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DOE OSTI2026

Large-scale white noise and cosmology

The generation of white noise on large scales is a generic property of the dynamics of physical systems described by local nonlinear partial differential equations. Nonlinearities prevent the small-scale dynamics from being erased by smoothing. Unresolved small-scale dynamics act as an uncorrelated (white or Poissonian) noise (seemingly stochastic but actually deterministic) contribution to large-scale dynamics. This white noise exists even when the dynamics is very nearly linear. In cases where the power spectrum is sub-Poissonian on large scales, this noise will dominate on the largest scale power no matter the amplitude of the inhomogeneities. Such is the case in the standard model of cosmology, where the primordial density power spectrum is expected to have an almost Harrison-Zel’dovich, P [ k ] ∼ k , spectrum on a much broader range of scales than can be observed. Even though linear gravitational evolution dominates nonlinear corrections by a factor of ∼ 10 5 , the nonobservation of white noise on the Hubble scale precludes the extrapolation of this power law below the comoving 1 pc scale. More generally, observation or nonobservation of large-scale white noise provides a powerful probe of the Universe on very small scales in the early Universe. Gravitational radiation, phase transitions, vorticity, and running of the spectral index are all phenomena that can be probed with large-scale white noise. Large-scale white noise is a nonoptional feature of all cosmological models but one which has not heretofore been appreciated.

Barenboim, Gabriela [Valencia U., IFIC; Valencia U↗

DOE OSTI2026

Constraints on Large-Scale White Noise in the Cosmic Density Field

We present observational constraints on large-scale white noise (LSWN) in the cosmic density field, a phenomenon predicted to arise from non-linear mode coupling during cosmological evolution. Building on the theoretical framework of Paper I, where we demonstrated that non-linearities inevitably redistribute power from small to large scales through mode mixing, we confront these predictions with current cosmological data. We modify the CLASS Boltzmann code to incorporate a white noise component $k_\mathrm{BH}/k$ in the primordial power spectrum and perform parameter estimation using current cosmological data. The non-detection of excess power on the largest observable scales places stringent upper bounds: $k_\mathrm{BH} \leq 1.80 \times 10^{-13}~\mathrm{Mpc}^{-1}$ at 99% confidence. These constraints imply the primordial power spectrum must deviate from perfect scale invariance on small scales, either through a cutoff at $k_{\mathrm{cut}} \lesssim 3~\mathrm{pc}^{-1}$ or through running of the spectral index with $α_s \lesssim -0.015$. Our results demonstrate that LSWN provides a powerful probe of the primordial spectrum at scales orders of magnitude smaller than directly observable, offering unique constraints on early-universe physics.

Barenboim, Gabriela [Valencia U., IFIC; Valencia U↗

DOE OSTI2018

The Small-Mass Limit and White-Noise Limit of an Infinite Dimensional Generalized Langevin Equation

We study asymptotic properties of the Generalized Langevin Equation (GLE) in the presence of a wide class of external potential wells with a power-law decay memory kernel. When the memory can be expressed as a sum of exponentials, a class of Markovian systems in infinite-dimensional spaces is used to represent the GLE. The solutions are shown to converge in probability in the small-mass limit and the white-noise limit to appropriate systems under minimal assumptions, of which no global Lipschitz condition is required on the potentials. With further assumptions about space regularity and potentials, we obtain L{sup 1} convergence in the white-noise limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗

DOE OSTI2026

Gravitational Waves as a Source of Large-Scale White Noise: New Constraints

A stochastic gravitational wave (GW) background sources a shear in the flow of cosmic fluid which, through non-linear mode coupling, generates large-scale white noise (LSWN) in the kurvature density field. Building on the LSWN framework of our previous work, we derive the amplitude of this GW-induced LSWN and translate the observational non-detection of LSWN into bounds on the production redshift and density of gravity waves. In particular, a minimal constraint on gravity waves with $z=0$ density parameter $Ω_\mathrm{GW0}^*$ in frequency band $f_*$ generated at redshift $z_*$ must satisfy ${z_*}^2\,Ω_\mathrm{GW0}^*<5\times10^7\,(f_*/\mathrm{nHz})^{3/2}$. This, for example, precludes the gravity waves recently detected by pulsar timing arrays \cite{NANOGrav:2023hvm} from being present before $z_*\sim10^8$, long after the quark hadron phase transition. While orders of magnitude stronger than other constraints on gravity waves, this is a minimal LSWN constraint as realistic modeling of early universe gravity wave production, including the granularity of the gravity-wave sources and the LSWN produced by the associated acoustic waves would probably tighten this constraint by orders of magnitude.

Barenboim, Gabriela [Valencia U., IFIC; Valencia U↗

DOE OSTI2019

The Entropy Maximum in Scale-Invariant Processes with 1/f {sup α} Power Spectrum: the Effect of White Noise Anisotropy

Extreme fluctuations are simulated by a system of nonlinear stochastic equations describing the interacting phase transitions. Random 1/f {sup α} processes are formed under the action of anisotropic white noise with α-dependence of the power spectra on frequency and exponent α ranging from 0.7 to 1.7. It is shown that fluctuations with 1/f {sup α} power spectra in the studied range of α correspond to the entropy maximum, which indicates the stability of such processes at different values of exponent α.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Optimal white-noise stochastic forcing for linear models of turbulent channel flow

In the present study an optimisation problem is formulated to determine the forcing of an eddy-viscosity-based linearised Navier–Stokes model in channel flow at $Re_\tau \approx 5200$ ( $Re_\tau$ is the friction Reynolds number), where the forcing is white-in-time and spatially decorrelated. The objective functional is prescribed such that the forcing drives a response to best match a set of velocity spectra from direct numerical simulation (DNS), as well as remaining sufficiently smooth. Strong quantitative agreement is obtained between the velocity spectra from the linear model with optimal forcing and from DNS, but only qualitative agreement between the Reynolds shear stress co-spectra from the model and DNS. The forcing spectra exhibit a level of self-similarity, associated with the primary peak in the velocity spectra, but they also reveal a non-negligible amount of energy spent in phenomenologically mimicking the non-self-similar part of the velocity spectra associated with energy cascade. By exploiting linearity, the effect of the individual forcing components is assessed and the contributions from the Orr mechanism and the lift-up effect are also identified. Finally, the effect of the strength of the eddy viscosity on the optimisation performance is investigated. The inclusion of the eddy viscosity diffusion operator is shown to be essential in modelling of the near-wall features, while still allowing the forcing of the self-similar primary peak. In particular, reducing the strength of the eddy viscosity results in a considerable increase in the near-wall forcing of wall-parallel components.

Mechanics↗

DOE OSTI2018

Achievable noise performance of spectroscopic prototype DEPFET detectors

A new generation of spectroscopic X-ray DEPFET detectors has been produced here in the course of the detector development for the Wide Field Imager (WFI) of Athena. These devices served to perform a detailed analysis of the noise composition, which was enabled by the development of appropriate test algorithms. A result of the analysis is the distinction of different components, which sum up to the total noise. In particular the contribution of shot noise, white noise and 1/f noise to the readout noise is determined as well as the signal noise caused by the generation of charge carriers. The resulting parametrization enables the adaptation and optimization of operation modes to given purposes. The studied prototype detectors included 64×64 pixels with a linear gate design and provided an excellent noise, below 1.6 e - ENC at a readout time faster than 10 μs/pixel and a temperature of -80 °C in rolling-shutter operation. This performance is enabled by an extended signal integration time. A further noise reduction is prevented by the signal noise, caused by charge carrier generation. In order to demonstrate the low noise properties of the DEPFET transistor, the measurement conditions were adapted and a noise of 0.95 e - ENC was measured at the expense of the sensor size—by operating only parts of the sensor in window mode—and dynamic range—by using the Al Kα line at about 1.49 keV for calibration.

47 OTHER INSTRUMENTATION↗

DOE OSTI2019

A Domain Decomposition Model Reduction Method for Linear Convection-Diffusion Equations with Random Coefficients

We developed a domain decomposition model reduction method for linear steady- state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equation with random diffusivity and the convection-dominated transport equation with random velocity. We investigated two types of random fields, i.e., colored noises and discrete white noises, both of which can lead to high-dimensional parametric dependence in practice. The motivation is to exploit domain decomposition to reduce the parametric dimension of local problems in subdomains, such that an entire parametric map can be approximated with a small number of expensive partial differential equation (PDE) simulations. The new method combines domain decomposition with model reduction and sparse polynomial approximation, so as to simultaneously handle the high dimensionality and irregular behavior of the PDEs under consideration. Here, the advantages of our method lie in three aspects: (i) online-offline decomposition, i.e., the online cost is independent of the size of the triangle mesh; (ii) sparse approximation of operators involving nonaffine high-dimensional random fields; (iii) an effective strategy to capture irregular behaviors, e.g., sharp transitions of the PDE solutions. Two numerical examples are provided to demonstrate the advantageous performance of our method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Here, we report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

42 ENGINEERING↗

DOE OSTI2018

Fractional Ornstein–Uhlenbeck noise

Highlights: •Calculation of the correlation function for the fractional Ornstein–Uhlenbeck noise. •Calculation of the mean energy of the harmonic oscillator driven by the fractional Ornstein–Uhlenbeck noise. •The model can be applied to the RLC circuit driven by a supercapacitor with the white noise. -- Abstract: Fractional Ornstein–Uhlenbeck noise is considered and investigated. The fractional Ornstein–Uhlenbeck noise may be linked with a supercapacitor driven by the white noise, and its correlation function for the stationary state shows monotonic and oscillatory decays. In the case of the oscillatory behavior the correlation function presents behaviors similar to those of the harmonic noise (harmonic oscillator driven by the white noise). For application, the Langevin equation with the harmonic potential driven by the fractional Ornstein–Uhlenbeck noise is considered; the first two moments and mean energy are investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Red Noise–based False Alarm Thresholds for Astrophysical Periodograms via Whittle’s Approximation to the Likelihood

Astronomers who search for periodic signals using Lomb–Scargle periodograms rely on false alarm level (FAL) estimates to identify statistically significant peaks. Although FALs are often calculated from white noise models, many astronomical time series suffer from red noise. Prewhitening is a statistical technique in which a continuum model is subtracted from the log power spectrum estimate, after which the observer can proceed with a white-noise treatment. Here we present a prewhitening-based method of calculating frequency-dependent FALs. We fit power laws and autoregressive models of order 1 to each Lomb–Scargle periodogram by minimizing the Whittle approximation to the negative log-likelihood (NLL), then calculate FALs based on the best-fit model power spectrum. Our technique is a novel extension of the Whittle NLL to datasets with uneven time sampling. We demonstrate FAL calculations using observations of α Cen B, GJ 581, HD 192310, synthetic data from the radial velocity (RV) fitting challenge, and Kepler observations of a differential rotator. The Kepler data analysis shows that only true rotation signals are detected by red noise FALs, while white noise FALs suggest all spurious peaks in the low-frequency range are significant. A high-frequency sinusoid injected into α Cen B logR$'$ HK observations exceeds the 1% red noise FAL despite having only 8.9% of the power of the dominant rotation signal. In a periodogram of HD 192310 RVs, peaks associated with differential rotation and planets are detected against the 5% red noise FAL without iterative model fitting or subtraction. The software for calculating red noise–based FALs is available on GitHub.

Astrostatistics (1882)↗

DOE OSTI2024

Binary pseudo-random array for calibration of interferometers with transmission spheres and cylinders

Binary pseudo-random array (BPRA) “white noise” artifacts are highly effective for characterizing the instrument transfer function (ITF) of surface topography metrology tools and wavefront measurement instruments. These BPRA artifacts feature all spatial frequencies within the instrument bandpass equally, resulting in a power spectral density with a white-noise-like character. This characteristic allows for direct ITF determination with uniform sensitivity across the entire spatial frequency range. We have developed a novel BPRA calibration standard that combines the diffractive pattern of a reflection computer-generated hologram (CGH) with the white noise generating BPRA pattern. By integrating these technologies using the same lithographic techniques, the resulting calibration sample enables ITF characterization of a Fizeau interferometer with a transmission sphere, or any nulling optic.

Munechika, K↗

DOE OSTI2023

Noise Optimization for MKIDs with Different Design Geometries and Material Selections

The separation and optimization of noise components is critical to microwave-kinetic inductance detector (MKID) development. We analyze the effect of several changes to the lumped-element inductor and interdigitated capacitor geometry on the noise performance of a series of MKIDs intended for millimeter-wavelength experiments. We extract the contributions from two-level system noise in the dielectric layer, the generation-recombination noise intrinsic to the superconducting thin-film, and system white noise from each detector noise power spectrum and characterize how these noise components depend on detector geometry, material, and measurement conditions such as driving power and temperature. We observe a reduction in the amplitude of two-level system noise with both an elevated sample temperature and an increased gap between the fingers within the interdigitated capacitors for both aluminum and niobium detectors. We also verify the expected reduction of the generation-recombination noise and associated quasiparticle lifetime with reduced inductor volume. This study also iterates over different materials, including aluminum, niobium, and aluminum manganese, and compares the results with an underlying physical model.

generation-recombination noise↗

DOE OSTI2022

Stochastic hydrodynamics and hydro-kinetics: Similarities and differences

The hydro-kinetic formalism has been used as a complementary approach to solving the Stochastic Differential Equations (SDE) corresponding to noisy hydrodynamics. The hydro-kinetic formalism consists of a deterministic set of relaxation type equations that tracks the evolution of 2-point correlation functions of stochastic hydrodynamic quantities. Hence they are comparatively easier to solve than the SDEs, which are computationally intensive and need to deal with arbitrarily large gradients. This work compares the two approaches for the propagation and diffusion of conserved charge fluctuations in the Bjorken hydrodynamic model. For white noise, the two approaches agree. For colored Catteneo noise, which is causal, the two approaches diverge. This is because white noise only induces two-point correlations, while Catteneo noise also induces higher-order correlations. Furthermore, this difference is quantified from the effects of causal evolution and influence from higher-order correlations induced by the Catteneo noise.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

On-Sky Performance of the SPT-3G Frequency-Domain Multiplexed Readout

Frequency-domain multiplexing (fMux) is an established technique for the readout of large arrays of transition-edge sensor (TES) bolometers. Each TES in a multiplexing module has a unique AC voltage bias that is selected by a resonant filter. This scheme provides for the operation and readout of multiple bolometers on a single pair of wires, reducing thermal loading onto sub-Kelvin stages. The current receiver on the South Pole Telescope, SPT-3G, uses a 68x fMux system to operate its large-format camera of ~16,000 TES bolometers. We present here the successful implementation and performance of the SPT-3G readout as measured on-sky. Characterization of the noise reveals a median pair-differenced 1/f knee frequency of 33 mHz, indicating that low-frequency noise in the readout will not limit SPT-3G’s measurements of sky power on large angular scales. Measurements further show that the median readout white noise level in each of the SPT-3G observing bands is below the expectation for photon noise, demonstrating that SPT-3G is operating in the photon-noise-dominated regime.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

A microwave SQUID multiplexer optimized for bolometric applications

A microwave SQUID (superconducting quantum interference device) has been optimized for reading out large arrays of superconducting transition-edge sensor (TES) bolometers. We present the scalable cryogenic multiplexer chip design that may be used to construct an 1820-channel multiplexer for the 4-8 GHz rf band. The key metrics of yield, sensitivity, and crosstalk are determined through measurements of 455 readout channels, which span 4-5 GHz. The median white-noise level is 45 pA/ $\sqrt{Hz}$, evaluated at 2 Hz, with a 1/f knee ≤ 20 mHz after common-mode subtraction. The white-noise level decreases the sensitivity of a TES bolometer optimized for detection of the cosmic microwave background at 150 GHz by only 3%. The measured crosstalk between any channel pair is ≤ 0.3%.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Simulations of axion minihalos

The axion, motivated as a solution to the strong CP problem, is also a viable dark matter candidate. The axion field takes random values in causally disconnected regions if the symmetry breaking that establishes the particle occurs after inflation, leading to white-noise density fluctuations at low wave numbers and forming dense minihalos with sub-planetary masses subsequently. There have been two recent proposals that appear capable of testing this scenario, namely using pulsar timing arrays and studying cosmological microlensing caustics. Motivated by these proposals, we use N-body simulations to study the formation of substructures from white-noise density fluctuations. The density profiles of our relaxed axion minihalos can be described by the Navarro–Frenk–White profile, and the minihalos’ concentration number agrees well with a simple, physically-motivated model. We develop a semi-analytic formula to fit the mass function from our simulation, which agrees broadly at different redshifts and only differs at factor of two level from classic halo mass functions. This analytic mass function allows us to consider uncertainties in the post-inflation axion scenario, as well as extrapolate our high-redshift simulations results to the present. Our work estimates the present-day abundance of axion substructures, as is necessary for predicting their effect on cosmological microlensing caustics and pulsar timing. Our calculations suggest that if pulsar timing and microlensing probes can reach recent sensitivity forecasts, they may be sensitive to the post-inflation axion dark matter scenario, even when accounting for uncertainties pertaining to axion strings. For pulsar timing, the most significant caveat is whether axion minihalos are disrupted by stars, which our estimates show is mildly important at the most relevant masses. In conclusion, as our gravitational simulations are scale invariant, the results can be extended to models where the dark matter is comprised of other axion-like particles and even clusters of primordial black holes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗