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Prediction of Redox Potentials for the Late Actinides Cm to Lr Using Electronic Structure Methods

Our previously developed computational method for calculating the aqueous redox potentials of the early actinides has been extended to the later elements in the actinide series: Cm, Bk, Cf, Es, Fm, Md, No, and Lr in multiple oxidation states. These calculations were performed using density functional theory with small-core pseudopotentials and their associated basis sets. Solvation effects were considered via a supermolecule-continuum approach, with 30 water molecules representing two solvation shells. Both the COSMO and SMD implicit solvation models were utilized. The structural parameters and hydration numbers for Cm(III), Bk(III), Bk(IV), and Cf(III) are in reasonable agreement with the available experimental data. For redox processes involving atomic cations in solution, the B3LYP/COSMO approach predicted redox potentials to within ±0.2 V of experiment for most redox couples, consistent with our prior work. Inclusion of spin-orbit corrections in specific redox pairs, especially those with the later actinides in high oxidation states, yields improved results relative to calculations including only scalar-relativistic corrections. The An +m /An(0) redox potentials were calculated using a Born-Haber cycle incorporating sublimation, ionization, and hydration energies. Due to a lack of experimental data, three sets of ionization energies were used for the Born-Haber cycle. The calculated An(III/0) potentials showed better agreement with experimental data when using the COSMO solvation model and the test set comprising the NIST recommended ionization energies. Furthermore, the Md(II/0) potential was better described with the SMD model, whereas No(II/0) was not well described by all methods. Finally, the computational approach was able to predict redox potentials that for most cases agreed with the current available experimental or estimated data.

Actinides

System, method, and computer program for creating geometry-compliant lattice structures

A system and method of creating a shape-conforming lattice structure for a part formed via additive manufacturing. The method includes receiving a computer model of the part and generating a finite element mesh. A lattice structure including a number of lattice cellular components may also be generated. Some of the mesh elements of the finite element mesh may be deformed so that the finite element mesh conforms to the overall shape of the part. The lattice structure may then be deformed so that the lattice structure has a cellular periodicity corresponding to the finite elements of the finite element mesh. In this way, the part retains the benefits of its overall shape and the benefits of lattice features without introducing structural weak points, directional stresses, and other structural deficiencies.

Vernon, Gregory John

Data-driven equation-free dynamics applied to many-protein complexes: The microtubule tip relaxation

Microtubules (MTs) constitute the largest components of the eukaryotic cytoskeleton and play crucial roles in various cellular processes, including mitosis and intracellular transport. The property allowing MTs to cater to such diverse roles is attributed to dynamic instability, which is coupled to the hydrolysis of GTP (guanosine-5'-triphosphate) to GDP (guanosine-5'-diphosphate) within the β-tubulin monomers. Understanding the equilibrium dynamics and the structural features of both GDP- and GTP-complexed MT tips, especially at an all-atom level, remains challenging for both experimental and computational methods because of their dynamic nature and the prohibitive computational demands of simulating large, many-protein systems. This study employs the “equation-free” multiscale computational method to accelerate the relaxation of all-atom simulations of MT tips toward their putative equilibrium conformation. Using large MT lattice systems (14 protofilaments × 8 heterodimers) comprising ~21-38 million atoms, we applied this multiscale approach to leapfrog through time and nearly double the computational efficiency in realizing relaxed all-atom conformations of GDP- and GTP-complexed MT tips. Commencing from an initial 4 μs unbiased all-atom simulation, we interleave coarse projective “equation-free” jumps with short bursts of all-atom molecular dynamics simulation to realize an additional effective simulation time of 1.875 μs. Our 5.875 μs of effective simulation trajectories for each system expose the subtle yet essential differences in the structures of MT tips as a function of whether β-tubulin monomer is complexed with GDP or GTP, as well as the lateral interactions within the MT tip, offering a refined understanding of features underlying MT dynamic instability. Furthermore, the approach presents a robust and generalizable framework for future explorations of large biomolecular systems at atomic resolution.

Wu, Jiangbo [University of Chicago, IL (United Sta

Finding MIDDLE Ground: Scalable and Secure Distributed Learning

Edge computing methods allow devices to efficiently train a high-performing, robust, and personalized model for predictive tasks. However, these methods succumb to privacy and scalability concerns such as adversarial data recovery and expensive model communication. Furthermore, edge computing methods unrealistically assume that all devices train an identical model. In practice, edge devices have varying computational and memory constraints which may not allow certain devices to have the space or speed to train a specific model. To overcome these issues, we propose MIDDLE: a model independent distributed learning algorithm which allows heterogeneous edge devices to assist each other’s training while communicating only non-sensitive information. MIDDLE unlocks the ability for edge devices, regardless of computational or memory constraints, to assist each other even with completely different model architectures. Furthermore, MIDDLE does not require model or gradient communication which greatly reduces communication size and time. We prove that MIDDLE attains the optimal convergence rate O(1/sqrt(TM)) of stochastic gradient descent for convex and non-convex smooth optimization (for total iterations T and batch size M). Finally, our experimental results demonstrate that MIDDLE (even in non-IID data settings) attains robust and high-performing models without model or gradient communication.

Bornstein, Marc I.

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Capturing many-body correlation effects with quantum and classical computing

Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects requires formalisms that provide a hierarchical infrastructure of approximations. These approximations lead to an increased overhead in classical computing methods and, therefore, decisions regarding the ranking of approximations and the quality of results must be made on purely numerical grounds. The emergence of quantum computing methods has the potential to change this situation. Here, in this study, we demonstrate the efficiency of the quantum phase estimator (QPE) in identifying core-level states relevant to x-ray photoelectron spectroscopy. We compare and validate the QPE predictions with exact diagonalization and real-time equation-of-motion coupled-cluster formulations, which are some of the most accurate methods for states dominated by collective correlation effects.

74 ATOMIC AND MOLECULAR PHYSICS

Harnessing Quantum Computing for Energy Materials: Opportunities and Challenges

Developing high-performance materials is critical for diverse energy applications to increase efficiency, improve sustainability and reduce costs. Classical computational methods have enabled important breakthroughs in energy materials development, but they face scaling and time-complexity limitations, particularly for high-dimensional or strongly correlated material systems. Quantum computing (QC) promises to offer a paradigm shift by exploiting quantum bits with their superposition and entanglement to address challenging problems intractable for classical approaches. This Perspective discusses the opportunities in leveraging QC to advance energy materials research and the challenges QC faces in solving complex and high-dimensional problems. We present cases on how QC, when combined with classical computing methods, can be used for the design and simulation of practical energy materials. We also outline the outlook for error-corrected, fault-tolerant QC capable of achieving predictive accuracy and quantum advantage for complex material systems.

Algorithms

Basic Energy Sciences Roundtable: Foundational Science to Accelerate Nuclear Energy Innovation

Energy security, availability, and reliability are among the greatest challenges facing the nation and the planet. An abundant potential source of energy resides in the fundamental atomic building blocks of the universe in the form of nuclear fission and fusion reactions. In fact, energy from nuclear fission currently provides the majority of the world’s zero-carbon electricity, and future fusion energy systems offer great promise; carbon-free nuclear energy technologies can be key to the world’s decarbonized energy future. Although contemporary fission systems use well-established technologies to supply safe and efficient baseload power, they could be more fuel efficient and less costly. Moving beyond massive light-water fission reactors to a variety of advanced nuclear systems—which will vary in size and operate in extremes of temperature, corrosivity, and other parameters—will place stringent conditions on materials and chemical systems. New demands will be placed on the coolants and solvents, the materials, and the monitoring tools used in these reactors. Fusion-based nuclear energy will require superior materials to withstand extremely high temperatures, plasma exposure, radiation damage, and implanted gases. The advantages associated with these new fission and fusion technologies will be realized only through continued advancements in the fundamental science underpinning our knowledge of the physics and chemistry of nuclear systems gained via improved experimental and computational methods. In July 2022, the U.S. Department of Energy’s Office of Basic Energy Sciences—in coordination with the Offices of Nuclear Energy, Fusion Energy Sciences, and Advanced Scientific Computing Research—held a virtual roundtable titled “Foundational Science to Accelerate Nuclear Energy Innovation” to discuss the scientific and technical barriers for advanced nuclear energy systems. Five priority research opportunities were identified to address these scientific and technical challenges and to accelerate progress toward the realization of next-generation fusion and fission energy systems. The foundational science gaps inhibiting the advancement of nuclear energy technologies are identified and tackled in five priority research opportunities. These opportunities pave the way to accelerate the development and ultimately the adoption of new nuclear energy systems. They include the fundamental aspects of ion-electron interactions; novel properties of next-generation coolants and solvents; interfacial dynamics, not only in solids, but in other aspects of nuclear reactors; novel operando and in situ monitoring and sensing; and artificial intelligence to accelerate condensed phases discovery. Building on the foundation established by previous Basic Energy Sciences workshops, these opportunities encompass recent advances in fundamental knowledge and focus on the experimental and computational methods needed to resolve major technical challenges for nuclear energy technologies. Through developing fundamental scientific insight as well as pushing the frontiers of modeling complex systems and probing the operation of materials and chemical systems in extreme environments, research motivated by the priorities identified here will further develop the promise, potential, and utilization of nuclear energy for a clean energy future.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Brochure for the DOE Office of Science Workshop on Envisioning Frontiers in AI and Computing for Biological Research

In February of 2025 a joint ASCR/BER workshop was held to identify key transformational research directions for understanding biology using artificial intelligence (AI), digital twins and high-performance (HPC) computational methods to facilitate scientific discovery and innovation in support of the Department of Energy mission. AI technologies offer exciting new groundbreaking methods to analyze large volumes of complex biological data, thereby greatly accelerating the ability to understand, predict, and design biological processes for beneficial purposes. In the laboratory, the bridging of AI-enabled automated experimental technologies, HPC and digital twins will provide potent tools for researchers to explore the fundamental nature of biology and harness its inherent metabolic potential for a variety of beneficial purposes. The focus of this workshop was on how high-performance computational methods can impact this objective by exploring digital twins, foundational models, and data-driven approaches with applications to advance automated laboratory experiments, modeling of complex living systems and engineering new functions into plants and microbial systems relevant to DOE mission. Workshop attendees with expertise in plant science, microbiology, mathematics, computer science, and AI assessed the current state of the science, trends, and AI challenges at the interface of plant and microbial systems biology and computational science to identify opportunities for high-impact research. This collaborative effort capitalized on ASCR's advancements in applied mathematics, computer science, and Exascale systems, and BER's expertise in basic genomics-enabled research on DOE relevant plant and microbial systems. The workshop culminated in four key priority research directions to guide future research and development within DOE Office of Science programs.

59 BASIC BIOLOGICAL SCIENCES

An eigenvalue-based method for computing the relaxed pressure in compressible multiphase flow with N phases

The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.

Eigenvalue algorithm

Summary Report of the FY24 DOE Contributions to the GIF VHTR CMVB

The Generation-IV Forum (GIF) Very-High-Temperature Reactor-Computational Methods Validation and Benchmark (VHTR-CMVB) initiative, involving organizations from Korea Atomic Energy Research Institute (KAERI) (South Korea), Institute of Nuclear and New Energy Technology of Tsinghua University (INET) (China), U.S. Department of Energy (DOE) (U.S.), Joint Research Centre (JRC) (Europe), and Japan Atomic Energy Agency (JAEA) (Japan), is dedicated to the verification and validation of tools for High-Temperature Gas-Cooled Reactors (HTGRs) analysis, using data shared by Computational Methods Validation and Benchmark (CMVB) signatories. For FY24, the US DOE CMVB has committed to several critical activities. Under WP1, led by the US, the integration of the High Temperature Gas Cooled Reactor - Pebble-Bed Module (HTR-PM) Phenomena Identification and Ranking Table (PIRT) into the comparative PIRT is progressing, with a new draft of the comparison tables issued earlier this year and currently being utilized by INET for their contribution. Neutronic validation efforts under WP3 include the preparation of the burnup analysis benchmark, preliminary calculations, and the development of reference models and results. In WP2, a validation exercise for hot gas mixing in the lower plenum of HTR-PM is in progress, using experimental data from INET (China) to validate modeling approaches. A model of the experimental facility has been developed using StarCCM+, with initial calculations slated for presentation at the GIF CMVB meeting this fall. Another WP2 activity focuses on validating numerical models for air-cooled Reactor Cavity Cooling System (RCCS) with experimental data from the Wisconsin Madison RCCS facility. A high-fidelity model, developed using NEK-RS, is currently being validated with available data from a low power forced convection test. These efforts are aimed at enhancing and confirming the accuracy of HTGR analysis tools, ensuring their alignment with experimental data and regulatory requirements.

22 GENERAL STUDIES OF NUCLEAR REACTORS

PDB-IHM: A System for Deposition, Curation, Validation, and Dissemination of Integrative Structures

Structures of many large biomolecular assemblies are now being determined using integrative approaches. In these approaches, information derived from multiple experimental and computational methods is combined to compute three-dimensional structures of multi-protein complexes and other macromolecular machines. A standalone prototype data resource for integrative structures called PDB-Dev was built, based on recommendations of the Integrative and Hybrid Methods (IHM) Task Force of the Worldwide Protein Data Bank (wwPDB). This effort included developing data standards and software tools for collecting, curating, validating, visualizing, archiving, and disseminating integrative structures that span diverse spatiotemporal scales and conformational states. Mechanisms have been created to validate integrative structures based on the experimental data underpinning them. Building upon this foundational framework, PDB-Dev has been further expanded to handle large dynamic macromolecular systems and integrative structures that combine, for example, experimental restraints with atomic coordinates computed by machine learning algorithms. Data standards and supporting tools have also been extended to capture information about biomolecular dynamics, such as conformational transitions and related kinetic data derived from biophysical methods. Recently, PDB-Dev was unified with the PDB archive and rebranded as PDB-IHM (pdb-ihm.org), further promoting FAIR (Findable, Accessible, Interoperable, and Reusable) principles of data stewardship for integrative structural biology.

IHMCIF

An Investigation of Thermal Properties of 2D Materials [Dissertation]

Studying the thermal conductivity of 2D materials is important due to the applications of 2D materials in fields such as thermal management, thermoelectricity, renewable energy, and sensors. As such, measurements of the thermal conductivity of these 2D materials become important to measure. Thermal conductivity is often difficult to measure for 2D materials due to their atomically thin nature and many experimental methods for doing so requiring contact with the sample, which can alter the thermal properties. A non-contact method for calculating the thermal conductivity of 2D materials supported on substrates in order to model the thermal conductivity of 2D materials for devices, is proposed and experimentally performed in this dissertation. The optothermal Raman technique is a useful non-contact diagnostic technique useful in determining the thermal conductivity of 2D materials. The optothermal Raman typically does not account for heat losses due to convection or radiation or substrate resistance, which are shown to be important factors to consider when developing an optothermal Raman model. Additionally, the calculation of the interfacial thermal conductance between the bottom surface of the sample and the top surface of the substrate, plays an important role in determining the final value of the thermal conductivity of a supported sample, and will yield differing results based on whether or not the conductance is calculated using an approach such as the Diffuse Mismatch Model (DMM) or calculated directly by varying the laser heating profile (usually done by changing the laser objective). This is shown to be the case for both graphene on Ni, graphene on Cu, and SnSe 2 on Cu. In addition to experimentally calculating the thermal conductivity of a 2D material with the optothermal Raman technique, the thermal conductivity of 2D materials can also be calculated using computational methods. The three-phonon method is a method which can be used to simulate phonon scattering processes and determine the thermal conductivity of semiconductors, wherein phonon scattering is the dominant mechanism which determines the thermal conductivity. The three-phonon method uses relaxation times for phonon scattering with other phonons, electrons, and other material system elements, such as isotopes or material defects, in order to create a single-mode relaxation time approximation (SMRTA), which is used to calculate the final value of the thermal conductivity. An important consideration when determining the thermal conductivity of a 2D material using this method is the device geometry, which is reflected in this work as the phonon-boundary scattering relaxation time. This inclusion is important along with the inclusion of phonon-electron scattering in accurately determining the thermal conductivity of a 2D material. In both the optothermal Raman experiments and the three-phonon method computations, strain is shown to have a demonstrable effect on the thermal conductivity of 2D materials. When a 1.1% strain was applied to the mechanical properties of SnSe, the three-phonon processes yielded a lower thermal conductivity than the no-strain case. For the optothermal Raman experiments, the strain induced in the Cu substrate and transferred to a single-layer graphene (SLG) sample yields a trend where the thermal conductivity of the SLG decreases with respect to strain applied. In the case where the interfacial thermal conductance was calculated directly, the conductance increased with respect to strain applied. This presents strain as a reliable and viable method for tuning the thermal properties of 2D materials for device applications.

36 MATERIALS SCIENCE

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING

Modeling Pb(II) Adsorption on Mineral Surfaces: Bridging Density Functional Theory and Experiment with Thermodynamic Insights

Despite decades of work on aqueous lead (Pb) adsorption on a-Fe2O3 (hematite) and a-Al2O3 (alumina), gaps between measurements and modeling obscure molecular-level understanding. Achieving well-matched geometries between theory and experimental for mineral-water interfaces is a hurdle, as surface functional group type and distribution must be accounted for in determining mechanisms. Additionally, computational methods that can describe the substrate are often not appropriate to capture aqueous effects. Progress requires focusing on well-studied and relevant systems, such as key facets (001),(012), and (110) of hematite and alumina, and ubiquitous contaminants such as aqueous Pb. In the past, bulk-parametrized bond-valence principles were used to rationalize Pb(II) adsorption trends. These approaches can break down at surfaces, where flexible bonding environments and adsorption-induced surface relaxations play a critical role. Here, we adapt and apply a density functional theory (DFT) and thermodynamics framework, integrating DFT-calculated energies with experimental data and electrochemical principles, to predict Pb(II) adsorption. Our model results capture trends across the full set of surfaces and predict that inner-sphere Pb(II) sorption on (001) alumina varies from unfavorable to weakly favorable across a range of pH conditions. This aligns with experiment insights that Pb(II) interacts at that surface through outer-sphere interactions. Extending to Fe(II) adsorption, we demonstrate a coverage-dependent site preference, potentially explaining disorder in overlayers grown by the oxidative adsorption of Fe(II) on hematite (001).

lead contamination

Metal additive manufacturing simulation across length, time, and computing scales

Metal additive manufacturing (AM) offers a unique opportunity for production of advanced materials and complex geometries. However, variability in microstructure and properties challenges conventional approaches to design, process optimization, qualification, and materials selection. Modeling and simulation can improve understanding of AM processing and materials, but also poses major challenges for existing computational methods. Simultaneously, modern scientific computing hardware has become increasingly complex, most notably with the adoption of hybrid architectures such as Graphical Processing Units (GPUs). If appropriately utilized, emerging computational capabilities provide an opportunity to reveal new insight into AM processing and the resulting material structure and properties. In this review we describe the computational AM landscape, identify critical gaps, and highlight opportunities to impact the development and application of AM. First, the requirements and challenges of representative AM problem statements will be defined. Here, these problems range from scientific studies to industrial applications and are designed to capture the breadth of challenges facing the AM community. Next, the current state of AM modeling and simulation is evaluated, broken down by enabling hardware and software, process simulation, microstructure simulation, and property simulation. Each section describes the diversity of simulation approaches and associated trade-offs in physical fidelity and computational expense. Each area is then assessed based on their suitability and readiness for current and developing computational architectures. Lastly, the greatest opportunities for future research and application are highlighted, including gaps in modeling capabilities, opportunities for near-term application, and key scientific challenges.

additive manufacturing

System and method for computed axial lithography (CAL) for 3D additive manufacturing

In one aspect the present disclosure relates to a system for forming a three dimensional (3D) object from a volume of photo-responsive material contained within a material container. A plurality of optical projection subsystems are adapted to be arranged at least partially circumferentially around a material container containing the volume of photo-responsive material, and are controlled by a controller. The optical projection subsystems direct optical projections at a plurality of angles θ through the volume of photo-responsive material. The optical projections are further directed about a z axis extending through the volume of photo-responsive material. The plurality of optical subsystems are further controlled by the controller to provide each of the optical projections with a calculated three-dimensional intensity distribution acting over a fixed temporal exposure period, which is sufficient to at least one of cure or remove selected portions of the volume of photo-responsive material, and leave other portions unmodified, to form a desired 3D part.

Kelly, Brett