Search NASA⌕ Search

SEARCH · Search NASA

Results for “Software behavior computation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Toward a smart data transfer node

Scientific computing systems are becoming significantly more complex, with distributed teams and complex workflows spanning resources from telescopes and light sources to fast networks and Internet of Things sensor systems. In such settings, no single, centralized administrative team and software stack can coordinate and manage all resources used by a single application. Indeed, we have reached a critical limit in manageability using current human-in-the-loop techniques. We therefore argue that resources must begin to respond automatically, adapting and tuning their behavior in response to observed properties of scientific workflows. Over time, machine learning methods can be used to identify effective strategies for autonomic, goal-driven management behaviors that can be applied end-to-end across the scientific computing landscape. Using the data transfer nodes that are widely deployed in modern research networks as an example, we explore the architecture, methods, and algorithms needed for a smart data transfer node to support future scientific computing systems that self-tune and self-manage.

97 MATHEMATICS AND COMPUTING↗

THERMAL MODELING OF HANFORD LEAD CANISTER’S HEATER BENCH TESTS

A computational fluid dynamics (CFD) model was built to simulate planned testing of heater assemblies for the Hanford Lead Canister (HLC) project. The HLC is a canister storage system that will contain heaters to simulate the decay heat of nuclear material and provide the canister storage system with environmental conditions equivalent to the operating conditions on a dry storage pad. The HLC will be equipped with long-term data collection and monitoring systems to provide an early warning of corrosion, pitting, cracking, or other signs of canister degradation that might threaten the integrity of the containment boundary over the potentially long term of dry storage. An important part of the HLC development is to confirm the function and ability of the electric heater assemblies that were specially designed to provide heating similar to the decay heat of nuclear material contained within the canister storage system. Heater bench testing is planned for early 2022 in a test configuration that does not include the canister. The goal of the bench testing is to verify that the heaters can replicate the decay heat of a canister with nuclear material and to validate the thermal models, which are critical to understanding the HLC’s thermal environment, including the local air flow within the canister storage system. Testing of the heater assemblies inside the canister system are planned in the future to validate canister level thermal models, and rigorous pre-deployment testing of the complete HLC cask and canister system is intended to be completed before the HLC is deployed in the 2025-2026 timeframe. This study presents the pre-test temperature predictions of the bench testing. A description of the heater assemblies and planned bench testing is presented. The model was developed with the commercial CFD code STAR-CCM+. An uncertainty analysis was run with the CFD model to determine the uncertainty in the temperature predictions and provide a range over which the predicted temperatures are expected to vary. The uncertainty analysis was performed by coupling STAR-CCM+ with the software Dakota, which provides advanced parametric analyses, including quantification of margins and uncertainty with computational models. This work is expected to provide insight into SNF canister behavior.

Suffield, Sarah R.↗

GridPACK Toolkit for Developing Power Grid Simulations on High Performance Computing Platforms

This paper describes the GridPACK™ framework, which is designed to help power grid engineers develop modeling software capable of running on todays high performance computers. The framework contains modules for setting up distributed power grid networks, assigning buses and branches with arbitrary behaviors to the network, creating distributed matrices and vectors, using parallel linear and non-linear solvers to solve algebraic equations, and mapping functionality to create matrices and vectors based on properties of the network. In addition, the framework contains additional functionality to support IO and to manage errors.

Palmer, Bruce J.↗

TASK ALLOCATION IN GEO-DISTRIBUTED CYBER-PHYSICAL SYSTEMS

This paper studies the task allocation algorithm for a distributed test facility (DTF), which aims to assemble geo-distributed cyber (software) and physical (hardware in the loop components into a prototype cyber-physical system (CPS). This allows low cost testing on an early conceptual prototype (ECP) of the ultimate CPS (UCPS) to be developed. The DTF provides an instrumentation interface for carrying out reliability experiments remotely such as fault propagation analysis and in-situ testing of hardware and software components in a simulated environment. Unfortunately, the geo-distribution introduces an overhead that is not inherent to the UCPS, i.e. a significant time delay in communication that threatens the stability of the ECP and is not an appropriate representation of the behavior of the UCPS. This can be mitigated by implementing a task allocation algorithm to find a suitable configuration and assign the software components to appropriate computational locations, dynamically. This would allow the ECP to operate more efficiently with less probability of being unstable due to the delays introduced by geo-distribution. The task allocation algorithm proposed in this work uses a Monte Carlo approach along with Dynamic Programming to identify the optimal network configuration to keep the time delays to a minimum.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Task allocation in geo-distributed cyber-physical systems - 256

This paper studies the task allocation algorithm for a distributed test facility (DTF), which aims to assemble geo-distributed cyber (software) and physical (hardware in the loop) components into a prototype cyber-physical system (CPS). This allows low cost testing on an early conceptual prototype (ECP) of the ultimate CPS (UCPS) to be developed. The DTF provides an instrumentation interface for carrying out reliability experiments remotely such as fault propagation analysis and in-situ testing of hardware and software components in a simulated environment. Unfortunately, the geo-distribution introduces an overhead that is not inherent to the UCPS, i.e. a significant time delay in communication that threatens the stability of the ECP and is not an appropriate representation of the behavior of the UCPS. This can be mitigated by implementing a task allocation algorithm to find a suitable configuration and assign the software components to appropriate computational locations, dynamically. This would allow the ECP to operate more efficiently with less probability of being unstable due to the delays introduced by geo-distribution. The task allocation algorithm proposed in this work uses a Monte Carlo approach along with Dynamic Programming to identify the optimal network configuration to keep the time delays to a minimum. (authors)

97 MATHEMATICS AND COMPUTING↗

ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs

Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. Here, this paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.

97 MATHEMATICS AND COMPUTING↗

Report on the ASCR Workshop on Modeling and Simulation of Exascale Systems and Applications

In the last few years, numerous studies commissioned by the Department of Energy (DOE), the Defense Advanced Research Projects Agency (DARPA), and others have examined the challenges that will have to be overcome for computational science to achieve exascale, a two order-of-magnitude increase in capability beyond what is possible today. Exponential growth in the number of devices (Moore’s Law) is expected to continue unabated, but the end of Dennard scaling, and hence the growth in performance of individual processors, has led to exponential growth in concurrency. Power consumption has also grown to the point where the cost of the electrical power for systems threatens to exceed the cost of acquiring them. Ever-shrinking devices, and the growth in their number, are expected to increase the rate of soft, or transient, errors such that applications will no longer be able to assume correct behavior of the underlying machine. Adapting to such systems will require new mathematical algorithms that minimize synchronization and data movement, and a new generation of scientific software. Rather than addressing these issues in isolation, a new process of “Co-Design” is being pursued in which application and computer scientists work toward the common goal of an exascale ecosystem of systems and applications. Modeling and simulation (ModSim) is a critical part of this process. It enables scientists and engineers to analyze future algorithms, applications, and computing systems, long before they are realized, and make the necessary design decisions such that exascale science is broadly achieved. Later, when exascale applications and systems are realized, ModSim technology will enable us to understand their behavior, debugging and optimizing them. Given the increasing importance of modeling and simulation, a workshop was organized by DOE/ASCR to assess the current state of the art and to identify research challenges that must be overcome in this field. Fifty experts, representing academia, industry, and government, participated in the workshop, and others contributed both beforehand and afterwards. This report summarizes their findings.

97 MATHEMATICS AND COMPUTING↗

Report on the ASCR Workshop on Modeling and Simulation of Exascale Systems and Applications

In the last few years, numerous studies commissioned by the Department of Energy (DOE), the Defense Advanced Research Projects Agency (DARPA), and others have examined the challenges that will have to be overcome for computational science to achieve exascale, a two order-of-magnitude increase in capability beyond what is possible today. Exponential growth in the number of devices (Moore's Law) is expected to continue unabated, but the end of Dennard scaling, and hence the growth in performance of individual processors, has led to exponential growth in concurrency. Power consumption has also grown to the point where the cost of the electrical power for systems threatens to exceed the cost of acquiring them. Ever-shrinking devices, and the growth in their number, are expected to increase the rate of soft, or transient, errors such that applications will no longer be able to assume correct behavior of the underlying machine. Adapting to such systems will require new mathematical algorithms that minimize synchronization and data movement, and a new generation of scientific software. Rather than addressing these issues in isolation, a new process of "Co-Design" is being pursued in which application and computer scientists work toward the common goal of an exascale ecosystem of systems and applications. Modeling and simulation (ModSim) is a critical part of this process. It enables scientists and engineers to analyze future algorithms, applications, and computing systems, long before they are realized, and make the necessary design decisions such that exascale science is broadly achieved. Later, when exascale applications and systems are realized, ModSim technology will enable us to understand their behavior, debugging and optimizing them. Given the increasing importance of modeling and simulation, a workshop was organized by DOE/ASCR to assess the current state of the art and to identify research challenges that must be overcome in this field. Fifty experts, representing academia, industry, and government, participated in the workshop, and others contributed both beforehand and afterwards. This report summarizes their findings.

97 MATHEMATICS AND COMPUTING↗

Data analysis and modeling pipelines for controlled networked social science experiments

There is large interest in networked social science experiments for understanding human behavior at-scale. Significant effort is required to perform data analytics on experimental outputs and for computational modeling of custom experiments. Moreover, experiments and modeling are often performed in a cycle, enabling iterative experimental refinement and data modeling to uncover interesting insights and to generate/refute hypotheses about social behaviors. The current practice for social analysts is to develop tailor-made computer programs and analytical scripts for experiments and modeling. This often leads to inefficiencies and duplication of effort. In this work, we propose a pipeline framework to take a significant step towards overcoming these challenges. Our contribution is to describe the design and implementation of a software system to automate many of the steps involved in analyzing social science experimental data, building models to capture the behavior of human subjects, and providing data to test hypotheses. The proposed pipeline framework consists of formal models, formal algorithms, and theoretical models as the basis for the design and implementation. We propose a formal data model, such that if an experiment can be described in terms of this model, then our pipeline software can be used to analyze data efficiently. The merits of the proposed pipeline framework is elaborated by several case studies of networked social science experiments.

97 MATHEMATICS AND COMPUTING↗

Performance Debugging and Tuning of Flash-X with Data Analysis Tools

State-of-the-art multiphysics simulations running on large scale leadership computing platforms have many variables contributing to their performance and scaling behavior. We recently encountered an interesting performance anomaly in Flash-X, a multiphysics multicomponent simulation software, when characterizing its performance behavior on several large-scale HPC platforms. The anomaly was tracked down to the interaction between the use of dynamic allocation of scratch data and data locality in the cache hierarchy. In this paper we present the details of unexpected performance variability of Flash-X, its extensive analysis using the performance measurement tool TAU to collect the data and Python data analysis libraries to explore the data, and our insights from this experience. In this process, we discovered and removed or mitigated two additional performance limiting bottlenecks for performance tuning.

Huck, Kevin↗

Wild Fire Computer Model Helps Firefighters

A high-tech computer model called HIGRAD/FIRETEC, the cornerstone of a collaborative effort between U.S. Forest Service Rocky Mountain Research Station and Los Alamos National Laboratory, provides insights that are essential for front-line fire fighters. The science team is looking into levels of bark beetle-induced conditions that lead to drastic changes in fire behavior and how variable or erratic the behavior is likely to be.

54 ENVIRONMENTAL SCIENCES↗

Virtual Observation System for Earth System Model: An Application to ACME Land Model Simulations

Investigating and evaluating physical-chemical-biological processes within an Earth system model (EMS) can be very challenging due to the complexity of both model design and software implementation. A virtual observation system (VOS) is presented to enable interactive observation of these processes during system simulation. Based on advance computing technologies, such as compiler-based software analysis, automatic code instrumentation, and high-performance data transport, the VOS provides run-time observation capability, in-situ data analytics for Earth system model simulation, model behavior adjustment opportunities through simulation steering. A VOS for a terrestrial land model simulation within the Accelerated Climate Modeling for Energy model is also presented to demonstrate the implementation details and system innovations.

58 GEOSCIENCES↗

An Unsteady State Gas Transport Model in Matrix Laboratory (MATLAB) for PWR Gas Management

Reactor Coolant System (RCS) hydrogen gas management can be a challenge at Pressurized Water Reactors (PWRs) during shutdown, startup, and steady state operation. Poor hydrogen control can result in higher general corrosion rates for RCS components and increases in critical path time for shutdown or startup. Also, performance indicator penalties may be accrued by entry into Electric Power Research Institute (EPRI) Action Level conditions or by accrual of Chemistry Effectiveness Index (CEI) penalties established by the Institute of Nuclear Power Operations (INPO). Furthermore, poor hydrogen control may increase industrial safety risk due to the creation of an explosive environment. Part of the hydrogen management difficulty arises from the interaction of several phenomena that require complex simulations to fully understand. While hydrogen gas transport models have been developed, the application of these models is limited by the computational intensity required to accurately model the dynamism inherent in plant shutdown or startup. Subsequently, a gas transport model is developed in a suitable computational program to meet these needs and provide input to an optimized RCS hydrogen management strategy for all operational modes. The gas transport model is used to model RCS hydrogen behavior for an example PWR during an End of Cycle (EOC) Forced Outage (FO) startup, a refueling outage (RFO) shutdown, and during nominal steady state operation. The computational software selected is Matrix Laboratory (MATLAB{sup R})

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Coastal Ohio Wind Project

The Coastal Ohio Wind Project intends to address problems that impede deployment of wind turbines in the coastal and offshore regions of Northern Ohio. The project evaluates different wind turbine designs and the potential impact of offshore turbines on migratory and resident birds by developing multidisciplinary research, which involves wildlife biology, electrical and mechanical engineering, and geospatial science. Firstly, the project conducts cost and performance studies of two- and three-blade wind turbines using a turbine design suited for the Great Lakes. The numerical studies comprised an analysis and evaluation of the annual energy production of two- and three-blade wind turbines to determine the levelized cost of energy. This task also involved wind tunnel studies of model wind turbines to quantify the wake flow field of upwind and downwind wind turbine-tower arrangements. The experimental work included a study of a scaled model of an offshore wind turbine platform in a water tunnel. The levelized cost of energy work consisted of the development and application of a cost model to predict the cost of energy produced by a wind turbine system placed offshore. The analysis found that a floating two-blade wind turbine presents the most cost effective alternative for the Great Lakes. The load effects studies showed that the two-blade wind turbine model experiences less torque under all IEC Standard design load cases considered. Other load effects did not show this trend and depending on the design load cases, the two-bladed wind turbine showed higher or lower load effects. The experimental studies of the wake were conducted using smoke flow visualization and hot wire anemometry. Flow visualization studies showed that in the downwind turbine configuration the wake flow was insensitive to the presence of the blade and was very similar to that of the tower alone. On the other hand, in the upwind turbine configuration, increasing the rotor blade angle of attack reduced the wake size and enhanced the vortices in the flow downstream of the turbine-tower compared with the tower alone case. Mean and rms velocity distributions from hot wire anemometer data confirmed that in a downwind configuration, the wake of the tower dominates the flow, thus the flow fields of a tower alone and tower-turbine combinations are nearly the same. For the upwind configuration, the mean velocity shows a narrowing of the wake compared with the tower alone case. The downwind configuration wake persisted longer than that of an upwind configuration; however, it was not possible to quantify this difference because of the size limitation of the wind tunnel downstream of the test section. The water tunnel studies demonstrated that the scale model studies could be used to adequately produce accurate motions to model the motions of a wind turbine platform subject to large waves. It was found that the important factors that affect the platform is whether the platform is submerged or surface piercing. In the former, the loads on the platform will be relatively reduced whereas in the latter case, the structure pierces the wave free surface and gains stiffness and stability. The other important element that affects the movement of the platform is depth of the sea in which the wind turbine will be installed. Furthermore, the wildlife biology component evaluated migratory patterns by different monitoring systems consisting of marine radar, thermal IR camera and acoustic recorders. The types of radar used in the project are weather surveillance radar and marine radar. The weather surveillance radar (1988 Doppler), also known as Next Generation Radar (NEXRAD), provides a network of weather stations in the US. Data generated from this network were used to understand general migratory patterns, migratory stopover habitats, and other patterns caused by the effects of weather conditions. At a local scale our marine radar was used to complement the datasets from NEXRAD and to collect additional monitoring parameters such as passage rates, flight paths, flight directions, and flight altitudes of nocturnal migrating species. Our work focused on the design and development of custom built marine radar that used t-bar and parabolic dish antennas. The marine radar used in the project was Furuno (XANK250) which was coupled with a XIR3000B digitizing card from Russell Technologies for collection of the radar data. The radar data was processed by open source radR processing software using different computational techniques and methods. Additional data from thermal IR imaging cameras were collected to detect heat emitted from objects and provide information on movements of birds and bats, data which we used for different animal flight behavior analysis. Lastly, the data from the acoustic recorders were used to provide the number of bird calls for assessing patterns and peak passage rates during migration. The development of the geospatial database included collection of different data sources that are used to support offshore wind turbine development. Many different data sets were collected and organized using initial version of web-based repository software tools that can accommodate distribution of rectified pertinent data sets such as the lake depth, lake bottom engineering parameters, extent of ice, navigation pathways, wind speed, important bird habitats, fish efforts and other layers that are relevant for supporting robust offshore wind turbine developments. Additional geospatial products developed during the project included few different prototypes for offshore wind farm suitability which can involve different stakeholders and participants for solving complex planning problems and building consensus. Some of the prototypes include spatial decision support system (SDSS) for collaborative decision making, a web-based Participatory Geographic Information System (PGIS) framework for evaluating importance of different decision alternatives using different evaluation criteria, and an Android application for collection of field data using mobile and tablet devices . In summary, the simulations of two- and three-blade wind turbines suggested that two-bladed machines could produce comparable annual energy as the three-blade wind turbines but have a lighter tower top weight, which leads to lower cost of energy. In addition, the two-blade rotor configuration potentially costs 20% less than a three blade configuration that produces the same power at the same site. The cost model analysis predicted a potential cost savings of approximately 15% for offshore two-blade wind turbines. The foundation design for a wind turbine in Lake Erie is likely to be driven by ice loads based on the currently available ice data and ice mechanics models. Hence, for Lake Eire, the cost savings will be somewhat smaller than the other lakes in the Great Lakes. Considering the size of cranes and vessels currently available in the Great Lakes, the cost optimal wind turbine size should be 3 MW, not larger. The surveillance data from different monitoring systems suggested that bird and bat passage rates per hour were comparable during heavy migrations in both spring and fall seasons while passage rates were significantly correlated to wind directions and wind speeds. The altitude of migration was higher during heavy migrations and higher over water relative to over land. Notable portions of migration on some spring nights occurred parallel the shoreline, often moving perpendicular to southern winds. The birds approaching the Western basin have a higher propensity to cross than birds approaching the Central basin of Lake Erie and as such offshore turbine development might be a better option further east towards Cleveland than in the Western basin. The high stopover density was more strongly associated with migration volume the following night rather than the preceding night. The processed mean scalar wind speeds with temporal resolutions as fine as 10-minute intervals near turbine height showed that August is the month with the weakest winds while December is the month, which typically has the strongest winds. The ice data suggests that shallow western basin of Lake Erie has higher ice cover duration many times exceeding 90 days during some winters.

17 WIND ENERGY↗

Exploration of multifidelity UQ sampling strategies for computer network applications.

Network modeling is a powerful tool to enable rapid analysis of complex systems that can be challenging to study directly using physical testing. Here, two approaches are considered: emulation and simulation. The former runs real software on virtualized hardware, while the latter mimics the behavior of network components and their interactions in software. Although emulation provides an accurate representation of physical networks, this approach alone cannot guarantee the characterization of the system under realistic operative conditions. Operative conditions for physical networks are often characterized by intrinsic variability (payload size, packet latency, etc.) or a lack of precise knowledge regarding the network configuration (bandwidth, delays, etc.); therefore uncertainty quantification (UQ) strategies should be also employed. UQ strategies require multiple evaluations of the system with a number of evaluation instances that roughly increases with the problem dimensionality, i.e., the number of uncertain parameters. It follows that a typical UQ workflow for network modeling based on emulation can easily become unattainable due to its prohibitive computational cost. In this paper, a multifidelity sampling approach is discussed and applied to network modeling problems. The main idea is to optimally fuse information coming from simulations, which are a low-fidelity version of the emulation problem of interest, in order to decrease the estimator variance. By reducing the estimator variance in a sampling approach it is usually possible to obtain more reliable statistics and therefore a more reliable system characterization. Several network problems of increasing difficulty are presented. For each of them, the performance of the multifidelity estimator is compared with respect to the single fidelity counterpart, namely, Monte Carlo sampling. For all the test problems studied in this work, the multifidelity estimator demonstrated an increased efficiency with respect to MC.

97 MATHEMATICS AND COMPUTING↗

HPC Usage Behavior Analysis and Performance Estimation with Machine Learning Techniques

Most researchers with little high performance computing (HPC) experience have difficulties productively using the supercomputing resources. To address this issue, we investigated usage behaviors of the world s fastest academic Kraken supercomputer, and built a knowledge-based recommendation system to improve user productivity. Six clustering techniques, along with three cluster validation measures, were implemented to investigate the underlying patterns of usage behaviors. Besides manually defining a category for very large job submissions, six behavior categories were identified, which cleanly separated the data intensive jobs and computational intensive jobs. Then, job statistics of each behavior category were used to develop a knowledge-based recommendation system that can provide users with instructions about choosing appropriate software packages, setting job parameter values, and estimating job queuing time and runtime. Experiments were conducted to evaluate the performance of the proposed recommendation system, which included 127 job submissions by users from different research fields. Great feedback indicated the usefulness of the provided information. The average runtime estimation accuracy of 64.2%, with 28.9% job termination rate, was achieved in the experiments, which almost doubled the average accuracy in the Kraken dataset.

Zhang, Hao↗

Computational Fluid Dynamics Modeling of the Fuel Reactor in NETL's 50 kW th Chemical Looping Facility

The National Energy Technology Laboratory (NETL) has explored chemical looping in its 50 kW th facility using a number of oxygen carriers. In this work, the results for methane conversion in the fuel reactor with a hematite iron ore as the oxygen carrier are analyzed. The experimental results are compared to predictions using CPFD's barracuda computational fluid dynamics (CFD) code with kinetics derived from the analysis of fixed bed data. It has been found through analytical techniques from thermal gravimetric analysis data as well as the same fixed bed data that the kinetics for the methane–hematite reaction follows a nucleation and growth or Johnson–Mehl–Avrami (JMA) reaction mechanism. barracuda does not accept nucleation and growth kinetics; however, there is enough sufficient variability of the solids dependence within the software such that the nucleation and growth behavior can be mimicked. This paper presents the method to develop the pseudo-JMA kinetics for barracuda extracted from the fixed bed data and then applies these values to the fuel reactor data to compare the computational results to experimental data obtained from 50 kW th unit for validation. Lastly, a fuel reactor design for near complete conversion is proposed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Determination of anharmonic free energy contributions: Low temperature phases of the Lennard-Jones system

We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available general software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Furthermore, several implications of the method are discussed.

36 MATERIALS SCIENCE↗