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At least 487 records · Page 27

Number of sites-based solver for determining coverages from steady-state mean-field micro-kinetic models

Kinetic models parameterized by ab-initio calculations have led to significant improvements in understanding chemical reactions in heterogeneous catalysis. These studies have been facilitated by implementations which determine steady-state coverages and rates of mean-field micro-kinetic models. As implemented in the open-source kinetic modeling program, CatMAP, the conventional solution strategy is to use a root-finding algorithm to determine the coverage of all intermediates through the steady-state expressions, constraining all coverages to be non-negative and to properly sum to unity. Though intuitive, this root-finding strategy causes issues with convergence to solution due to these imposed constraints. In this work, we avoid explicitly imposing these constraints, solving the mean-field steady-state micro-kinetic model in the space of number of sites instead of solving it in the space of coverages. Here, we transform the constrained root-finding problem to an unconstrained least-squares minimization problem, leading to significantly improved convergence in solving micro-kinetic models and thus enabling the efficient study of more complex catalytic reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Aerodynamics of an airfoil with a jet issuing from its surface

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.

Tavella, D. A.↗

Tools for Designing and Analyzing Structures

Structural Design and Analysis Toolset is a collection of approximately 26 Microsoft Excel spreadsheet programs, each of which performs calculations within a different subdiscipline of structural design and analysis. These programs present input and output data in user-friendly, menu-driven formats. Although these programs cannot solve complex cases like those treated by larger finite element codes, these programs do yield quick solutions to numerous common problems more rapidly than the finite element codes, thereby making it possible to quickly perform multiple preliminary analyses - e.g., to establish approximate limits prior to detailed analyses by the larger finite element codes. These programs perform different types of calculations, as follows: 1. determination of geometric properties for a variety of standard structural components; 2. analysis of static, vibrational, and thermal- gradient loads and deflections in certain structures (mostly beams and, in the case of thermal-gradients, mirrors); 3. kinetic energies of fans; 4. detailed analysis of stress and buckling in beams, plates, columns, and a variety of shell structures; and 5. temperature dependent properties of materials, including figures of merit that characterize strength, stiffness, and deformation response to thermal gradients

Luz, Paul L.↗

Direct numerical simulation of sheared turbulent flow

The summer assignment to study sheared turbulent flow was divided into three phases which were: (1) literature survey, (2) computational familiarization, and (3) pilot computational studies. The governing equations of fluid dynamics or Navier-Stokes equations describe the velocity, pressure, and density as functions of position and time. In principle, when combined with conservation equations for mass, energy, and thermodynamic state of the fluid a determinate system could be obtained. In practice the Navier-Stokes equations have not been solved due to the nonlinear nature and complexity of these equations. Consequently, the importance of experiments in gaining insight for understanding the physics of the problem has been an ongoing process. Reasonable computer simulations of the problem have occured as the computational speed and storage of computers has evolved. The importance of the microstructure of the turbulence dictates the need for high resolution grids in extracting solutions which contain the physical mechanisms which are essential to a successful simulation. The recognized breakthrough occurred as a result of the pioneering work of Orzag and Patterson in which the Navier-Stokes equations were solved numerically utilizing a time saving toggling technique between physical and wave space, known as a spectral method. An equally analytically unsolvable problem, containing the same quasi-chaotic nature as turbulence, is known as the three body problem which was studied computationally as a first step this summer. This study was followed by computations of a two dimensional (2D) free shear layer.

Harris, Vascar G.↗

Developing a framework for qualitative engineering: Research in design and analysis of complex structural systems

The research is focused on automating the evaluation of complex structural systems, whether for the design of a new system or the analysis of an existing one, by developing new structural analysis techniques based on qualitative reasoning. The problem is to identify and better understand: (1) the requirements for the automation of design, and (2) the qualitative reasoning associated with the conceptual development of a complex system. The long-term objective is to develop an integrated design-risk assessment environment for the evaluation of complex structural systems. The scope of this short presentation is to describe the design and cognition components of the research. Design has received special attention in cognitive science because it is now identified as a problem solving activity that is different from other information processing tasks (1). Before an attempt can be made to automate design, a thorough understanding of the underlying design theory and methodology is needed, since the design process is, in many cases, multi-disciplinary, complex in size and motivation, and uses various reasoning processes involving different kinds of knowledge in ways which vary from one context to another. The objective is to unify all the various types of knowledge under one framework of cognition. This presentation focuses on the cognitive science framework that we are using to represent the knowledge aspects associated with the human mind's abstraction abilities and how we apply it to the engineering knowledge and engineering reasoning in design.

Franck, Bruno M.↗

An Overview of Computational Aeroacoustic Modeling at NASA Langley

The use of computational techniques in the area of acoustics is known as computational aeroacoustics and has shown great promise in recent years. Although an ultimate goal is to use computational simulations as a virtual wind tunnel, the problem is so complex that blind applications of traditional algorithms are typically unable to produce acceptable results. The phenomena of interest are inherently unsteady and cover a wide range of frequencies and amplitudes. Nonetheless, with appropriate simplifications and special care to resolve specific phenomena, currently available methods can be used to solve important acoustic problems. These simulations can be used to complement experiments, and often give much more detailed information than can be obtained in a wind tunnel. The use of acoustic analogy methods to inexpensively determine far-field acoustics from near-field unsteadiness has greatly reduced the computational requirements. A few examples of current applications of computational aeroacoustics at NASA Langley are given. There remains a large class of problems that require more accurate and efficient methods. Research to develop more advanced methods that are able to handle the geometric complexity of realistic problems using block-structured and unstructured grids are highlighted.

Lockard, David P.↗

Complex Langevin and other approaches to the sign problem in quantum many-body physics

In this work, we review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, including the classic reweighting method, alternative Hubbard–Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗

Robotic Planning under Uncertainty in Spatiotemporal Environments in Expeditionary Science

In the expeditionary sciences, spatiotemporally varying environments -- hydrothermal plumes, algal blooms, lava flows, or animal migrations -- are ubiquitous. Mobile robots are uniquely well-suited to study these dynamic, mesoscale natural environments. We formalize expeditionary science as a sequential decision-making problem, modeled using the language of partially-observable Markov decision processes (POMDPs). Solving the expeditionary science POMDP under real-world constraints requires efficient probabilistic modeling and decision-making in problems with complex dynamics and observational models. Previous work in informative path planning, adaptive sampling, and experimental design have shown compelling results, largely in static environments, using data-driven models and information-based rewards. However, these methodologies do not trivially extend to expeditionary science in spatiotemporal environments: they generally do not make use of scientific knowledge such as equations of state dynamics, they focus on information gathering as opposed to scientific task execution, and they make use of decision-making approaches that scale poorly to large, continuous problems with long planning horizons and real-time operational constraints. In this work, we discuss these and other challenges related to probabilistic modeling and decision-making in expeditionary science, and present some of our preliminary work that addresses these gaps. We ground our results in a real expeditionary science deployment of an autonomous underwater vehicle (AUV) in the deep ocean for hydrothermal vent discovery and characterization. Our concluding thoughts highlight remaining work to be done, and the challenges that merit consideration by the reinforcement learning and decision-making community.

Preston, Victoria↗

A forward method for optimal stochastic nonlinear and adaptive control

A computational approach is taken to solve the optimal nonlinear stochastic control problem. The approach is to systematically solve the stochastic dynamic programming equations forward in time, using a nested stochastic approximation technique. Although computationally intensive, this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual dimensionality problem associated with solving the dynamic programming equations backward in time. It is shown that the cost degrades monotonically as the complexity of the algorithm is reduced. This provides a strategy for suboptimal control with clear performance/computation tradeoffs. A numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method.

Bayard, David S.↗

Progress in computing nozzle/plume flow fields

The long-term goal is to develop the capability to predict chemically-reacting, multi-stream nozzle and plume flow fields. Two basic Navier-Stokes solvers, including the widely used F-3D code, are upgraded to include several upwind difference schemes and portable chemistry packages. Current computational capabilities for solving equilibrium single-stream and multi-stream, frozen gas, and finite rate chemistry problems are described. A variety of complex nozzle and plume flows were computed. Solutions presented include axisymmetric plume flow for ideal and equilibrium air, 3-D NASP nozzle/afterbody flow, and an internal nozzle calculation comparing various finite-rate chemistry packages.

Ruffin, Stephen M.↗

Three-dimensional aspects of radiative transfer in remote sensing of precipitation: Application to the 1986 COHMEX storm

Several multifrequency techniques for passive microwave estimation of precipitation based on the absorption and scattering properties of hydrometers have been proposed in the literature. In the present study, plane-parallel limitations are overcome by using a model based on the discrete-ordinates method to solve the radiative transfer equation in three-dimensional rectangular domains. This effectively accounts for the complexity and variety of radiation problems encountered in the atmosphere. This investigation presents result for plane-parallel and three-dimensional radiative transfer for a precipitating system, discusses differences between these results, and suggests possible explanations for these differences. Microphysical properties were obtained from the Colorado State University Regional Atmospehric Modeling System and represent a hailstorm observed during the 1986 Cooperative Huntsville Meteorological Experiment. These properties are used as input to a three-dimensional radiative transfer model in order to simulate satellite observation of the storm. The model output consists of upwelling brightness temperatures at several of the frequencies on the Special Sensor Microwave/Imager. The radiative transfer model accounts for scattering and emission of atmospheric gases and hydrometers in liquid and ice phases. Brightness temperatures obtained from the three-dimensional model of this investigation indicate that horizontal inhomogeneities give rise to brightness temperature fields that can be quite different from fields obtained using plane-parallel radiative transfer theory. These differences are examined for various resolutions of the satellite sensor field of view. In adddition, the issue of boundary conditions for three-dimensional atmospheric radiative transfer is addressed.

Haferman, J. L.↗

Reductive Analysis with Compiler-Guided Large Language Models for Input-Centric Code Optimizations

Input-centric program optimization aims to optimize code by considering the relations between program inputs and program behaviors. Despite its promise, a long-standing barrier for its adoption is the difficulty of automatically identifying critical features of complex inputs. This paper introduces a novel technique, reductive analysis through compiler-guided Large Language Models (LLMs), to solve the problem through a synergy between compilers and LLMs. It uses a reductive approach to overcome the scalability and other limitations of LLMs in program code analysis. The solution, for the first time, automates the identification of critical input features without heavy instrumentation or profiling, cutting the time needed for input identification by 44× (or 450× for local LLMs), reduced from 9.6 hours to 13 minutes (with remote LLMs) or 77 seconds (with local LLMs) on average, making input characterization possible to be integrated into the workflow of program compilations. Optimizations on those identified input features show similar or even better results than those identified by previous profiling-based methods, leading to optimizations that yield 92.6% accuracy in selecting the appropriate adaptive OpenMP parallelization decisions, and 20-30% performance improvement of serverless computing while reducing resource usage by 50-60%.

Input-Centric Optimization↗

Chemical Reaction and Flow Modeling in Fullerene and Nanotube Production

The development of processes to produce fullerenes and carbon nanotubes has largely been empirical. Fullerenes were first discovered in the soot produced by laser ablation of graphite [1]and then in the soot of electric arc evaporated carbon. Techniques and conditions for producing larger and larger quantities of fullerenes depended mainly on trial and error empirical variations of these processes, with attempts to scale them up by using larger electrodes and targets and higher power. Various concepts of how fullerenes and carbon nanotubes were formed were put forth, but very little was done based on chemical kinetics of the reactions. This was mainly due to the complex mixture of species and complex nature of conditions in the reactors. Temperatures in the reactors varied from several thousand degrees Kelvin down to near room temperature. There are hundreds of species possible, ranging from atomic carbon to large clusters of carbonaceous soot, and metallic catalyst atoms to metal clusters, to complexes of metals and carbon. Most of the chemical kinetics of the reactions and the thermodynamic properties of clusters and complexes have only been approximated. In addition, flow conditions in the reactors are transient or unsteady, and three dimensional, with steep spatial gradients of temperature and species concentrations. All these factors make computational simulations of reactors very complex and challenging. This article addresses the development of the chemical reaction involved in fullerene production and extends this to production of carbon nanotubes by the laser ablation/oven process and by the electric arc evaporation process. In addition, the high-pressure carbon monoxide (HiPco) process is discussed. The article is in several parts. The first one addresses the thermochemical aspects of modeling; and considers the development of chemical rate equations, estimates of reaction rates, and thermodynamic properties where they are available. The second part addresses modeling of the arc process for fullerene and carbon nanotube production using O-D, 1-D and 2-D fluid flow models. The third part addresses simulations of the pulsed laser ablation process using time-dependent techniques in 2-D, and a steady state 2-D simulation of a continuous laser ablation process. The fourth part addresses steady state modeling in O-D and 2-D of the HiPco process. In each of the simulations, there is a variety of simplifications that are made that enable one to concentrate on one aspect or another of the process. There are simplifications that can be made to the chemical reaction models , e.g. reduction in number of species by lumping some of them together in a representative species. Other simulations are carried out by eliminating the chemistry altogether in order to concentrate on the fluid dynamics. When solving problems with a large number of species in more than one spatial dimension, it is almost imperative that the problem be decoupled by solving for the fluid dynamics to find the fluid motion and temperature history of "particles" of fluid moving through a reactor. Then one can solve the chemical rate equations with complex chemistry following the temperature and pressure history. One difficulty is that often mixing with an ambient gas is involved. Therefore, one needs to take dilution and mixing into account. This changes the ratio of carbon species to background gas. Commercially available codes may have no provision for including dilution as part of the input. One must the write special solvers for including dilution in decoupled problems. The article addresses both ful1erene production and single-walled carbon nanotube (SWNT) production. There are at least two schemes or concepts of SWNT growth. This article will only address growth in the gas phase by carbon and catalyst cluster growth and SW T formation by the addition of carbon. There are other models that conceive of SWNT growth as a phase separation process from clusters me up carbon and metal catalyst, with the carbon precipitating from the cluster as it cools. We will not deal with that concept in this article. Further research is needed to determine the rates at which these composite clusters form, evaporate, and segregate.

Scott, Carl D.↗

Concurrent implementation of the Crank-Nicolson method for heat transfer analysis

To exploit the significant gains in computing speed provided by Multiple Instruction Multiple Data (MIMD) computers, concurrent methods for practical problems need to be investigated and test problems implemented on actual hardware. One such problem class is heat transfer analysis which is important in many aerospace applications. This paper compares the efficiency of two alternate implementations of heat transfer analysis on an experimental MIMD computer called the Finite Element Machine (FEM). The implicit Crank-Nicolson method is used to solve concurrently the heat transfer equations by both iterative and direct methods. Comparison of actual timing results achieved for the two methods and their significance relative to more complex problems are discussed.

Ransom, J. B.↗

A network flow model for load balancing in circuit-switched multicomputers

In multicomputers that utilize circuit switching or wormhole routing, communication overhead depends largely on link contention - the variation due to distance between nodes is negligible. This has a major impact on the load balancing problem. In this case, there are some nodes with excess load (sources) and others with deficit load (sinks) and it is required to find a matching of sources to sinks that avoids contention. The problem is made complex by the hardwired routing on currently available machines: the user can control only which nodes communicate but not how the messages are routed. Network flow models of message flow in the mesh and the hypercube were developed to solve this problem. The crucial property of these models is the correspondence between minimum cost flows and correctly routed messages. To solve a given load balancing problem, a minimum cost flow algorithm is applied to the network. This permits one to determine efficiently a maximum contention free matching of sources to sinks which, in turn, tells one how much of the given imbalance can be eliminated without contention.

Bokhari, Shahid H.↗