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DOE OSTI2022

Priors on red galaxy stochasticity from hybrid effective field theory

ABSTRACT We investigate the stochastic properties of typical red galaxy samples in a controlled numerical environment. We use halo occupation distribution (HOD) modelling to create mock realizations of three separate bright red galaxy samples consistent with data sets used for clustering and lensing analyses in modern galaxy surveys. Second-order Hybrid Effective Field Theory (HEFT) is used as a field-level forward model to describe the full statistical distribution of these tracer samples, and their stochastic power spectra are directly measured and compared to the Poisson shot-noise prediction. While all of the galaxy samples we consider are hosted within haloes with sub-Poisson stochasticity, we observe that the galaxy samples themselves possess stochasticities that range from sub-Poisson to super-Poisson, in agreement with predictions from the halo model. As an application of our methodology, we place priors on the expected degree of non-Poisson stochasticity in cosmological analyses using such samples. We expect these priors will be useful in reducing the complexity of the full parameter space for future analyses using second-order Lagrangian bias models. More generally, the techniques outlined here present the first application of HEFT methods to characterize models of the galaxy–halo connection at the field level, revealing new connections between once-disparate modelling frameworks.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Non-linear stochastic growth rates and redshift space distortions

The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc -1 to 25 per cent at k ~ 0.45 h Mpc -1 at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 10 12 M ⊙ h -1 , compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -f LT δ, where f LT is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc -1 . Furthermore, the stochasticity in the θ – δ relation is not so simply described by 2LPT, and we discuss its impact on measurements of f LT from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of f LT extracted using models which assume a linear, deterministic expression.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Stochastic properties of ultralight scalar field gradients

Ultralight axion-like particles are well-motivated dark matter candidates that are the target of numerous direct detection efforts. In the vicinity of the Solar System, such particles can be treated as oscillating scalar fields. The velocity dispersion of the Milky Way determines a coherence time of about 10 6 oscillations, beyond which the amplitude of the axion field fluctuates stochastically. Any analysis of data from an axion direct detection experiment must carefully account for this stochastic behavior to properly interpret the results. This is especially true for experiments sensitive to the gradient of the axion field that are unable to collect data for many coherence times. Indeed, the direction, in addition to the amplitude, of the axion field gradient fluctuates stochastically. We present the first complete stochastic treatment for the gradient of the axion field, including multiple computationally efficient methods for performing likelihood-based data analysis, which can be applied to any axion signal, regardless of coherence time. Additionally, we demonstrate that ignoring the stochastic behavior of the gradient of the axion field can potentially result in failure to discover a true axion signal

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Stochastic Assembly Leads to Alternative Communities with Distinct Functions in a Bioreactor Microbial Community

The processes and mechanisms of community assembly and its relationships to community functioning are central issues in ecology. Both deterministic and stochastic factors play important roles in shaping community composition and structure, but the connection between community assembly and ecosystem functioning remains elusive, especially in microbial communities. Here, we used microbial electrolysis cell reactors as a model system to examine the roles of stochastic assembly in determining microbial community structure and functions. Under identical environmental conditions with the same source community, ecological drift (i.e., initial stochastic colonization) and subsequent biotic interactions created dramatically different communities with little overlap among 14 identical reactors, indicating that stochastic assembly played dominant roles in determining microbial community structure. Neutral community modeling analysis revealed that deterministic factors also played significant roles in shaping microbial community structure in these reactors. Most importantly, the newly formed communities differed substantially in community functions (e.g., H 2 production), which showed strong linkages to community structure. This study is the first to demonstrate that stochastic assembly plays a dominant role in determining not only community structure but also ecosystem functions. Elucidating the links among community assembly, biodiversity, and ecosystem functioning is critical to understanding ecosystem functioning, biodiversity preservation, and ecosystem management.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2017

Stochastic Parameterization: Toward a New View of Weather and Climate Models

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Impacts of Stochastic Mixing in Idealized Convection-Permitting Simulations of Squall Lines

This study investigates impacts of altering subgrid-scale mixing in “convection-permitting” kilometer-scale horizontal-grid-spacing (Δ h ) simulations by applying either constant or stochastic multiplicative factors to the horizontal mixing coefficients within the Weather Research and Forecasting Model. In quasi-idealized 1-km Δ h simulations of two observationally based squall-line cases, constant enhanced mixing produces larger updraft cores that are more dilute at upper levels, weakens the cold pool, rear-inflow jet, and front-to-rear flow of the squall line, and degrades the model’s effective resolution. Reducing mixing by a constant multiplicative factor has the opposite effect on all metrics. Completely turning off parameterized horizontal mixing produces bulk updraft statistics and squall-line mesoscale structure closest to an LES “benchmark” among all 1-km simulations, although the updraft cores are too undilute. The stochastic mixing scheme, which applies a multiplicative factor to the mixing coefficients that varies stochastically in time and space, is employed at 0.5-, 1-, and 2-km Δ h . It generally reduces midlevel vertical velocities and enhances upper-level vertical velocities compared to simulations using the standard mixing scheme, with more substantial impacts at 1- and 2-km Δ h compared to 0.5-km Δ h . Further, the stochastic scheme also increases updraft dilution to better agree with the LES for one case, but has less impact on the other case. Stochastic mixing acts to weaken the cold pool but without a significant impact on squall-line propagation. It also does not affect the model’s overall effective resolution unlike applying constant multiplicative factors to the mixing coefficients.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2012

Application of Stochastic Radiative Transfer Theory to the ARM Cloud-Radiative Parameterization Problem

This project had two primary goals: (1) development of stochastic radiative transfer as a parameterization that could be employed in an AGCM environment, and (2) exploration of the stochastic approach as a means for representing shortwave radiative transfer through mixed-phase layer clouds. To achieve these goals, climatology of cloud properties was developed at the ARM CART sites, an analysis of the performance of the stochastic approach was performed, a simple stochastic cloud-radiation parameterization for an AGCM was developed and tested, a statistical description of Arctic mixed phase clouds was developed and the appropriateness of stochastic approach for representing radiative transfer through mixed-phase clouds was assessed. Significant progress has been made in all of these areas and is detailed in the final report.

58 GEOSCIENCES↗

DOE OSTI2018

Summer term 2018 work with IMC radiative transport in binary stochastic media

In the quest for new and improved methods to solve thermal radiation transport in stochastic media, this summer project was to characterize radation transport in a deterministic lattice problem that represents a real, binary stochastic media. A representative geometry for a binary stochastic media consisting of a cube of a high volume fraction media containing constant-diameter non-overlappying spheres randomly distributed within was run previously. Previous thermal radiation wave problems in binary stochastic media displayed three characteristic thermal energy deposition wavefronts in the following order, front of the spheres, bulk material, and the backs of the spheres. Several physical aspects of the representative geometry for a stochastic binary media using an optically thin background with optically thick spheres were analyzed. This analysis includes wave speed propagation using a one dimensional diffusion approximation, energy fluence transmission, and material energy deposition. The approaches to analysis included representing one sphere of the high opacity material in a diffusive background of the low opacity material, as well as repeating spheres in a column con guration with reflective boundary conditions to approximate a lattice. Additionally, both atomic mix and Levermore-Pomraning homogenization schemes were compared against the representative cube geometry as well as the sphere column lattice geometry. The wave speed analysis with a one dimensional Marshak diffusion wave was largely ineffective at determining an effective opacity value to which a problem could be homogenized, likely due to low mean free path resolution within the problem. However, the sphere column lattice geometry showed promising results for approximating the energy fluence transmitted through the problem domain. One concern with the sphere column lattice geometry indicated the high forward-bias effect of fluence reaching the problem boundary due to streaming paths around the spheres in the case of small mean free path resolution of the background material.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Developing and Testing a Novel Stochastic Ice Microphysics Parameterization for Cloud and Climate Models Using ARM Field Campaign Data (Final Progress Report)

The major goals of this project were: 1) to use field campaign measurements from DOE’s Atmospheric Radiation Measurement (ARM) program to characterize variability of important parameters describing properties of ice particles in the atmosphere; 2) based on this observational analysis, to develop a parameterization scheme for weather and climate models that stochastically varies these parameters, and implement the new scheme into a weather model called the Weather Research and Forecasting model (WRF); 3) to use WRF coupled with the new stochastic scheme to simulate ARM field campaign thunderstorm cases and analyze how accounting for this parameter variability affects the model simulations. This work was performed jointly between the National Center for Atmospheric Research, University of Oklahoma, and University of Utah. To accomplish these goals, we extended an approach previously developed to characterize the variability in the size distribution of ice particles to parameters that are explicitly represented in models (i.e., relationships between ice particle mass and size, and between particle fall velocity and size). Our project was, to our knowledge, the first to apply observationally-constrained estimates of this parameter variability describing mass-size and fall velocity-size in a modeling framework. Our results showed efficacy of the approach, evaluated using ARM observations. Similarly, to our knowledge, work in this project was the first to propose and evaluate in detail a stochastic approach for unresolved turbulent mixing in high-resolution model simulations against detailed, benchmark large eddy simulations and ARM observations. Results showed some promising behavior, particularly with increased mixing and dilution of air in thunderstorm cores with surrounding environmental air, bringing the stochastic simulations closer to the benchmark large eddy simulations; however, results were somewhat degraded using stochastic mixing compared to observations from the AMIE/DYNAMO field campaign. This project also further refined and applied a modeling methodology called “piggybacking” that can robustly separate dynamical and thermodynamic impacts of model changes, and comparison studies of different models based on cases developed from ARM observations. Finally, this project directly supported three graduate students who completed their PhDs as well as a postdoctoral research fellow.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code

Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Stochastics and EUV Patterning in the 1x-nm Regime

The problem of stochastics in photoresist patterning is gaining increased attention. Understanding this problem requires new modeling methods. Here we describe the use of the Multivariate Poisson Propagation Model (MPPM) to study the relative importance of a variety of stochastic terms in both chemically amplified and non-chemically amplified resists. The results show that for the chemically amplified case, materials stochastic effects are on par with photon stochastics effects. The model is used to study both line-width roughness (LWR) impacts as well as contact size variations (CDU). As one might expect, contact CDU follows the same trends as LWR, but places even more sever constraints on the stochastic terms when considering the same feature size. Noting the contact patterning challenge, we also describe a phase-shift mask patterning method enabling the photon effect to be greatly reduced. At equivalent CDU, we demonstrate an effective 7x reduction in required source dose when patterning 25-nm half pitch contacts.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES). Stochastic characteristics of these LES waked wind velocity field, including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR) with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study’s overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.

17 WIND ENERGY↗

NASA NTRS1978

Stochastic partial differential equations in turbulence related problems

The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.

Chow, P.-L.↗

NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗

NASA NTRS2010

Vestibular Stochastic Resonance as a Method to Improve Balance Function: Optimization of Stimulus Characteristics

Stochastic resonance (SR) is a mechanism by which noise can assist and enhance the response of neural systems to relevant sensory signals. Application of imperceptible SR noise coupled with sensory input through the proprioceptive, visual, or vestibular sensory systems has been shown to improve motor function. Specifically, studies have shown that that vestibular electrical stimulation by imperceptible stochastic noise, when applied to normal young and elderly subjects, significantly improved their ocular stabilization reflexes in response to whole-body tilt as well as balance performance during postural disturbances. The goal of this study was to optimize the characteristics of the stochastic vestibular signals for balance performance during standing on an unstable surface. Subjects performed a standardized balance task of standing on a block of 10 cm thick medium density foam with their eyes closed for a total of 40 seconds. Stochastic electrical stimulation was applied to the vestibular system through electrodes placed over the mastoid process behind the ears during the last 20 seconds of the test period. A custom built constant current stimulator with subject isolation delivered the stimulus. Stimulation signals were generated with frequencies in the bandwidth of 1-2 Hz and 0.01-30 Hz. Amplitude of the signals were varied in the range of 0- +/-700 micro amperes with the RMS of the signal increased by 30 micro amperes for each 100 micro amperes increase in the current range. Balance performance was measured using a force plate under the foam block and inertial motion sensors placed on the torso and head segments. Preliminary results indicate that balance performance is improved in the range of 10-25% compared to no stimulation conditions. Subjects improved their performance consistently across the blocks of stimulation. Further the signal amplitude at which the performance was maximized was different in the two frequency ranges. Optimization of the frequency and amplitude of the signal characteristics of the stochastic noise signals on maximizing balance performance will have a significant impact in its development as a unique system to aid recovery of function in astronauts after long duration space flight or for people with balance disorders.

Mulavara, Ajitkumar↗

NASA NTRS2010

Stimulus Characteristics for Vestibular Stochastic Resonance to Improve Balance Function

Stochastic resonance (SR) is a mechanism by which noise can enhance the response of neural systems to relevant sensory signals. Studies have shown that imperceptible stochastic vestibular electrical stimulation, when applied to normal young and elderly subjects, significantly improved their ocular stabilization reflexes in response to whole-body tilt as well as balance performance during postural disturbances. The goal of this study was to optimize the amplitude characteristics of the stochastic vestibular signals for balance performance during standing on an unstable surface. Subjects performed a standard balance task of standing on a block of foam with their eyes closed. Bipolar stochastic electrical stimulation was applied to the vestibular system using constant current stimulation through electrodes placed over the mastoid process behind the ears. Amplitude of the signals varied in the range of 0-700 microamperes. Balance performance was measured using a force plate under the foam block, and inertial motion sensors were placed on the torso and head. Balance performance with stimulation was significantly greater (10%-25%) than with no stimulation. The signal amplitude at which performance was maximized was in the range of 100-300 microamperes. Optimization of the amplitude of the stochastic signals for maximizing balance performance will have a significant impact on development of vestibular SR as a unique system to aid recovery of function in astronauts after long-duration space flight or in patients with balance disorders.

Mulavara, Ajitkumar↗

NASA NTRS2012

HyDE Framework for Stochastic and Hybrid Model-Based Diagnosis

Hybrid Diagnosis Engine (HyDE) is a general framework for stochastic and hybrid model-based diagnosis that offers flexibility to the diagnosis application designer. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. Several alternative algorithms are available for the various steps in diagnostic reasoning. This approach is extensible, with support for the addition of new modeling paradigms as well as diagnostic reasoning algorithms for existing or new modeling paradigms. HyDE is a general framework for stochastic hybrid model-based diagnosis of discrete faults; that is, spontaneous changes in operating modes of components. HyDE combines ideas from consistency-based and stochastic approaches to model- based diagnosis using discrete and continuous models to create a flexible and extensible architecture for stochastic and hybrid diagnosis. HyDE supports the use of multiple paradigms and is extensible to support new paradigms. HyDE generates candidate diagnoses and checks them for consistency with the observations. It uses hybrid models built by the users and sensor data from the system to deduce the state of the system over time, including changes in state indicative of faults. At each time step when observations are available, HyDE checks each existing candidate for continued consistency with the new observations. If the candidate is consistent, it continues to remain in the candidate set. If it is not consistent, then the information about the inconsistency is used to generate successor candidates while discarding the candidate that was inconsistent. The models used by HyDE are similar to simulation models. They describe the expected behavior of the system under nominal and fault conditions. The model can be constructed in modular and hierarchical fashion by building component/subsystem models (which may themselves contain component/ subsystem models) and linking them through shared variables/parameters. The component model is expressed as operating modes of the component and conditions for transitions between these various modes. Faults are modeled as transitions whose conditions for transitions are unknown (and have to be inferred through the reasoning process). Finally, the behavior of the components is expressed as a set of variables/ parameters and relations governing the interaction between the variables. The hybrid nature of the systems being modeled is captured by a combination of the above transitional model and behavioral model. Stochasticity is captured as probabilities associated with transitions (indicating the likelihood of that transition being taken), as well as noise on the sensed variables.

Narasimhan, Sriram↗

NASA NTRS2014

Improving Sensorimotor Function and Adaptation using Stochastic Vestibular Stimulation

Astronauts experience sensorimotor changes during adaption to G-transitions that occur when entering and exiting microgravity. Post space flight, these sensorimotor disturbances can include postural and gait instability, visual performance changes, manual control disruptions, spatial disorientation, and motion sickness, all of which can hinder the operational capabilities of the astronauts. Crewmember safety would be significantly increased if sensorimotor changes brought on by gravitational changes could be mitigated and adaptation could be facilitated. The goal of this research is to investigate and develop the use of electrical stochastic vestibular stimulation (SVS) as a countermeasure to augment sensorimotor function and facilitate adaptation. For this project, SVS will be applied via electrodes on the mastoid processes at imperceptible amplitude levels. We hypothesize that SVS will improve sensorimotor performance through the phenomena of stochastic resonance, which occurs when the response of a nonlinear system to a weak input signal is optimized by the application of a particular nonzero level of noise. In line with the theory of stochastic resonance, a specific optimal level of SVS will be found and tested for each subject [1]. Three experiments are planned to investigate the use of SVS in sensory-dependent tasks and performance. The first experiment will aim to demonstrate stochastic resonance in the vestibular system through perception based motion recognition thresholds obtained using a 6-degree of freedom Stewart platform in the Jenks Vestibular Laboratory at Massachusetts Eye and Ear Infirmary. A range of SVS amplitudes will be applied to each subject and the subjectspecific optimal SVS level will be identified as that which results in the lowest motion recognition threshold, through previously established, well developed methods [2,3,4]. The second experiment will investigate the use of optimal SVS in facilitating sensorimotor adaptation to system disturbances. Subjects will adapt to wearing minifying glasses, resulting in decreased vestibular ocular reflex (VOR) gain. The VOR gain will then be intermittently measured while the subject readapts to normal vision, with and without optimal SVS. We expect that optimal SVS will cause a steepening of the adaptation curve. The third experiment will test the use of optimal SVS in an operationally relevant aerospace task, using the tilt translation sled at NASA Johnson Space Center, a test platform capable of recreating the tilt-gain and tilt-translation illusions associated with landing of a spacecraft post-space flight. In this experiment, a perception based manual control measure will be used to compare performance with and without optimal SVS. We expect performance to improve in this task when optimal SVS is applied. The ultimate goal of this work is to systematically investigate and further understand the potential benefits of stochastic vestibular stimulation in the context of human space flight so that it may be used in the future as a component of a comprehensive countermeasure plan for adaptation to G-transitions.

Galvan, R. C.↗