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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.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems

We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with 10 5 interacting two-level systems. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Superdiffusive heat conduction in semiconductor alloys. II. Truncated Lévy formalism for experimental analysis

Nearly all experimental observations of quasiballistic heat flow are interpreted using Fourier theory with modified thermal conductivity. Detailed Boltzmann transport equation (BTE) analysis, yet, reveals that the quasi-ballistic motion of thermal energy in semiconductor alloys is no longer Brownian but instead exhibits Lévy dynamics with fractal dimension α < 2 . In this work, we present a framework that enables full three-dimensional experimental analysis by retaining all essential physics of the quasiballistic BTE dynamics phenomenologically. A stochastic process with just two fitting parameters describes the transition from pure Lévy superdiffusion as short length and time scales to regular Fourier diffusion. The model provides accurate fits to time domain thermoreflectance raw experimental data over the full modulation frequency range without requiring any “effective” thermal parameters and without any a priori knowledge of microscopic phonon scattering mechanisms. Identified α values for InGaAs and SiGe match ab initio BTE predictions within a few percent. Our results provide experimental evidence of fractal Lévy heat conduction in semiconductor alloys. The formalism additionally indicates that the transient temperature inside the material differs significantly from Fourier theory and can lead to improved thermal characterization of nanoscale devices and material interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Reaction dynamics and in-medium nucleon-nucleon cross section with 12 C+ 1 H at 95 MeV/nucleon

Reaction dynamics and effective in-medium nucleon-nucleon (NN) cross section are studied, using the antisymmetrized molecular dynamics (AMD) model with one of the simplest heavy ion collisions, 12 C+ ⁢1 H. The roles of different stochastic processes are studied, which are installed in the original AMD. One is the diffusion process as a part of the quantum fluctuation originated from the Fermi motion during the time evolution of the wave packets in the mean field (AMD/D). The second is a coalescence treatment for light clusters with A ≤ 8 (AMD/D-COALS). The third is the collision process, installed in AMD with different form of the in-medium NN cross sections. These different processes are examined, using the experimental angular distributions and energy spectra of light charged particles and intermediate mass fragments. The effective in-medium NN cross sections are evaluated from the simulated AMD events and compared with the experimentally extracted values. A good agreement is obtained between the AMD values from the 12 C + 1 H reaction at 95 MeV/nucleon and the experimental results for nuclear matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Jamming and tiling in fragmentation of rectangles

We investigate a stochastic process where a rectangle breaks into smaller rectangles through a series of horizontal and vertical fragmentation events. We focus on the case where both the vertical size and the horizontal size of a rectangle are discrete variables. Because of this constraint, the system reaches a jammed state where all rectangles are sticks, that is, rectangles with minimal width. Sticks are frozen as they cannot break any further. The average number of sticks in the jammed state, S , grows as S ≃ A /√2π ln A with rectangle area A in the large-area limit, and remarkably, this behavior is independent of the aspect ratio. The distribution of stick length has a power-law tail, and further, its moments are characterized by a nonlinear spectrum of scaling exponents. Here, we also study an asymmetric breakage process where vertical and horizontal fragmentation events are realized with different probabilities. In this case, there is a phase transition between a weakly asymmetric phase where the length distribution is independent of system size and a strongly asymmetric phase where this distribution depends on system size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Probabilistic structure of the geodynamo

One of the most intriguing features of Earth's axial magnetic dipole field, well known from the geological record, is its occasional and unpredictable reversal of polarity. Understanding the phenomenon is rendered very difficult by the highly nonlinear nature of the underlying magnetohydrodynamic problem. Numerical simulations of the liquid outer core, where regeneration occurs, are only able to model conditions that are far from Earth-like. On the analytical front, the situation is not much better; basic calculations, such as relating the average rate of reversals to various core parameters, have apparently been intractable. Here, we present a framework for solving such problems. Starting with the magnetic induction equation, we show that by considering its sources to be stochastic processes with fairly general properties, we can derive a differential equation for the joint probability distribution of the dominant toroidal and poloidal modes. This can be simplified to a Fokker-Planck equation and, with the help of an adiabatic approximation, reduced even further to an equation for the dipole amplitude alone. From these equations various quantities related to the magnetic field, including the average reversal rate, field strength, and time to complete a reversal, can be computed as functions of a small number of numerical parameters. As a result, these parameters in turn can be computed from physical considerations or constrained by paleomagnetic, numerical, and experimental data.

58 GEOSCIENCES↗
DOE OSTI2023

Unified, Geometric Framework for Nonequilibrium Protocol Optimization

Controlling thermodynamic cycles to minimize the dissipated heat is a long-standing goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic metric—determined via a linear response approach—can be directly derived from the same objective function that is optimized in the optimal transport problem, thus providing a unified perspective on thermodynamic geometries. As a result, we investigate this unified geometric framework in two model systems and observe that our procedure for optimizing control protocols is robust beyond linear response.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Full Counting Statistics of Charge in Chaotic Many-Body Quantum Systems

We investigate the full counting statistics of charge transport in U(1)-symmetric random unitary circuits. We consider an initial mixed state prepared with a chemical potential imbalance between the left and right halves of the system and study the fluctuations of the charge transferred across the central bond in typical circuits. Using an effective replica statistical mechanics model and a mapping onto an emergent classical stochastic process valid at large on-site Hilbert space dimension, we show that charge transfer fluctuations approach those of the symmetric exclusion process at long times, with subleading t –1/2 quantum corrections. Here, we discuss our results in the context of fluctuating hydrodynamics and macroscopic fluctuation theory of classical nonequilibrium systems and check our predictions against direct matrix-product state calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Coherent Transfer of Lattice Entropy via Extreme Nonlinear Phononics in Metal Halide Perovskites

Entropy transfer in metal halide perovskites, characterized by significant lattice anharmonicity and low stiffness, underlies the remarkable properties observed in their optoelectronic applications, ranging from solar cells to lasers. The conventional view of this transfer involves stochastic processes occurring within a thermal bath of phonons, where the lattice arrangement and energy flow from higher- to lower-frequency modes. Here, we unveil a comprehensive chronological sequence detailing a conceptually distinct coherent transfer of entropy in a prototypical perovskite CH 3 NH 3 Pbl 3 . The terahertz periodic modulation imposes vibrational coherence into electronic states, leading to the emergence of mixed (vibronic) quantum beat between approximately 3 and 0.3 THz. We highlight a well-structured bidirectional time-frequency transfer of these diverse phonon modes, each developing at different times and transitioning from high to low frequencies from 3 to 0.3 THz, before reversing direction and ascending to around 0.8 THz. First-principles molecular dynamics simulations disentangle a complex web of coherent-phononic coupling pathways and identify the salient roles of the initial modes in shaping entropy evolution at later stages. Capitalizing on coherent entropy transfer and dynamic anharmonicity presents a compelling opportunity to exceed the fundamental thermodynamic (Shockley-Queisser) limit of photoconversion efficiency and to pioneer novel optoelectronic functionalities. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Composite Robust $H_\infty$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer

Here in this note, the robust stochastic stabilization and robust H_infinity control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, a composite hierarchical control scheme is proposed that integrates the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite hierarchical controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation. It has been shown that the disturbance rejection performance can also be achieved. A numerical example is provided to show the potential of the proposed techniques and encouraging results have been obtained.

42 ENGINEERING↗
DOE OSTI2022

Data-driven Minimum Entropy Control for Stochastic Nonlinear Systems using the Cumulant-Generating Function

Here, we present a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.

42 ENGINEERING↗
DOE OSTI2017

Bounded-Degree Approximations of Stochastic Networks

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Spatial and successional dynamics of microbial biofilm communities in a grassland stream ecosystem

Biofilms represent a metabolically active and structurally complex component of freshwater ecosystems. Ephemeral prairie streams are hydrologically harsh and prone to frequent perturbation. Elucidating both functional and structural community changes over time within prairie streams provides a general understanding of microbial responses to environmental disturbance. In this study, we examined microbial succession of biofilm communities at three sites in a third-order stream at Konza Prairie over a 2- to 64-day period. Microbial abundance (bacterial abundance, chlorophyll a concentrations) increased and never plateaued during the experiment. Net primary productivity (net balance of oxygen consumption and production) of the developing biofilms did not differ statistically from zero until 64 days suggesting a balance of the use of autochthonous and allochthonous energy sources until late succession. Bacterial communities (MiSeq analyses of the V4 region of 16S rRNA) established quickly. Bacterial richness, diversity and evenness were high after 2 days and increased over time. Several dominant bacterial phyla (Beta-, Alphaproteobacteria, Bacteroidetes, Gemmatimonadetes, Acidobacteria, Chloroflexi) and genera ( Luteolibacter, Flavobacterium, Gemmatimonas, Hydrogenophaga ) differed in relative abundance over space and time. Bacterial community composition differed across both space and successional time. Pairwise comparisons of phylogenetic turnover in bacterial community composition indicated that early-stage succession (≤16 days) was driven by stochastic processes, whereas later stages were driven by deterministic selection regardless of site. Finally, our data suggest that microbial biofilms predictably develop both functionally and structurally indicating distinct successional trajectories of bacterial communities in this ecosystem.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

TH-A-BRF-02: BEST IN PHYSICS (JOINT IMAGING-THERAPY) - Modeling Tumor Evolution for Adaptive Radiation Therapy

Purpose: To develop mathematical models of tumor geometry changes under radiotherapy that may support future adaptive paradigms. Methods: A total of 29 cervical patients were scanned using MRI, once for planning and weekly thereafter for treatment monitoring. Using the tumor volumes contoured by a radiologist, three mathematical models were investigated based on the assumption of a stochastic process of tumor evolution. The “weekly MRI” model predicts tumor geometry for the following week from the last two consecutive MRI scans, based on the voxel transition probability. The other two models use only the first pair of consecutive MRI scans, and the transition probabilities were estimated via tumor type classified from the entire data set. The classification is based on either measuring the tumor volume (the “weekly volume” model), or implementing an auxiliary “Markov chain” model. These models were compared to a constant volume approach that represents the current clinical practice, using various model parameters; e.g., the threshold probability β converts the probability map into a tumor shape (larger threshold implies smaller tumor). Model performance was measured using volume conformity index (VCI), i.e., the union of the actual target and modeled target volume squared divided by product of these two volumes. Results: The “weekly MRI” model outperforms the constant volume model by 26% on average, and by 103% for the worst 10% of cases in terms of VCI under a wide range of β. The “weekly volume” and “Markov chain” models outperform the constant volume model by 20% and 16% on average, respectively. They also perform better than the “weekly MRI” model when β is large. Conclusion: It has been demonstrated that mathematical models can be developed to predict tumor geometry changes for cervical cancer undergoing radiotherapy. The models can potentially support adaptive radiotherapy paradigm by reducing normal tissue dose. This research was supported in part by the Ontario Consortium for Adaptive Interventions in Radiation Oncology (OCAIRO) funded by the Ontario Research Fund (ORF) and the MITACS Accelerate Internship Program.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

Control of long-distance motion of single molecules on a surface

Spatial control over molecular movement is typically limited because motion at the atomic scale follows stochastic processes. Here, we used scanning tunneling microscopy to bring single molecules into a stable orientation of high translational mobility where they moved along precisely defined tracks. Single dibromoterfluorene molecules moved over large distances of 150 nanometers with extremely high spatial precision of 0.1 angstrom across a silver (111) surface. The electrostatic nature of the effect enabled the selective application of repulsive and attractive forces to send or receive single molecules. The high control allows us to precisely move an individual and specific molecular entity between two separate probes, opening avenues for velocity measurements and thus energy dissipation studies of single molecules in real time during diffusion and collision.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Global Diversity and Biogeography of the Zostera marina Mycobiome

Seagrasses are marine flowering plants that provide critical ecosystem services in coastal environments worldwide. Marine fungi are often overlooked in microbiome and seagrass studies, despite terrestrial fungi having critical functional roles as decomposers, pathogens, or endophytes in global ecosystems. Here, we characterize the distribution of fungi associated with the seagrass Zostera marina, using leaves, roots, and rhizosphere sediment from 16 locations across its full biogeographic range. Using high-throughput sequencing of the ribosomal internal transcribed spacer (ITS) region and 18S rRNA gene, we first measured fungal community composition and diversity. We then tested hypotheses of neutral community assembly theory and the degree to which deviations suggested that amplicon sequence variants (ASVs) were plant selected or dispersal limited. Finally, we identified a core mycobiome and investigated the global distribution of differentially abundant ASVs. We found that the fungal community is significantly different between sites and that the leaf mycobiome follows a weak but significant pattern of distance decay in the Pacific Ocean. Generally, there was evidence for both deterministic and stochastic factors contributing to community assembly of the mycobiome, with most taxa assembling through stochastic processes. The Z. marina core leaf and root mycobiomes were dominated by unclassified Sordariomycetes spp., unclassified Chytridiomycota lineages (including Lobulomycetaceae spp.), unclassified Capnodiales spp., and Saccharomyces sp. It is clear from the many unclassified fungal ASVs and fungal functional guilds that knowledge of marine fungi is still rudimentary. Further studies characterizing seagrass-associated fungi are needed to understand the roles of these microorganisms generally and when associated with seagrasses. Fungi have important functional roles when associated with land plants, yet very little is known about the roles of fungi associated with marine plants, like seagrasses. In this study, we report the results of a global effort to characterize the fungi associated with the seagrass Zostera marina across its full biogeographic range. Although we defined a putative global core fungal community, it is apparent from the many fungal sequences and predicted functional guilds that had no matches to existing databases that general knowledge of seagrass-associated fungi and marine fungi is lacking. This work serves as an important foundational step toward future work investigating the functional ramifications of fungi in the marine ecosystem.

ITS2↗
DOE OSTI2021

Microbiome Aggregated Traits and Assembly Are More Sensitive to Soil Management than Diversity

How soil is managed, particularly for agriculture, exerts stresses upon soil microbiomes, resulting in altered community structures and functional states. Understanding how soil microbiomes respond to combined stresses is important for predicting system performance under different land use scenarios, aids in identification of the most environmentally benign managements, and provides insight into how system function can be recovered in degraded soils. We use a long-established field experiment to study the effects of combined chronic (press) disturbance of the magnitude of organic carbon inputs with acute (pulse) effects of physical disturbance by tillage and chemical disturbance due to inorganic fertilization and pesticide application. We show that because of the variety of ways it can be assessed, biodiversity—here based on microbial small subunit rRNA gene phylotypes—does not provide a consistent view of community change. In contrast, aggregated traits associated with soil microbiomes indicate general loss of function, measured as a reduction of average genome lengths, associated with chronic reduction of organic inputs in arable or bare fallow soils and altered growth strategies associated with rRNA operon copy number in prokaryotes, as well as a switch to pathogenicity in fungal communities. In addition, pulse disturbance by soil tillage is associated with an increased influence of stochastic processes upon prokaryote community assembly, but fungicide used in arable soils results in niche assembly of fungal communities compared to untilled grassland. Overall, bacteria, archaea, and fungi do not share a common response to land management change, and estimates of biodiversity do not capture important facets of community adaptation to stresses adequately.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗
DOE OSTI2020

UQ Toolkit v 2.0

The Uncertainty Quantification (UQ) Toolkit is a software library for the characterizaton and propagation of uncertainties in computational models. For the characterization of uncertainties, Bayesian inference tools are provided to infer uncertain model parameters, as well as Bayesian compressive sensing methods for discovering sparse representations of high-dimensional input-output response surfaces, and also Karhunen-Loève expansions for representing stochastic processes. Uncertain parameters are treated as random variables and represented with Polynomial Chaos expansions (PCEs). The library implements several spectral basis function types (e.g. Hermite basis functions in terms of Gaussian random variables or Legendre basis functions in terms of uniform random variables) that can be used to represent random variables with PCEs. For propagation of uncertainty, tools are provided to propagate PCEs that describe the input uncertainty through the computational model using either intrusive methods (Galerkin projection of equations onto basis functions) or non-intrusive methods (perform deterministic operation at sampled values of the random values and project the obtained results onto basis functions).

Safta, Cosmin↗