrophysical problems., 62 pages, 20 figures

The peeling theorem of general relativity predicts that the Weyl curvature scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an asymptotically flat spacetime, fall off asymptotically as r^(n-5) along outgoing radial null geodesics. This leads to the interpretation of Psi_4 as outgoing gravitational radiation at large distances from the source. We have performed numerical simulations in full general relativity of a binary black hole inspiral and merger, and have computed the Weyl scalars in the standard tetrad used in numerical relativity. In contrast with previous results, we observe that all the Weyl scalars fall off according to the predictions of the theorem., 7 pages, 3 figures, published version

This paper describes the Alpaca runtime tools. These tools leverage the component infrastructure of the Cactus Framework in a novel way to enable runtime steering, monitoring, and interactive control of a simulation. Simulation data can be observed graphically, or by inspecting values of variables. When GPUs are available, images can be generated using volume ray casting on the live data. In response to observed error conditions or automatic triggers, users can pause the simulation to modify or repair data, or change runtime parameters. In this paper we describe the design of our implementation of these features and illustrate their value with three use cases.

I describe the observed departures of strongly‐gravitating systems from the predictions of Newton’s theory and summarize one of the most powerful techniques to model general‐relativistic effects, based on the concept of a 3+1 decomposition of Einstein’s equation and a direct numerical solution of the resulting system.

As scientific applications extend to the simulation of more and more complex systems, they involve an increasing number of abstraction levels, at each of which errors can emerge and across which they can propagate; tools for correctness evaluation and enforcement at every level (from the code level to the application level) are therefore necessary. Whilst code-level debugging tools are already a well established standard, application-level tools are lagging behind, possibly due to their stronger dependence on the application's details. In this paper, we describe the programming model introduced by the Cactus framework, review the High Performance Computing (HPC) challenges that Cactus is designed to address, and illustrate the correctness strategies that are currently available in Cactus at the code, component, and application level., Comment: 11 pages, 5 figures, presented at the 2009 Workshop on Component-Based High Performance Computing (CBHPC 2009)

We present results obtained by scattering a scalar field off the curved background of a coalescing binary black hole system. A massless scalar field is evolved on a set of fixed backgrounds, each provided by a spatial hypersurface generated numerically during a binary black hole merger. We show that the scalar field scattered from the merger region exhibits quasinormal ringing once a common apparent horizon surrounds the two black holes. This occurs earlier than the onset of the perturbative regime as measured by the start of the quasinormal ringing in the gravitational waveforms. We also use the scalar quasinormal frequencies to associate a mass and a spin with each hypersurface, and observe the compatibility of this measure with the horizon mass and spin computed from the dynamical horizon framework., Comment: 10 Pages and 6 figures

17 pags. ; 11 figs. ; appendix A-B, A model for a flat isotropic universe with a negative cosmological constant Lambda and a massless scalar field as sole matter content is studied within the framework of loop quantum cosmology. By application of the methods introduced for the model with Lambda=0, the physical Hilbert space and the set of Dirac observables are constructed. As in that case, the scalar field plays here the role of an emergent time. The properties of the system are found to be similar to those of the k=1 Friedmann-Robertson-Walker (FRW) model: for small energy densities, the quantum dynamics reproduces the classical one, whereas, due to modifications at near-Planckian densities, the big bang and big crunch singularities are replaced by a quantum bounce connecting deterministically the large semiclassical epochs. Thus in loop quantum cosmology the evolution is qualitatively cyclic., We would like to thank Abhay Ashtekar, Wojciech Kamin´ski, and Parampreet Singh for extensive discussions and helpful comments. We also profited from discussions with Martin Bojowald and Jerzy Lewandowski. This work was supported in part by the National Science Foundation (NSF) Grant No. PHY-0456913 and the Eberly research funds. T. P. acknowledges financial aid provided by the I3P framework of CSIC and the European Social Fund and Foundation for Polish Science, ‘‘Master’’ grant. E. B. acknowledges the support of the Center for Gravitational Wave Physics, funded by the National Science Foundation under Cooperative Agreement No. PHY-0114375.

This chapter surveys pervasive computing with a focus on how its constraint for transparency affects issues of resource management and security. The goal of pervasive computing is to render computing transparent, such that computing resources are ubiquitously offered to the user and services are proactively performed for a user without his or her intervention. The task of integrating computing infrastructure with everyday life without making it excessively invasive brings about trade-offs between flexibility and robustness, efficiency and effectiveness, as well as autonomy and reliability. While efficiency in resource management is not the primary goal of pervasive computing, it should be considered in order to best utilize a limited set of resources (bandwidth, computing, etc.) so as to avoid congestion and creation of a visible and distracting bottleneck in the eyes of the user. As solutions to efficiently manage the resources in a pervasive computing environment, three techniques will be examined: the distributed caching and sharing of data between mobile hosts, the broadcasting of services by public service providers and the ability for mobile hosts to adaptively adjust the quality of offered services. Likewise, security is often an afterthought in many computing projects, though it should be of high consideration in a pervasive environment where users share public resources to operate on private data. Specifically, how can a user be authenticated in this environment with minimal or no user intervention? Solutions such as single sign-on via smartcards and biometrics will be examined to carry out authentication in a pervasive environment. As the feasibility of ubiquitous computing and its real potential for mass applications are still a matter of controversy, this chapter will look into the underlying issues of resource management and authentication to discover how these can be handled in a least invasive fashion. The discussion will conclude with an overview of the solutions proposed by current pervasive computing efforts, both in the area of generic platforms and for dedicated applications such as pervasive education and healthcare.

Over the past year and a half, a number of groups have produced stable runs of a binary black hole system evolving through merger and ringdown. In [2][3], in particular, the tremendous speedup to the field was driven by special sets of gauge evolution equations, capable of handling several issues that have traditionally plagued black hole simulations: avoiding the singularity, guaranteeing a constraint satisfying solution at least in the exterior region, and advecting the holes through the numerical grid.Since several successful recipes have already been proposed, the goal of this study is to review them and analyze the consistency of the published results. A preliminary comparison of the waveform outcome of each different gauge prescription is presented.

We use high-redshift type Ia supernova and compact radio source data in order to test the infrared (IR) fixed point model of the late Universe which was proposed recently. It describes a cosmology with a time dependent cosmological constant and Newton constant whose dynamics arises from an underlying renormalization group flow near an IR-attractive fixed point. Without any finetuning or quintessence field it yields $\Omega_{\rm M}=\Omega_{\Lambda}=1/2$. Its characteristic $t^{4/3}$-dependence of the scale factor leads to a distance-redshift relation whose predictions are compared both to the supernova and to the radio source data. According to the $\chi^2$ test, the fixed point model reproduces the data at least as well as the best-fit (Friedmann-Robertson-Walker) standard cosmology.Furthermore, we extend the original fixed point model by assuming that the fixed point epoch is preceded by an era with constant $G$ and $\Lambda$. By means of a Monte Carlo simulation we show that the data expected from the forthcoming SNAP satellite mission could detect the transition to the fixed point regime provided it took place at a redshift of less than about 0.5., Comment: 45 pages, revtex4, 8 figures, to appear on JCAP