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Results for “statistical mechanics models”

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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NASA NTRS1990

Surface characterizations of color threshold

The paper evaluates how well three different parametric shapes, ellipsoids, rectangles, and parallelograms, serve as models of three-dimentional detection contours. The constraints of the procedures for deriving the best-fitting shapes on inferences about the theoretical visual detection mechanisms are described. Results of two statistical tests show that only the parallelogram fits the data with more precision than the variance in repeated threshold measurements, and thus provides a slightly better fit than the other two shapes. Nevertheless it does not serve as a better guide than the ellipsoidal model for interpolating from the measurements to thresholds in novel color directions.

Poirson, Allen B.↗

DOE OSTI2023

Harness the power of atomistic modeling and deep learning in biofuel separation

Biofuels offer a remarkable, sustainable energy source for a future of clean energy. The development of efficient biofuel separation plays a crucial role in achieving cost-effective utilization of biofuel. In this chapter, we provide an overview of the recent advancements in atomistic-level modeling and deep learning in the rational design of novel, efficient biofuel separation. The fundamental principles of quantum and statistical mechanics are covered in appropriate detail to highlight their underlying differences in theory. The methodologies of several molecular representations and deep learning algorithms applicable to biofuel separation are briefly demonstrated as well. The applications, successes, and risks of employing density functional theory, ab initio molecular dynamics, classical molecular dynamics, and deep learning are provided to showcase their recent accomplishments in biofuel separation as well as potential improvements in both methodology and application. Lastly, a vision for the future growth of these methods is illustrated.

deep learning, artificial intelligence, biofuels, ↗

NASA NTRS1994

Damage and strength of composite materials: Trends, predictions, and challenges

Research on damage mechanisms and ultimate strength of composite materials relevant to scaling issues will be addressed in this viewgraph presentation. The use of fracture mechanics and Weibull statistics to predict scaling effects for the onset of isolated damage mechanisms will be highlighted. The ability of simple fracture mechanics models to predict trends that are useful in parametric or preliminary designs studies will be reviewed. The limitations of these simple models for complex loading conditions will also be noted. The difficulty in developing generic criteria for the growth of these mechanisms needed in progressive damage models to predict strength will be addressed. A specific example for a problem where failure is a direct consequence of progressive delamination will be explored. A damage threshold/fail-safety concept for addressing composite damage tolerance will be discussed.

Obrien, T. Kevin↗

NASA NTRS2010

Physics of Life: A Model for Non-Newtonian Properties of Living Systems

This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

Zak, Michail↗

DOE OSTI2024

Physics-informed machine learning of the correlation functions in bulk fluids

The Ornstein–Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids. In this work, machine learning models, notably physics-informed neural networks and physics-informed neural operator networks, are explored to solve the OZ equation. The physics-informed machine learning models demonstrate great accuracy and high efficiency in solving the forward and inverse OZ problems of various bulk fluids. The results highlight the significant potential of physics-informed machine learning for applications in thermodynamic state theory.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

The emergence of experiments capable of probing quantum dynamics at the single-molecule level requires the development of new theoretical tools capable of simulating and analyzing these dynamics beyond an ensemble-averaged description. In this article, we present an efficient method for sampling and simulating the dynamics of the individual quantum systems that make up an ensemble and apply it to study the nonequilibrium dynamics of the ubiquitous spin-boson model. We generate an ensemble of single-system trajectories, and we analyze this trajectory ensemble using tools from classical statistical mechanics. Our results demonstrate that the dynamics of quantum coherence is highly heterogeneous at the single-system level due to variations in the initial bath configuration, which significantly affects the transient exchange of coherence between the system and its bath. Here, we observe that single systems tend to retain coherence over time scales longer than that of the ensemble. We also compute a novel thermodynamic entanglement entropy that quantifies a thermodynamic driving force favoring system–bath entanglement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Energy consumption and cooperation for optimal sensing

Abstract The reliable detection of environmental molecules in the presence of noise is an important cellular function, yet the underlying computational mechanisms are not well understood. We introduce a model of two interacting sensors which allows for the principled exploration of signal statistics, cooperation strategies and the role of energy consumption in optimal sensing, quantified through the mutual information between the signal and the sensors. Here we report that in general the optimal sensing strategy depends both on the noise level and the statistics of the signals. For joint, correlated signals, energy consuming (nonequilibrium), asymmetric couplings result in maximum information gain in the low-noise, high-signal-correlation limit. Surprisingly we also find that energy consumption is not always required for optimal sensing. We generalise our model to incorporate time integration of the sensor state by a population of readout molecules, and demonstrate that sensor interaction and energy consumption remain important for optimal sensing.

Ngampruetikorn, Vudtiwat↗

NASA NTRS2020

Concept for an On-orbit Capture and Orientation Module for Potential Mars Sample Return

An orbiting sample Capture and Orient Module (COM) architecture for a Capture, Contain, and Return System (CCRS) payload concept for an Earth Return Orbiter (ERO) was developed to enable on-orbit capture, orientation, and transfer of a Mars sample container into a containment vessel for potential Mars Sample Return (MSR). The module is composed of a capture mechanism for containing the Orbiting Sample (OS), a capture cone to capture and contain the OS, an orientation mechanism to orient the OS, an External Transfer Mechanism (ETM) to cage the OS during capture and assemble it into the containment vessel, a capture trigger to trigger capture mechanism and ETM closure during OS capture, and a sensing system to inspect the OS and confirm capture and orientation. Statistical modeling and simulations of the OS during capture were performed to analyze the time to contact and perturbations to the spacecraft at first contact. A half-scale functional prototype of the module was developed to demonstrate end-to-end operation.

Younse, Paulo↗

DOE OSTI2024

Modern chemical graph theory

Abstract Graph theory has a long history in chemistry. Yet as the breadth and variety of chemical data is rapidly changing, so too do graph encoding methods and analyses that yield qualitative and quantitative insights. Using illustrative cases within a basic mathematical framework, we showcase modern chemical graph theory's utility in Chemists' analysis and model development toolkit. The encoding of both experimental and simulation data is discussed at various levels of granularity of information. This is followed by a discussion of the two major classes of graph theoretical analyses: identifying connectivity patterns and partitioning methods. Measures, metrics, descriptors, and topological indices are then introduced with an emphasis upon enhancing interpretability and incorporation into physical models. Challenging data cases are described that include strategies for studying time dependence. Throughout, we incorporate recent advancements in computer science and applied mathematics that are propelling chemical graph theory into new domains of chemical study. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Structure and Mechanism > Computational Materials Science Structure and Mechanism > Molecular Structures

Leite, Leonardo S. G.↗

NASA NTRSDate not supplied

Simulation and Modeling of Hypersonic Turbulent Boundary Layers Subject to Favorable Pressure Gradients due to Streamline Curvature

Direct numerical simulations (DNS) of favorable-pressure-gradient turbulent boundary layers are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models.The wall geometry and flow conditions of the DNS are representative of the experimental data for a Mach 4.9 turbulent boundary layer that was tested on a two-dimensional planar convexwall model in the high-speed blow-down wind tunnel located at the National Aerothermochemistry Laboratory at Texas A&M University. The favorable pressure gradient is induced bythe streamwise surface curvature. The DNS results will be compared with experimental measurements and RANS computations for the same flow conditions and wall geometry. The DNS datasets will also be analyzed to provide an improved physical understanding of hypersonic boundary-layer turbulence subject to mechanical nonequilibrium, including the validity of Morkovin’s hypothesis and the various available compressibility transformations, as well as to obtain turbulence statistics that are relevant to RANS modeling, including the distribution ofeddy viscosity, the budgets of turbulent kinetic energy and Reynolds stresses, and the velocity-temperature correlations. The RANS predictions will be obtained by using both the commonly used one- and two-equation models that assume a constant turbulent Prandtl number and an algebraic, variable Prandtl number model for the turbulent energy flux.

turbulent boundary layers↗

NASA NTRS1988

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

Yu, Sheng-Tao↗

DOE OSTI2026

Thermodynamically consistent incorporation of the Langmuir adsorption model into compressible fluctuating hydrodynamics

For a gas–solid interfacial system where chemical species undergo reversible adsorption, we develop a mesoscopic stochastic modeling method that simulates both gas-phase hydrodynamics and surface coverage dynamics by coupling the Langmuir adsorption model with compressible fluctuating hydrodynamics. To this end, we derive a thermodynamically consistent mass–energy update scheme that accounts for how the mass and energy variables in the gas and surface subsystems should be updated according to the changes in the number of molecules of each species in each subsystem due to adsorption and desorption events. By performing a stochastic analysis for the ideal Langmuir model and the full hydrodynamic system, we analytically confirm that our mass–energy update scheme captures thermodynamic equilibrium predicted by equilibrium statistical mechanics. We find that an internal energy correction term is needed, which is attributed to the difference in the mean kinetic energy of gas molecules colliding with the surface from that computed from the Maxwell–Boltzmann distribution. By performing an equilibrium simulation study for an ideal gas mixture of CO and Ar, with CO undergoing reversible adsorption, we validate our overall simulation method and implementation.

Adsorption↗

DOE OSTI2020

Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation

Classical molecular dynamics simulates the time evolution of molecular systems through the phase space spanned by the positions and velocities of the constituent atoms. Molecular-level thermodynamic, kinetic, and structural data extracted from the resulting trajectories provide valuable information for the understanding, engineering, and design of biological and molecular materials. The cost of simulating many-body atomic systems makes simulations of large molecules prohibitively expensive, and the high-dimensionality of the resulting trajectories presents a challenge for analysis. Driven by advances in algorithms, hardware, and data availability, there has been a flare of interest in recent years in the applications of machine learning – especially deep learning – to molecular simulation. Furthermore, these techniques have demonstrated great power and flexibility in both extracting mechanistic understanding of the important nonlinear collective variables governing the dynamics of a molecular system, and in furnishing good low-dimensional system representations with which to perform enhanced sampling or develop long-timescale dynamical models. It is the purpose of this article to introduce the key machine learning approaches, describe how they are married with statistical mechanical theory into domain-specific tools, and detail applications of these approaches in understanding and accelerating biomolecular simulation.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRSDate not supplied

Supersonic Traveling Crossflow Wave Characteristics in Ground and Flight Tests

This paper continues analysis of data acquired in a series of supersonic crossflow transition experiments on a 65° swept- wing model tested in both wind tunnel and flight. Flow visualization data are summarized to provide context for the swept-wing instability mechanisms of interest. Unsteady pressure measurements obtained near the wing model leading edge (LE) are studied using 2nd- and 3rd-order statistical methods to extract traveling crossflow wave characteristics from these data. Comparisons between tunnel and flight data with boundary-layer (BL) Linear Stability Theory (LST) predictions provide insights into BL transition phenomena similarities and differences observed in tests using the same swept-wing model configurations. Comparisons of unsteady pressure data results for wing LE configurations with and without distributed-roughness-element (DRE) patterns installed, suggest traveling crossflow disturbance growth is reduced when this type of flow control is applied. A brief stud y of different background surface roughness levels on the wing LE suggests the potential for another flow control approach to promote laminar flow on swept wings using streamwise-biased surface finishes.

Lewis R Owens↗

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↗

NASA NTRS1986

Investigation of advanced fault insertion and simulator methods

The cooperative agreement partly supported research leading to the open-literature publication cited. Additional efforts under the agreement included research into fault modeling of semiconductor devices. Results of this research are presented in this report which is summarized in the following paragraphs. As a result of the cited research, it appears that semiconductor failure mechanism data is abundant but of little use in developing pin-level device models. Failure mode data on the other hand does exist but is too sparse to be of any statistical use in developing fault models. What is significant in the failure mode data is that, unlike classical logic, MSI and LSI devices do exhibit more than 'stuck-at' and open/short failure modes. Specifically they are dominated by parametric failures and functional anomalies that can include intermittent faults and multiple-pin failures. The report discusses methods of developing composite pin-level models based on extrapolation of semiconductor device failure mechanisms, failure modes, results of temperature stress testing and functional modeling. Limitations of this model particularly with regard to determination of fault detection coverage and latency time measurement are discussed. Indicated research directions are presented.

Dunn, W. R.↗

DOE OSTI2023

Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.

Engineering↗

DOE OSTI2021

Phase-field model of precipitation processes with coherency loss

A phase-field model is proposed to simulate coherency loss coupled with microstructure evolution. A special field variable is employed to describe the degree of coherency loss of each particle and its evolution is governed by a Ginzburg-Landau type kinetic equation. For the sake of computational efficiency, a flood-fill algorithm is introduced that can drastically reduce the required number of field variables, which allows the model to efficiently simulate a large number of particles sufficient for characterizing their statistical features during Ostwald ripening. The model can incorporate size dependence of coherency loss, metastability of coherent particles, and effectively incorporate the underlying mechanisms of coherency loss by introducing a so-called differential energy criterion. The model is applied to simulate coarsening of Al 3 Sc precipitates in aluminum alloy and comprehensively compared with experiments. Our results clearly show how the particle size distribution is changed during coherency loss and affects the coarsening rate.

36 MATERIALS SCIENCE↗