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At least 937 records · Page 52

Development of an end state vision to implement digital monitoring in nuclear plants

Transitioning from an onsite Maintenance & Diagnostics Center to cloud-based services offers many new opportunities with computing power and storage, but also new challenges in terms of networking and security. This report will cover everything required for that transition including data processing and uploading to cloud services, feature selection, model creation, and result visualization for decision making. Although there are several other cloud-based services (e.g. Amazon Web Services and Google Cloud), this report explores Microsoft Azure to simplify nomenclature and maintain a consistent focus. Many of the services offered by Microsoft Azure are also available in the other cloud-based services, and their differences have been recorded in other literature. The Azure services most important to a nuclear power plant including networking & security, storage & databases, and Artificial Intelligence (AI) are reviewed here. Networking covers all aspects related to communication to Azure resources including security, privacy, and redundancy. Storage & databases includes data storage, upgrading, patching, backups, and monitoring. The AI services allows the user access to the machine learning (ML) techniques developed with Azure including automated ML, anomaly detection, computer vision, and natural language processing. This report summaries the features, capabilities, and challenges when using cloud-based services in a user-friendly manner.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Poisson_CCD: A dedicated simulator for modeling CCDs

A dedicated simulator, Poisson_CCD, has been constructed which models astronomical CCDs by solving Poisson’s equation numerically and simulating charge transport within the CCD. The potentials and free carrier densities within the CCD are self-consistently solved for, giving realistic results for the charge distribution within the CCD storage wells. The simulator has been used to model the CCDs that are being used to construct the LSST digital camera. The simulator output has been validated by comparing its predictions with several different types of CCD measurements, including astrometric shifts, brighter-fatter induced pixel–pixel covariances, saturation effects, and diffusion spreading. The code is open source and freely available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient Scalable Contact Network Generation from Population Data

Modeling the contacts among a population is critical to understanding the dynamics of a disease outbreak. Contact networks, where nodes are individuals and edges are contacts among them, are used to represent these complex individual-level interactions. In this work, we are given the daily activity schedules of an urban population that represent the activity location and time of individuals in a population during a single twenty four hour period over multiple days. Using collocation to determine contact between individuals, our goal is to extract hourly contact networks from large-scale activity data. We improve upon the existing adjacency matrix-based method by implementing our custom sparse matrix multiplication algorithm. Starting with a Python implementation, we achieve a 1600x speed up in the computation with a fast custom designed sparse matrix multiplier algorithm implemented in the C++ language. This work is central to future parallel designs of the problem.

97 MATHEMATICS AND COMPUTING↗

Draft ASME Code Case to qualify L-PBF 316H material for Section III, Division 5 applications

This report documents the AMMT program’s development and submission of a draft ASME Code Case to qualify Laser Powder Bed Fusion (L PBF) Type 316H stainless steel for Section III, Divi-sion 5 Class A and SM high temperature nuclear applications. It summarizes the technical basis, the comprehensive high temperature mechanical test database assembled between 2023–2026, and the proposed code language and qualification framework submitted to ASME. The work was co-ordinated across multiple national laboratories and leverages prior ASME efforts to integrate additive manufacturing into the Boiler & Pressure Vessel Code. The body of the report describes the experimental database and analysis supporting the Code Case: tensile, creep, fatigue, creep fatigue, and thermal aging tests collected from multiple additive manufacturing sites, machine types, and powder lots, with material processed by a solution anneal heat treatment. The dataset — including both full size and subsized specimens and tests oriented parallel and perpendicular to build direction — shows limited tensile anisotropy, tensile properties comparable to wrought 316H, creep strength within the scatter of wrought material, but markedly reduced creep ductility above about 650 °C associated with rapid σ phase formation in L PBF microstructures. The draft Code Case itself prescribes a staged qualification model (manufacturing process qualification, component qualification, and per build witness testing), treats L PBF components as equivalent to Type 316 weld metal for design and inspection, and requires mechanical, chemical, and metallographic controls tied to ASTM/ISO 52946. Key acceptance criteria include tensile tests within a 90% prediction interval of the AMMT dataset, a creep fatigue screening test adapted from ASME Section III, Division 5, Subsection HB, HBB 2800 but with the cycle acceptance reduced to 100 for L PBF material, and double volumetric inspection of production components. The report concludes that the present data support treating L PBF 316H as analogous to conventional fusion weld metal for Division 5 design and inspection, while highlighting important caveats: the σ phase driven loss of creep ductility above ~650 °C, preliminary indications of enhanced creep fatigue sensitivity in some lots, and remaining gaps in long term aging and additional cyclic testing. Recommended next actions include completing outstanding cyclic and long duration creep/aging tests on the solution annealed condition, supporting inclusion of the 316H chemistry and heat treatment in ASTM/ISO 52946, and continuing engagement with ASME and NRC during balloting and review to enable industry adoption.

Messner, Mark C. (ORCID:0000000200404385)↗

Novel principal component analysis tool based on python for analysis of complex spectra of time-of-flight secondary ion mass spectrometry

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) is a powerful surface analysis tool, which can simultaneously provide elemental, isotopic, and molecular information with part per million (ppm) sensitivity. However, each spectrum may be composed of hundreds of ion signals, which makes the spectra data complex. Principal component analysis (PCA) is a multivariate analysis technique that has been widely used to figure out the variances among samples in ToF-SIMS spectra data analysis and is showing great success in the explanation of complex ToF-SIMS spectra. So far, several software tools have been developed for PCA of ToF-SIMS spectra; however, none of them are freely available. Such a situation leads to some difficulties in extending applications of PCA to various research fields. More importantly, it has long been challenging for common researchers to understand PCA plots and extract chemical differences among samples. In this work, we developed a new and flexible software tool (named “advanced spectra pca toolbox”) based on python for PCA of complex ToF-SIMS spectra along with an easy-to-read manual. It can generate data analysis reports automatically to explain chemical differences among samples, allowing less experienced researchers to easily understand tricky PCA results. Moreover, it is expandable and compatible with artificial intelligence/machine learning functions. Pure goethite and different lignin adsorbed goethite samples were used as a model system to demonstrate our new software tool, proving that our software tool can be readily used in complex spectra data processing. Our new software tool is open-source, convenient, flexible, and expandable. We expect this open-source tool will benefit the ToF-SIMS community.

47 OTHER INSTRUMENTATION↗

A universal implementation of radiative effects in neutrino event generators

Due to the similarities between electron-nucleus (eA) and neutrino-nucleus scattering (νA), eA data can contribute key information to improve cross-section modeling in eA and hence in νA event generators. However, to compare data and generated events, either the data must be radiatively corrected or radiative effects need to be included in the event generators. We implemented a universal radiative corrections program that can be used with all reaction mechanisms and any eA event generator. Our program includes real photon radiation by the incident and scattered electrons, and virtual photon exchange and photon vacuum polarization diagrams. It uses the “extended peaking” approximation for electron radiation and neglects charged hadron radiation. This method, validated with GENIE, can also be extended to simulate νA radiative effects. This work facilitates data-event-generator comparisons used to improve νA event generators for the next-generation of neutrino experiments. Program Title: emMCRadCorr CPC Library link to program files:https://doi.org/10.17632/hmsxg82vnf.1 Developer's repository link:https://github.com/e4nu/emMCRadCorr Licensing provisions: AGPLv3 Programming language:C++ Nature of problem: Radiative effects can significantly modify the event kinematics and the resulting cross-sections. Such effects must be accounted for when comparing event generators to eA data. Existing radiative correction codes are tailored to specific processes and topologies, and are limited to a restricted phase space defined by the spectrometer acceptance. Therefore, a more general approach is required to apply radiative corrections to semi-inclusive and exclusive eA measurements. Solution method: Our program incorporates real photon radiation from both the incident and scattered electrons, as well as virtual photon exchange and photon vacuum polarization effects. It employs the “extended peaking” approximation for electron radiation while neglecting contributions from charged hadron radiation. The code is fully decoupled from event generator codes and can be used for all event generators in the market.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

tapir: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions

The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require equally precise theoretical predictions to make full use of the acquired data. To match the experimental precision, second-, third- and, for certain quantities, even higher-order calculations in perturbative quantum field theory are required. To facilitate such calculations, computer software automating as many steps as possible is required. Yet, each calculation poses different challenges and thus, a high level of configurability is required. In this context we present tapir: a tool for identification, manipulation and minimization of Feynman integral families. It is designed to integrate in toolchains based on the computer algebra system FORM, the use of which is common practice in the field. tapir can be used to reduce the complexity of multi-loop problems with cut-filters, topology mapping, partial fraction decomposition and alike. Program Title:tapir CPC Library link to program files:https://doi.org/10.17632/ptc9t46xyn.1 Developer's repository link:https://gitlab.com/tapir-devs/tapir Licensing provisions: GPLv3 Programming language:python 3, C++ Nature of problem: Multi-loop computations require the automatization of a large number of different tasks related to Feynman integral topologies. Among them are the identification and minimization of integral topologies, partial fraction decomposition of topologies in the case of linearly dependent propagators as well as mapping scalar products of loop momenta to scalar functions. Solution method: The minimization of topologies is performed by comparison of their respective Nickel indices [1], even further minimization utilizes Pak's algorithm [2]. To efficiently map scalar products of loop momenta to scalar functions FORM [3] code is generated. Additional comments including restrictions and unusual features: Minimization based on Pak's algorithm slows down for many lines and scales. A coarser minimization using the Nickel indices, however, is still possible. [1]B. Nickel, D. Meiron, G.A.J. Baker, Compilation of 2-pt and 4-pt graphs for continuous spin model, Report, University of Guelph, 1977.[2]A. Pak, J. Phys. Conf. Ser. 368 (2012) 012049, https://doi.org/10.1088/1742-6596/368/1/012049, arXiv:1111.0868.[3]B. Ruijl, T. Ueda, J. Vermaseren, FORM version 4.2, arXiv:1707.06453, 7 2017.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Toward the Detection of Polyglot Files

Standardized file types play a key role in the development and use of computer software. However, it is possible to confound standardized file type processing by creating a file that is valid in multiple file types. The resulting polyglot (many languages) file can confuse file type identification, allowing elements of the file to evade analysis. This is especially problematic for malware detection systems that rely on file type identification for feature extraction. Although work has been done to identify file types using more comprehensive methods than file signatures, accurate identification of polyglot files remains an open problem. Since malware detection systems routinely perform file type-specific feature extraction, polyglot files need to be filtered out prior to ingestion by these systems. Otherwise, malicious content could pass through undetected. To address the problem of polyglot detection we assembled a data set using the mitra tool. We then evaluated the performance of the most commonly used file identification tools, including file, polydet, binwalk, and TrID. Our analysis demonstrates that existing file type detection tools fail to provide reliable polyglot detection. We then evaluated the ability of a range of machine and deep learning models to detect polyglot files. The most performant models were MalConv2 and Catboost, which demonstrated the highest recall on our data set with 95.16% and 95.45%, respectively. These models outperformed existing methods and could be incorporated into a malware detector’s file processing pipeline to filter out potentially malicious polyglots before file type-dependent feature extraction takes place.

Koch, Luke↗

Toward the Detection of Polyglot Files

Standardized file types play a key role in the development and use of computer software. However, it is possible to confound standardized file type processing by creating a file that is valid in multiple file types. The resulting polyglot (many languages) file can confuse file type identification, allowing elements of the file to evade analysis. This is especially problematic for malware detection systems that rely on file type identification for feature extraction. Although work has been done to identify file types using more comprehensive methods than file signatures, accurate identification of polyglot files remains an open problem. Since malware detection systems routinely perform file type-specific feature extraction, polyglot files need to be filtered out prior to ingestion by these systems. Otherwise, malicious content could pass through undetected. To address the problem of polyglot detection we assembled a data set using the mitra tool. We then evaluated the performance of the most commonly used file identification tools, including file, polydet, binwalk, and TrID. Our analysis demonstrates that existing file type detection tools fail to provide reliable polyglot detection. We then evaluated the ability of a range of machine and deep learning models to detect polyglot files. The most performant models were MalConv2 and Catboost, which demonstrated the highest recall on our data set with 95.16% and 95.45%, respectively. These models outperformed existing methods and could be incorporated into a malware detector’s file processing pipeline to filter out potentially malicious polyglots before file type-dependent feature extraction takes place.

Koch, Lucas↗

Processing Meteorological Data for the CAP-88 PC Model at Los Alamos National Laboratory

The Environmental Protection and Compliance-Compliance Programs (EPC-CP) group at Los Alamos National Laboratory (LANL) uses the Clean Air Act Assessment Package 1988 (CAP-88, Littleton 2020) PC model (Version 4.1) to estimate radiological doses for a set of areal sectors surrounding a release location, in order to satisfy the Environmental Protection Agency (EPA) National Emission Standards for Hazardous Air Pollutants (NESHAP) dose calculation requirement in 40 CFR 61 Subpart H. Among several types of data that must be prepared for CAP-88 input is a text file of meteorological data (“WIND” file), consisting of the joint frequency of wind direction, wind speed, and atmospheric stability categories. EPC-CP produces customized WIND files by running a CAP-88 utility program on a user generated text file of wind data in a different format, known as a STability ARray (STAR) file (Turner, 1964). At LANL, EPC-CP meteorologists prepare customized STAR files with data over desired time periods at selected meteorological towers. A custom program written in Precision Visuals -Workstation Analysis and Visualization Environment (PV-WAVE), a commercial Fortran-like language, is used to read LANL meteorological data and write a STAR file; the executable filename is “Star.out”. However, the outdated PV-WAVE utility program is being phased out by EPC-CP, due to the inefficient process to run it and an inability to modify the code. To preserve the ability to create customized meteorological data for CAP-88 in a way that will be easy to use and maintain, a new replacement utility program, written in the Python programming language, has been developed. The new, improved program reads a data file from any LANL meteorological tower, and at each desired observation time, determines the wind direction, wind speed, and stability categories defined in the CAP-88 documentation. The frequencies of all combinations of the three sets of categories are calculated and written to a file in the STAR format, which can later be converted to a WIND file for input into CAP-88.

54 ENVIRONMENTAL SCIENCES↗

Rational design of heterogeneous single-site catalysts via surface organometallic chemistry

Single-site heterogeneous catalysts offer an attractive route to unite the molecular precision of homogeneous catalysis with the durability and practical advantages of solids. Surface organometallic chemistry (SOMC) provides a particularly powerful strategy for this purpose by grafting molecular precursors onto tailored surfaces and converting support functionalities into ligand environments for isolated metal centers. As a result, SOMC brings the language and logic of coordination chemistry to heterogeneous catalysis, where the support becomes an integral part of the active site coordination sphere. This Review surveys recent progress in the rational design of SOMC-derived single-site catalysts, with emphasis on synthetic routes, post synthetic transformations, and the deliberate tuning of catalytic behavior through metal-support interactions. Discussions are made on how support identity, hydroxyl topology, acidity, and redox activity shape the geometry, electronic structure, and oxidation state of supported metal sites, as well as how these factors determine activity, selectivity, and stability. We also examine a central limitation of these systems: despite their molecularly informed design, supported single sites often exist as structurally distributed ensembles rather than uniform species, particularly on amorphous supports. This site heterogeneity, along with catalyst dynamics under operating conditions, remains a major barrier to definitive structure-activity relationships. Therefore, emerging approaches that combine advanced characterization, first-principles modeling, ensemble kinetics, and machine learning to resolve active-site structure and guide catalyst development are highlighted. Together, these advances position SOMC as a versatile coordination chemistry framework for the predictive design of heterogeneous catalysts with well-defined molecularly tailored active sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The high intensity diffractometer for residual stress analysis (HIDRA), a third generation residual stress mapping neutron diffractometer at the high flux isotope reactor

This paper describes the hardware and software upgrades, operation, and performance of the high intensity diffractometer for residual stress analysis (HIDRA) instrument, a residual stress mapping neutron diffractometer located at the High Flux Isotope Reactor at Oak Ridge National Laboratory in Oak Ridge Tennessee, USA. Following a major upgrade in 2018, the new instrument has a single 3 He multiwire 2D 30 × 30 cm 2 position sensitive detector, yielding a field of view of 17° 2θ. Further, the increase in the field of view (from 4° 2θ) from the previous model instrument has contributed to the tremendous improvement in the out of plane solid angle such that the 3D count rate could be obtained easily. Accordingly, the hardware, software, Data Acquisition System (DAS), and so on have also been updated. Finally, all these enhanced features of HIDRA have been ably demonstrated by conducting multi directional diffraction measurements in the quenched 750-T74 aluminum, and the evolved and improved strain/stress mappings are presented.

3D printing↗

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗

The black hole interior from non-isometric codes and complexity

Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of “non-isometric codes protected by computational complexity”. We show that many previous ideas, such as the existence of a large number of “null states”, a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, “state-dependent/state-specific” operator reconstruction, and the “simple entropy” approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Gender in Mineral Names

Minerals are the fundamental constituents of Earth, and mineral names appear in scientific literature for disciplines including geology, chemistry, materials science, biology, and medicine, among others. Choosing a name is the full responsibility of the authors of new mineral proposals submitted to the International Mineralogical Association (IMA). Scientific nomenclature and its traditions have evolved over time and, consequently, mineral names track changes in the landscape of mineralogy with respect to language, technology, and culture. To evaluate these changes, the namesake information for all 5896 minerals approved by the IMA or ‘grandfathered’ into use as of December 2022 was recorded and categorized within a workable database. The compiled information yields diverse insights into the intersection of science and culture and could also be used to project future trends. In this study, we used the name database to investigate gender diversity among mineral eponyms. More than half (c. 54%) of all mineral species are named after people, the identities of whom are largely a reflection of the people that have historically been involved, in one way or another, in the geosciences and in the mining industry. Of the 2738 people with minerals named for them, approximately 6.1% are (interpreted to be) women. Nearly all minerals named for women were named during the last sixty years, although the rate of growth in the year-on-year percentage of women among new mineral namesakes has slowed since about 1985. If current and historical trends hold, our model predicts that women will not comprise more than about 10.35% of newly established mineral namesakes in future years. The representation of women among mineral namesakes also differs starkly among countries. For example, Russians comprise 43.11% of women with minerals named for them, but account for only 15.12% of all eponyms. However, there are additional disparities beyond the proportions of namesakes. For scientists who were alive when a mineral was named for them, women were an average of 3.74 years older than men when evaluated over the same timespan (1954–2022). These results demonstrate that gender-based disparities are imprinted into current mineral nomenclature and indicate that gender parity among new mineral namesakes is impossible without unprecedented changes in the upstream demographics that are most likely to affect naming trends.

58 GEOSCIENCES↗

Pairwise Multiparticle States and the Monopole Unitarity Puzzle

We suggest a novel resolution for a decades old mystery-what happens when a positron scatters off a minimal grand-unification-theory monopole in an s wave, a puzzle first discussed by Callan in 1983. Using the language of on shell amplitudes and pairwise helicity we suggest that the final state contains two up quarks and a down quark in an entangled "pairwise" multiparticle state-the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our new pairwise state appears only in more than two dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Space-Time Fluid (Unabridged)

Purpose: This essay is a retelling of general relativity in a language in which space-time geometry is expressed as a fluid. This trivial and useful reformulation gives 1) a non-perturbative covariant description of cosmological inhomogeneities and 2) a simple formula describing how cosmic inhomogeneities are generated on super-horizon scales. Methods: Equating the Ricci curvature with the associated matter stress-energy gives a description of space-time geometry in terms of fluid properties. These locally measurable (covariant) non-perturbative quantities are in some ways superior to commonly used "gauge invariant" quantities. The dynamics of a quantity (kurvature) which describes cosmological inhomogeneities is described in detail. A detailed comparison is made of space-time fluid dynamics with that of a classical (Newtonian physics) fluid. Results: The fluid lexicon permits an unambiguous definition of the velocity of space-time. The evolution of the space-time fluid is in many ways identical with that of the classical fluid when expressed in Lagrangian coordinates. Kurvature is a measure of the specific binding energy of the fluid and is a most useful covariant measure of cosmological inhomogeneities. For plausible matter models kurvature will increase, even on super-horizon scales, due to non-linear hydrodynamic effects rather than gravity. This phenomena is also exhibited by classical fluids. Conclusion: The space-time fluid representation of geometrodynamics gives a simple and useful description of the evolution of cosmological inhomogeneities.

Stebbins, Albert [Fermilab] (ORCID:000000023807725↗

CEGANN: CRYSTAL EDGE GRAPH ATTENTION NEURAL NETWORK

SF-22-156 Machine learning (ML) models and applications in materials design and discovery typically involve the use of feature representations or descriptors followed by a learning algorithm that maps them to user desired properties of interest. Most popular mathematical formulation-based descriptors are not unique across atomic environments and suffer from transferability issues across different application domains and/or material classes. The CEGANN code provides a unified interface to facilitate material characterization across materials across multiple scales (from atomic to mesoscale) and diverse classes of materials ranging from metals oxides, non-metals, and even hierarchical materials such as zeolites and semi ordered materials such as mesophases. CEGANN implements a Graph Attention Network (GAT) type convolution architecture. The details of network architecture can be found in the paper https://doi.org/10.48550/arXiv.2207.10168. The software comes with pretrained examples and dataset for the classification of the following representative systems: (1) Structure-level representation such as space group (2) Structural dimensionality (e.g., bulk, 2D, clusters etc.) (3) Grain boundary identification (4) Nucleation and growth of a zeolite polymorph (5) Characterization of binary mesophases and their phase transitions (6) Growth of ice. The code is written in python programming language.

CHAN, HENRYT↗