Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic processes”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Higher moments of primordial non-Gaussianity and N-body simulations

We perform cosmological N-body simulations with non-Gaussian initial conditions generated from two independent fields. The dominant contribution to the perturbations comes from a purely Gaussian field, but we allow the second field to have local non-Gaussianity that need not be weak. This scenario allows us to adjust the relative importance of non-Gaussian contributions beyond the skewness, producing a scaling of the higher moments different from (and stronger than) the scaling in the usual single field local ansatz. We compare semi-analytic prescriptions for the non-Gaussian mass function, large scale halo bias, and stochastic bias against the simulation results. We discuss applications of this work to large scale structure measurements that can test a wider range of models for the primordial fluctuations than is usually explored.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Quantifying the 'naturalness' of the curvaton model

We investigate the probability of obtaining an observable curvature perturbation, using as an example the minimal curvaton-higgs (MCH) model. We determine ''probably observable'' and ''probably excluded'' regions of parameter space assuming generic initial conditions and applying a stochastic approach for the curvaton's evolution during inflation. Inflation is assumed to last longer than the N{sub obs} ≅ 55 observable e-folds, and the total number of e-folds of inflation determines the particular ranges of parameters that are probable. For the MCH model, these ''probably observable'' regions always lie within the range 8 × 10{sup 4} GeV ≤ m{sub σ} ≤ 2 × 10{sup 7} GeV, where m{sub σ} is the curvaton mass, and the Hubble scale at horizon exit is chosen as H{sub *} = 10{sup 10} GeV. Because the ''probably observable'' region depends on the total duration of inflation, information on parameters in the Lagrangian from particle physics and from precision CMB observations can therefore provide information about the total duration of inflation, not just the last N{sub obs} e-folds. This method could also be applied to any model that contains additional scalar fields to determine the probability that these scalar fields contribute to the curvature perturbation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Non-perturbative approach for curvature perturbations in stochastic δ N formalism

In our previous paper [1], we have proposed a new algorithm to calculate the power spectrum of the curvature perturbations generated in inflationary universe with use of the stochastic approach. Since this algorithm does not need the perturbative expansion with respect to the inflaton fields on super-horizon scale, it works even in highly stochastic cases. For example, when the curvature perturbations are very large or the non-Gaussianities of the curvature perturbations are sizable, the perturbative expansion may break down but our algorithm enables to calculate the curvature perturbations. We apply it to two well-known inflation models, chaotic and hybrid inflation, in this paper. Especially for hybrid inflation, while the potential is very flat around the critical point and the standard perturbative computation is problematic, we successfully calculate the curvature perturbations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Theory of non-Gaussianity in warm inflation

The theory and methodology is developed to compute the bispectrum in warm inflation, leading to results for the non-linearity parameter and the shape of the bispectrum. Particular attention is paid to the study of the bispectrum in the regime of weak dissipation and how stochastic fluctuations affect the bispectrum. It is shown that, in contrast to the strong dissipative regime, the amplitude of non-Gaussianity is strongly dependent on the parameters governing the microscopic physics in the intermediate and weak dissipation warm inflation regimes. The most important results concern the shape of the bispectrum, which has two different, but distinct, forms in the weak and strong dissipative regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Cosmological perturbations for an inflaton field coupled to radiation

Within the framework of the interacting fluid formalism, we provide the numerical solution to the Boltzmann equation describing the evolution of an inflaton field coupled to radiation. We study the behavior of the system during the slow-roll regime, in the case in which an additional stochastic source term is included in the set of equations, and we recover the expression for the cosmological perturbations previously obtained in the Warm inflation scenarios.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The adhesion model as a field theory for cosmological clustering

The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale structure, adding a stochastic force to account for power generated from very short, highly non-linear scales that is uncorrelated with the initial power spectrum. The dynamics of this Stochastic Adhesion Model (SAM) is reminiscent of the well known Kardar-Parisi-Zhang equation with the difference that the viscosity and the noise spectrum are time dependent. Choosing the viscosity proportional to the growth factor D restricts the form of noise spectrum through a 1-loop renormalization argument. For this choice, the SAM field theory is renormalizable to one loop. We comment on the suitability of this model for describing the non-linear regime of the CDM power spectrum and its utility as a relatively simple approach to cosmological clustering.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The bispectrum in the Effective Field Theory of Large Scale Structure

We study the bispectrum in the Effective Field Theory of Large Scale Structure, consistently accounting for the effects of short-scale dynamics. We begin by proving that, as long as the theory is perturbative, it can be formulated to arbitrary order using only operators that are local in time. We then derive all the new operators required to cancel the UV-divergences and obtain a physically meaningful prediction for the one-loop bispectrum. In addition to new, subleading stochastic noises and the viscosity term needed for the one-loop power spectrum, we find three new effective operators. The three new parameters can be constrained by comparing with N-body simulations. The best fit is precisely what is suggested by the structure of UV-divergences, hence justifying a formula for the EFTofLSS bispectrum whose only fitting parameter is already fixed by the power spectrum. This result predicts the bispectrum of N-body simulations up to k{sub max}≈0.22 h Mpc{sup −1} at 0z=, an improvement by nearly a factor of two as compared to one-loop standard perturbation theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

No evidence for the blue-tilted power spectrum of relic gravitational waves

In this paper, we constrain the tilt of the power spectrum of relic gravitational waves by combining the data from BICEP2/Keck Array and Planck (BKP) and the Laser Interferometer Gravitational-Waves Observatory (LIGO). Supposing the linearly uniform priors for both the tensor-to-scalar ratio r and the tensor tilt n{sub t}, we find n{sub t}=0.66{sup +1.83}{sub −1.44} at the 68% confidence level from the data of BKP B-modes. By further adding the LIGO upper limit on the intensity of stochastic gravitational-wave background, the constraint becomes n{sub t}=−0.76{sup +1.37}{sub −0.52} at the 68% confidence level by assuming that the tensor amplitude has the similar order of the upper bounds from current CMB experiments. We find that there is no evidence for a blue-tilted power spectrum of relic gravitational waves and either sign of the index of tensor power spectrum is compatible with the current data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Gravitational waves from Affleck-Dine condensate fragmentation

We compute the stochastic gravitational wave production from Affleck-Dine condensate fragmentation in the early universe, focusing on an effective potential with a logarithmic mass correction that typically arises in gravity mediated supersymmetry breaking scenarios. We find that a significant gravitational wave background can be generated when Q-balls are being formed out of the condensate fragmentation. This gravitational wave background has a distinct multi-peak power spectrum where the trough is closely linked to the supersymmetry breaking scale and whose frequencies are peaked around kHz for TeV supersymmetry breaking.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A cosmic ALP background and the cluster soft X-ray excess in A665, A2199 and A2255

It has been proposed that an excess in soft X-ray emission observed from many galaxy clusters can be explained by conversion into photons of axion-like particles (ALPs) in the cluster's magnetic field. Previously it has been shown that conversion of this primordially-generated background of relativistic ALPs—a cosmic ALP background (CAB)—can explain the observed soft X-ray excess in both the centre and the outskirts of the Coma cluster. Here we extend this work to the three clusters A665, A2199 and A2255. We use a stochastic, power law model of the cluster magnetic field to numerically calculate ALP-photon conversion probabilities to predict the CAB-generated soft X-ray flux in these clusters. The simulated magnetic fields include models with non-standard (i.e. not turbulent Kolmogorov) power spectra, the index of the spectrum changes from cluster to cluster and even within the cluster A2255. We compare this flux to ROSAT PSPC observations of the three clusters, and use these observations to constrain the CAB parameter space. Assuming these non-standard magnetic field power spectra are valid, we find the CAB can reproduce the magnitude of the observed excess in A2199 and A2255 for the same CAB parameters that match the observed soft excess in the Coma cluster. We also find good fit to the morphology of the excesses in these clusters. Simulation of CAB conversion in the cluster A665 is in mild tension with the other clusters due to producing a small but observable excess at large radii where none is observed. This tension is alleviated considering the uncertainty on predicting the count rate in the ROSAT detector, and on the systematics affecting the magnetic field determination. Overall we find good agreement between the CAB parameters for the four clusters studied so far.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

CMB anisotropies generated by a stochastic background of primordial magnetic fields with non-zero helicity

We consider the impact of a stochastic background of primordial magnetic fields with non-vanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the TB and EB cross-correlation in the CMB pattern. We finally show the impact of including the helical term on the power spectra of CMB anisotropies up to multipoles with ℓ ∼ O(10{sup 3})

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Late time solution for interacting scalar in accelerating spaces

We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter ε. We show that, if the scalar potential is scale invariant (which is the case when scalar contains quartic self-interaction and couples non-minimally to gravity), the late-time solution on accelerating FLRW spaces can be described by a probability distribution function (PDF) ρ which is a function of φ/H only, where φ=φ( x-vector ) is the scalar field and H=H(t) denotes the Hubble parameter. We give explicit late-time solutions for ρarrow ρ{sub ∞}(φ/H), and thereby find the order ε corrections to the Starobinsky-Yokoyama result. This PDF can then be used to calculate e.g. various n-point functions of the (self-interacting) scalar field, which are valid at late times in arbitrary accelerating space-times with ε= constant.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Precision measurement of the local bias of dark matter halos

We present accurate measurements of the linear, quadratic, and cubic local bias of dark matter halos, using curved 'separate universe' N-body simulations which effectively incorporate an infinite-wavelength overdensity. This can be seen as an exact implementation of the peak-background split argument. We compare the results with the linear and quadratic bias measured from the halo-matter power spectrum and bispectrum, and find good agreement. On the other hand, the standard peak-background split applied to the Sheth and Tormen (1999) and Tinker et al. (2008) halo mass functions matches the measured linear bias parameter only at the level of 10%. The prediction from the excursion set-peaks approach performs much better, which can be attributed to the stochastic moving barrier employed in the excursion set-peaks prediction. We also provide convenient fitting formulas for the nonlinear bias parameters b{sub 2}(b{sub 1}) and b{sub 3}(b{sub 1}), which work well over a range of redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Renormalizing a viscous fluid model for large scale structure formation

Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher order vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

From wires to cosmology

We provide a statistical framework for characterizing stochastic particle production in the early universe via a precise correspondence to current conduction in wires with impurities. Our approach is particularly useful when the microphysics is uncertain and the dynamics are complex, but only coarse-grained information is of interest. We study scenarios with multiple interacting fields and derive the evolution of the particle occupation numbers from a Fokker-Planck equation. At late times, the typical occupation numbers grow exponentially which is the analog of Anderson localization for disordered wires. Some statistical features of the occupation numbers show hints of universality in the limit of a large number of interactions and/or a large number of fields. For test cases, excellent agreement is found between our analytic results and numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

On the reach of perturbative methods for dark matter density fields

We study the mapping from Lagrangian to Eulerian space in the context of the Effective Field Theory (EFT) of Large Scale Structure. We compute Lagrangian displacements with Lagrangian Perturbation Theory (LPT) and perform the full non-perturbative transformation from displacement to density. When expanded up to a given order, this transformation reproduces the standard Eulerian Perturbation Theory (SPT) at the same order. However, the full transformation from displacement to density also includes higher order terms. These terms explicitly resum long wavelength motions, thus making the resulting density field better correlated with the true non-linear density field. As a result, the regime of validity of this approach is expected to extend that of the Eulerian EFT, and match that of the IR-resummed Eulerian EFT. This approach thus effectively enables a test of the IR-resummed EFT at the field level. We estimate the size of stochastic, non-perturbative contributions to the matter density power spectrum. We find that in our highest order calculation, at redshift z = 0 the power spectrum of the density field is reproduced with an accuracy of 1% (10%) up to k = 0.25 hMpc{sup −1} (k = 0.46 hMpc{sup −1}). We believe that the dominant source of the remaining error is the stochastic contribution. Unfortunately, on these scales the stochastic term does not yet scale as k{sup 4} as it does in the very low k regime. Thus, modeling this contribution might be challenging.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

On the reach of perturbative descriptions for dark matter displacement fields

We study Lagrangian Perturbation Theory (LPT) and its regularization in the Effective Field Theory (EFT) approach. We evaluate the LPT displacement with the same phases as a corresponding N-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra. We reliably detect a non-vanishing leading order EFT coefficient and a stochastic displacement term, uncorrelated with the LPT terms. This stochastic term is expected in the EFT framework, and, to the best of our understanding, is not an artifact of numerical errors or transients in our simulations. This term constitutes a limit to the accuracy of perturbative descriptions of the displacement field and its phases, corresponding to a 1% error on the non-linear power spectrum at k = 0.2 h{sup −1}Mpc at z = 0. Predicting the displacement power spectrum to higher accuracy or larger wavenumbers thus requires a model for the stochastic displacement.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Quantum decoherence during inflation from gravitational nonlinearities

We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation ζ due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state Ψ in the Schrödinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorter-wavelength) modes of ζ as an environment. We show that inflation produces phase oscillations in the wave functional Ψ[ζ(x)], which suppress off-diagonal components of the reduced density matrix, leaving a diagonal mixture of different classical configurations. Gravitational nonlinearities thus provide a minimal mechanism for generating classical stochastic perturbations from inflation. We identify the time when decoherence occurs, which is delayed after horizon crossing due to the weak coupling, and find that Hubble-scale modes act as the decohering environment. We also comment on the observational relevance of decoherence and its relation to the squeezing of the quantum state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗