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At least 649 records · Page 36

Aneutronic Fusion in Collision of Oppositely Directed Plasmoids

Tri-Alpha and Helion energy companies have proposed an approach as the near future fusion reactor. The method used in this kind of reactor for attaining high fusion yield is based on the formation and throwing of two plasmoids toward each other. In this study, the optimized reaction rate for interpenetration of two head on colliding plasmoids is investigated. Calculations are performed by supposing the velocity of plasmoids ions as Maxwellian distribution function. Fusion output-to-input power ratio (Q factor) was computed by evaluation of the velocity-averaged cross sections and also ion−electron and ion−ion Coulomb power loss. A fluid model including a computational code has been used for the precise calculations of fusion power balance. The optimum interpenetration velocity and plasmoids parameters required to reach the ignition are studied for aneutronic fusion fuels, such as p–{sup 11}B and D–{sup 3}He, as well as D−T and D−D fuels. The results of investigation show that the breakeven is attainable in specific collision velocity and plasma temperature for each fuel. Also, the plasma density has to be around 10{sup 20} ions/cm{sup 3}.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Virtual prototyping of liquid metal blanket performance in fusion pilot plant

Liquid metal blanket is a dominant design option for the next step fusion devices responsible for harvesting energy from fusion reaction, and simultaneously producing fuel for the same reaction through tritium breeding. Liquid metal blankets introduce additional complexity to the design due to fluid motion, fluid structure interaction, and magnetohydrodynamic (MHD) effects arising from the motion of the conducting fluid through the magnetic field. They are also directly affected by the plasma heat flux and neutronic fluence. PPPL is currently developing a virtual prototyping system for numerical analysis of the liquid metal blankets for future fusion devices. The system has a customized 3D computational fluid dynamics (CFD) code in its core, allowing MHD flow and conjugate heat transfer analysis in blankets fluids and solids. The code was successfully used before for dual coolant blanket analysis [A. Khodak et al., Fusion Eng. and Des. 137 (2018)]. Recently the same code was modified to allow verified simulation of MHD flows at high Hartmann numbers of several thousand typical for blanket applications. CFD code receives volumetric heat source distribution from the neutronic analysis based on MCNP code. In addition, direct tritium breeding simulation will be performed allowing optimization of the blanket performance. 2D axisymmetric version of neutronics code will be used for rapid optimization, with 3D version employed for detailed analysis. The surface heat distribution on the plasma facing wall will be defined by the software HEAT allowing 3D modeling of the heat flux based on the magnetic field distribution including gyro-orbit effects. Results of thermal analysis are imported into structural analysis code also included in the system. Finally, direct import of CAD geometry will be used for analyzing all components and as a result design option can be efficiently optimized.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Integrated Radiation Transport and Nuclear Fuel Performance for Assembly-Level Simulations

The Advanced Multi-Physics (AMP) Nuclear Fuel Performance code (AMPFuel) is focused on predicting the temperature and strain within a nuclear fuel assembly to evaluate the performance and safety of existing and advanced nuclear fuel bundles within existing and advanced nuclear reactors. AMPFuel was extended to include an integrated nuclear fuel assembly capability for (one-way) coupled radiation transport and nuclear fuel assembly thermo-mechanics. This capability is the initial step toward incorporating an improved predictive nuclear fuel assembly modeling capability to accurately account for source-terms, such as neutron flux distribution, coolant conditions and assembly mechanical stresses, of traditional (single-pin) nuclear fuel performance simulation. A novel scheme is introduced for transferring the power distribution from the Scale/Denovo (Denovo) radiation transport code (structured, Cartesian mesh with smeared materials within each cell) to AMPFuel (unstructured, hexagonal mesh with a single material within each cell), allowing the use of a relatively coarse spatial mesh (10 million elements) for the radiation transport and a fine spatial mesh (3.3 billion elements) for thermo-mechanics with very little loss of accuracy. With this novel capability, AMPFuel was used to model an entire 1717 pressurized water reactor fuel assembly with many of the features resolved in three dimensions (for thermo-mechanics and/or neutronics). A full assembly calculation was executed on Jaguar using 40,000 cores in under 10 hours to model over 160 billion degrees of freedom for 10 loading steps. The single radiation transport calculation required about 50% of the time required to solve the thermo-mechanics with a single loading step, which demonstrates that it is feasible to incorporate, in a single code, a high-fidelity radiation transport capability with a high-fidelity nuclear fuel thermo-mechanics capability and anticipate acceptable computational requirements. The results of the full assembly simulation clearly show the axial, radial, and azimuthal variation of the neutron flux, power, temperature, and deformation of the assembly, highlighting behavior that is neglected in traditional axisymmetric fuel performance codes that do not account for assembly features, such as guide tubes and control rods.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Comparison of Radiation Models for a Turbulent Piloted Methane/Air Jet Flame: A Frozen-Field Study

Numerical modeling of radiative transfer in nongray reacting media is a challenging problem in computational science and engineering. The choice of radiation models is important for accurate and efficient high-fidelity combustion simulations. Different applications usually involve different degrees of complexity, so there is yet no consensus in the community. In this paper, the performance of different radiative transfer equation (RTE) solvers and spectral models for a turbulent piloted methane/air jet flame are studied. The flame is scaled from the Sandia Flame D with a Reynolds number of 22,400. Three classes of RTE solvers, namely the discrete ordinates method, spherical harmonics method, and Monte Carlo method, are examined. The spectral models include the Planck-mean model, the full-spectrum k-distribution (FSK) method, and the line-by-line (LBL) calculation. The performances of different radiation models in terms of accuracy and computational cost are benchmarked. The results have shown that both RTE solvers and spectral models are critical in the prediction of radiative heat source terms for this jet flame. The trade-offs between the accuracy, the computational cost, and the implementation difficulty are discussed in detail. The results can be used as a reference for radiation model selection in combustor simulations.

David, Chloe↗

A matrix-algebraic formulation of distributed-memory maximal cardinality matching algorithms in bipartite graphs

We describe parallel algorithms for computing maximal cardinality matching in a bipartite graph on distributed-memory systems. Unlike traditional algorithms that match one vertex at a time, our algorithms process many unmatched vertices simultaneously using a matrix-algebraic formulation of maximal matching. This generic matrix-algebraic framework is used to develop three efficient maximal matching algorithms with minimal changes. The newly developed algorithms have two benefits over existing graph-based algorithms. First, unlike existing parallel algorithms, cardinality of matching obtained by the new algorithms stays constant with increasing processor counts, which is important for predictable and reproducible performance. Second, relying on bulk-synchronous matrix operations, these algorithms expose a higher degree of parallelism on distributed-memory platforms than existing graph-based algorithms. We report high-performance implementations of three maximal matching algorithms using hybrid OpenMP-MPI and evaluate the performance of these algorithm using more than 35 real and randomly generated graphs. On real instances, our algorithms achieve up to 200 × speedup on 2048 cores of a Cray XC30 supercomputer. Even higher speedups are obtained on larger synthetically generated graphs where our algorithms show good scaling on up to 16,384 cores.

97 MATHEMATICS AND COMPUTING↗

Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations

The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Simulation of a non-equilibrium helium plasma bullet emerging into oxygen at high pressure (250–760 Torr) and interacting with a substrate

A two-dimensional computational study of a plasma bullet emanating from a helium gas jet in oxygen ambient at high pressure (250–760 Torr) was performed, with emphasis on the bullet interaction with a substrate. Power was applied in the form of a trapezoidal +5 kV pulse lasting 150 ns. A neutral gas transport model was employed to predict the concentration distributions of helium and oxygen in the system. These were then used in a plasma dynamics model to investigate the characteristics of the plasma bullet during its propagation and interaction with a substrate. Upon ignition, the discharge first propagated as a surface wave along the inner wall of the containing tube, and then exited the tube with a well-defined ionization front (streamer or plasma bullet). The plasma bullet evolved from a hollow (donut-shaped) feature to one where the maximum of ionization was on axis. The bullet propagated in the gap between the tube exit and the substrate with an average speed of ~2 × 10 5 m/s. Upon encountering a metal substrate, the bullet formed a conductive channel to the substrate. Upon encountering a dielectric substrate, the bullet turned into an ionization wave propagating radially along the substrate surface. For a conductive substrate, the radial species fluxes to the surface peaked on the symmetry axis. For a dielectric substrate, a ring-shaped flux distribution was observed. The “footprint” of plasma-surface interaction increased either by decreasing the gap between tube exit and substrate, decreasing the relative permittivity of an insulating substrate, or decreasing pressure. As the system pressure was lowered from 760 to 250 Torr, the discharge was initiated earlier, and the plasma bullet propagation speed increased. A reverse electric field developed during the late stages of the ramp-down of the pulse, which accelerated electrons forming a brief backward discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Perspectives on AI Architectures and Codesign for Earth System Predictability

Abstract Recently, the U.S. Department of Energy (DOE), Office of Science, Biological and Environmental Research (BER), and Advanced Scientific Computing Research (ASCR) programs organized and held the Artificial Intelligence for Earth System Predictability (AI4ESP) workshop series. From this workshop, a critical conclusion that the DOE BER and ASCR community came to is the requirement to develop a new paradigm for Earth system predictability focused on enabling artificial intelligence (AI) across the field, laboratory, modeling, and analysis activities, called model experimentation (ModEx). BER’s ModEx is an iterative approach that enables process models to generate hypotheses. The developed hypotheses inform field and laboratory efforts to collect measurement and observation data, which are subsequently used to parameterize, drive, and test model (e.g., process based) predictions. A total of 17 technical sessions were held in this AI4ESP workshop series. This paper discusses the topic of the AI Architectures and Codesign session and associated outcomes. The AI Architectures and Codesign session included two invited talks, two plenary discussion panels, and three breakout rooms that covered specific topics, including 1) DOE high-performance computing (HPC) systems, 2) cloud HPC systems, and 3) edge computing and Internet of Things (IoT). We also provide forward-looking ideas and perspectives on potential research in this codesign area that can be achieved by synergies with the other 16 session topics. These ideas include topics such as 1) reimagining codesign, 2) data acquisition to distribution, 3) heterogeneous HPC solutions for integration of AI/ML and other data analytics like uncertainty quantification with Earth system modeling and simulation, and 4) AI-enabled sensor integration into Earth system measurements and observations. Such perspectives are a distinguishing aspect of this paper. Significance Statement This study aims to provide perspectives on AI architectures and codesign approaches for Earth system predictability. Such visionary perspectives are essential because AI-enabled model-data integration has shown promise in improving predictions associated with climate change, perturbations, and extreme events. Our forward-looking ideas guide what is next in codesign to enhance Earth system models, observations, and theory using state-of-the-art and futuristic computational infrastructure.

54 ENVIRONMENTAL SCIENCES↗

Perspectives on AI Architectures and Co-design for Earth System Predictability

Recently, the U.S. Department of Energy (DOE), Office of Science, Biological and Environmental Research (BER), and Advanced Scientific Computing Research (ASCR) programs organized and held the Artificial Intelligence for Earth System Predictability (AI4ESP) workshop series. From this workshop, a critical conclusion that the DOE BER and ASCR community came to is the requirement to develop a new paradigm for Earth system predictability focused on enabling artificial intelligence (AI) across the field, laboratory, modeling, and analysis activities, called model experimentation (ModEx). BER’s ModEx is an iterative approach that enables process models to generate hypotheses. The developed hypotheses inform field and laboratory efforts to collect measurement and observation data, which are subsequently used to parameterize, drive, and test model (e.g., process based) predictions. A total of 17 technical sessions were held in this AI4ESP workshop series. This paper discusses the topic of the AI Architectures and Codesign session and associated outcomes. The AI Architectures and Codesign session included two invited talks, two plenary discussion panels, and three breakout rooms that covered specific topics, including 1) DOE high-performance computing (HPC) systems, 2) cloud HPC systems, and 3) edge computing and Internet of Things (IoT). We also provide forward-looking ideas and perspectives on potential research in this codesign area that can be achieved by synergies with the other 16 session topics. These ideas include topics such as 1) reimagining codesign, 2) data acquisition to distribution, 3) heterogeneous HPC solutions for integration of AI/ML and other data analytics like uncertainty quantification with Earth system modeling and simulation, and 4) AI-enabled sensor integration into Earth system measurements and observations. Such perspectives are a distinguishing aspect of this paper.

58 GEOSCIENCES↗

Sub-microsecond Transformers for Jet Tagging on FPGAs

We present the first sub-microsecond transformer implementation on an FPGA achieving competitive performance for state-of-the-art high-energy physics benchmarks. Transformers have shown exceptional performance on multiple tasks in modern machine learning applications, including jet tagging at the CERN Large Hadron Collider (LHC). However, their computational complexity prohibits use in real-time applications, such as the hardware trigger system of the collider experiments up until now. In this work, we demonstrate the first application of transformers for jet tagging on FPGAs, achieving $\mathcal{O}(100)$ nanosecond latency with superior performance compared to alternative baseline models. We leverage high-granularity quantization and distributed arithmetic optimization to fit the entire transformer model on a single FPGA, achieving the required throughput and latency. Furthermore, we add multi-head attention and linear attention support to hls4ml, making our work accessible to the broader fast machine learning community. This work advances the next-generation trigger systems for the High Luminosity LHC, enabling the use of transformers for real-time applications in high-energy physics and beyond.

Laatu, Lauri [Imperial Coll., London]↗

Reinforcement Learning for Load-balanced Parallel Particle Tracing

We explore an online reinforcement learning (RL) paradigm to dynamically optimize parallel particle tracing performance in distributed-memory systems. Our method combines three novel components: (1) a work donation algorithm, (2) a high-order workload estimation model, and (3) a communication cost model. First, we design an RL-based work donation algorithm. Our algorithm monitors workloads of processes and creates RL agents to donate data blocks and particles from high-workload processes to low-workload processes to minimize program execution time. The agents learn the donation strategy on the fly based on reward and cost functions designed to consider processes' workload changes and data transfer costs of donation actions. Second, we propose a workload estimation model, helping RL agents estimate the workload distribution of processes in future computations. Third, we design a communication cost model that considers both block and particle data exchange costs, helping RL agents make effective decisions with minimized communication costs. We demonstrate that our algorithm adapts to different flow behaviors in large-scale fluid dynamics, ocean, and weather simulation data. Our algorithm improves parallel particle tracing performance in terms of parallel efficiency, load balance, and costs of I/O and communication for evaluations with up to 16,384 processors.

Distributed and parallel particle tracing↗

A Modular and Transferable Reinforcement Learning Framework for the Fleet Rebalancing Problem

Mobility on demand (MoD) systems show great promise in realizing flexible and efficient urban transportation. However, significant technical challenges arise from operational decision making associated with MoD vehicle dispatch and fleet rebalancing. For this reason, operators tend to employ simplified algorithms that have been demonstrated to work well in a particular setting. To help bridge the gap between novel and existing methods, we propose a modular framework for fleet rebalancing based on model-free reinforcement learning (RL) that can leverage an existing dispatch method to minimize system cost. In particular, by treating dispatch as part of the environment dynamics, a centralized agent can learn to intermittently direct the dispatcher to reposition free vehicles and mitigate against fleet imbalance. We formulate RL state and action spaces as distributions over a grid partitioning of the operating area, making the framework scalable and avoiding the complexities associated with multiagent RL. Numerical experiments, using real-world trip and network data, demonstrate that RL reduces waiting time by 28% to 38% for the same-day evaluation, 17% to 44% for cross-day evaluation, and 22% to 25% for cross-season evaluation compared with no rebalancing scenarios. This approach has several distinct advantages over baseline methods including: improved system cost; high degree of adaptability to the selected dispatch method; and the ability to perform scale-invariant transfer learning between problem instances with similar vehicle and request distributions.

33 ADVANCED PROPULSION SYSTEMS↗

Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations

Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling

Computational models are used in a variety of fields to improve our understanding of complex physical phenomena. Recently, the realism of model predictions has been greatly enhanced by transitioning from deterministic to stochastic frameworks, where the effects of the intrinsic variability in parameters, loads, constitutive properties, model geometry and other quantities can be more naturally included. A general stochastic system may be characterized by a large number of arbitrarily distributed and correlated random inputs, and a limited support response with sharp gradients or event discontinuities. This motivates continued research into novel adaptive algorithms for uncertainty propagation, particularly those handling high dimensional, arbitrarily distributed random inputs and non-smooth stochastic responses. Here, we generalize a previously proposed multi-resolution approach to uncertainty propagation to develop a method that improves computational efficiency, can handle arbitrarily distributed random inputs and non-smooth stochastic responses, and naturally facilitates adaptivity, i.e., the expansion coefficients encode information on solution refinement. Our approach relies on partitioning the stochastic space into elements that are subdivided along a single dimension, or, in other words, progressive refinements exhibiting a binary tree representation. We also show how these binary refinements are particularly effective in avoiding the exponential increase in the multi-resolution basis cardinality and significantly reduce the regression complexity for moderate to high dimensional random inputs. The performance of the approach is demonstrated through previously proposed uncertainty propagation benchmarks and stochastic multi-scale finite element simulations in cardiovascular flow.

59 BASIC BIOLOGICAL SCIENCES↗

Computational Thermal Hydraulics of a High-Performance Low-Enriched-Uranium Annular Target for HFIR Irradiation

Molybdenum-99 has historically been generated via isolation from fissioned highly enriched uranium (HEU) targets. Here, this isotope is in high demand due to its daily use across the world in radiopharmaceutical medical procedures. The primary objective of this work was to design and analyze an experimental target assembly containing one low-enriched-uranium (LEU) annular target for irradiation at the High Flux Isotope Reactor (HFIR). Efforts included incorporating spatially dependent energy sources from neutron and gamma interactions, quantifying thermal contact conductance at material interfaces, performing grid-independent studies, comparing turbulence models, and simulating various steady-state and transient scenarios relevant for irradiation qualification and eventual insertion. These models provide velocity, pressure, and temperature distributions in both space and time. Such results enable the selection of an appropriate irradiation location, fission rate density, and flow-limiting orifice size and demonstrate compliance with HFIR safety requirements such that insertion into the reactor can be approved. This analysis shows that across all scenarios, wetted surface temperatures remain below the coolant saturation temperature with no net vapor formation in the coolant. In every scenario, all components stay below 30% of the aluminum 6061 melting temperature. Computational fluid dynamics and system-level models predict peak target temperatures that agree within 4%, though the predicted axial location of the peak differs by about 10% of the heated length due to differences in flow development length. These results de-risk the irradiation of LEU (annular targets) and strengthen a domestic, HEU-independent 99 Mo supply by providing important fuel performance data to form the foundation for a robust licensing basis.

Molybdenum-99↗

A machine learning approach to galaxy properties: joint redshift–stellar mass probability distributions with Random Forest

We demonstrate that highly accurate joint redshift–stellar mass probability distribution functions (PDFs) can be obtained using the Random Forest (RF) machine learning (ML) algorithm, even with few photometric bands available. As an example, we use the Dark Energy Survey (DES), combined with the COSMOS2015 catalogue for redshifts and stellar masses. We build two ML models: one containing deep photometry in the griz bands, and the second reflecting the photometric scatter present in the main DES survey, with carefully constructed representative training data in each case. We validate our joint PDFs for 10 699 test galaxies by utilizing the copula probability integral transform and the Kendall distribution function, and their univariate counterparts to validate the marginals. Benchmarked against a basic set-up of the template-fitting code bagpipes, our ML-based method outperforms template fitting on all of our predefined performance metrics. In addition to accuracy, the RF is extremely fast, able to compute joint PDFs for a million galaxies in just under 6 min with consumer computer hardware. Such speed enables PDFs to be derived in real time within analysis codes, solving potential storage issues. As part of this work we have developed galpro 1, a highly intuitive and efficient python package to rapidly generate multivariate PDFs on-the-fly. galpro is documented and available for researchers to use in their cosmology and galaxy evolution studies.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermodynamics, Kinetics and Structural Evolution of ε-LiVOPO 4 over Multiple Lithium Intercalation

ε -Li x VOPO 4 is a promising multi-electron cathode for rechargeable lithium-ion bat- teries that has an extremely high theoretical capacity of 318 mAh/g. In this w ork, we demonstrate the stable cycling of more than one Li in solid-state-syn thesized ε - LiVOPO 4 over more than 20 cycles for the first time. Using a combination of densit y functional theory (DFT) calculations, X-ray pair distribution funct ion (PDF) analy- sis and X-ray Absorption Near Edge Structure (XANES) measurements, we pre sent a comprehensive analysis of the thermodynamics, kinetics and stru ctural evolution of ε -Li x VOPO 4 over the entire lithiation range. We identify two intermediate ph ases at x = 1 . 5 and 1.75 in the low-voltage regime using DFT calculations, and the comput ed and electrochemically measured voltage profiles are in excellent agree ment. Operando PDF techniques show a reversible hysteretic change in the short ( < 2° A) V-O bond lengths coupled with an irreversible extension of the long V-O bond ( > 2.4 °A) dur- ing low-voltage cycling. These observations are confirmed with EXAFS spe ctra. We identify hydrogen intercalation from the electrolyte decomposition as a likely explana- tion for the ~ 2 . 4°A V-O bond and its irreversible extension. In terms of electronic conductivity, we find Li x VOPO 4 to be a large band gap insulator across the entire lithiation range, and calculated small polaron migration barriers are similar to those of the olivine LiMPO 4 cathodes. Finally, we demonstrate that ε -LiVOPO 4 is likely to be a one-dimensional diffuser using climbing-image nudged elastic ban d calculations. These results highlight the importance of nano-sizing and carbon coating in achieving good electrochemical performance in this material.

Lin, Yuh-Chieh↗