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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Synthesis and spectroscopic characterization of actinyl(VI) tetrahalide coordination compounds containing 2, 2'-bipyridine

A series of three new actinide tetrahalide coordination compounds containing 2,2'-bipyridinium (H 2 bpy) have been synthesized by room temperature evaporation and characterized via single crystal X-ray diffraction, Raman spectroscopy, and infrared spectroscopy. The solid-state compounds (Np1, U1, and U2) contain the AnO 2 2+ cation coordinated to four halide (chloride or bromide) atoms to form the anionic tetrahalide molecular unit [AnO 2 X 4 ] 2– (X = Cl, Br) and are charge balanced by the 2,2'-bipyridinium cations that engage in electrostatic interactions with the actinyl complex. Np1 (N 2 C 10 H 10 )[NpO 2 Cl 4 ] contains 2,2'-bipyridine in the cis conformation where both the nitrogen atoms are directed towards the [NpO 2 Cl 4 ] 2– monomer. Within U1 (N 2 C 10 H 9 )[UO 2 Cl 4 ], the 2,2'-bipyridine is in a trans conformation, and found in the same orientation in the isomorphous structure U2 (N 2 C 10 H 9 )[UO 2 Br 4 ]. The compounds were further characterized by vibrational spectroscopy with specific interest in the actinyl cation. Raman spectroscopy provided information on the actinyl symmetric stretch (ν 1 ) whereas IR spectroscopy is used to determine the location of the asymmetric stretch (ν 3 ). Here, spectral similarities are observed between the two isomorphous structures, but slight variations across the series of structures are found to be associated with bipyridine bands in the various conformations. Additional analysis of these vibrational features in U1 and U2 provided information on the actinyl force constants, allowing insight into the relative uranyl bond strength that was compared to similar tetrahalide compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A multiphase flow model of water droplets dielectrophoretic-induced air dehumidification phenomena

Air humidity in indoor spaces plays a critical role in human comfort and health. Dehumidification systems are used for building humidity controls, but they can take significant energy consumption, especially in geographic locations with high outdoor humidity and warm climates. Consequently, there is a growing demand for innovative dehumidification processes that consume minimal energy. Dielectrophoretic air dehumidification represents one such promising approach. However, it has not garnered significant attention due to the absence of engineering models and simulation tools capable of evaluating its performance and limitations at large-scale airflows. A new numerical multiphase CFD model, which is also experimentally validated, is developed in a customized Reacting Foam solver based on OpenFOAM® version 9. The newly developed model seeks to decrease substantial energy consumption and lower costs by leveraging the dielectrophoretic phenomenon to regulate moisture levels in the air. The solver integrates a hybrid Eulerian-Lagrangian framework to track the droplet's trajectory and growth rate while solving the continuum equations for the moist air. An electrospray produces electrically charged droplets, which grow during their in-flight trajectories as water vapor condenses onto their surfaces. The role of electrostatic forces in promoting vapor condensation within a high-gradient electrical field is investigated, and the dielectrophoretic vapor nucleation process on charged water droplets is discussed. The CFD model was validated against results from the literature and from proof-of-concept experiments conducted by the authors, which showed a 2 % air dehumidification with a single electrospray and airflow rate of 5 cubic feet per minute. The simulation results indicated that augmenting the number of electrically charged spray droplets increased the dehumidification of the air to 25 %. The initial mean droplet diameter, the orientation of the injector and relative humidity significantly influence the assessment of dehumidification. As a result, scaling up this approach to larger airflow volumes is identified as a potential future research direction.

42 ENGINEERING↗
DOE OSTI2025

Numerical analysis of air dehumidification through electrospray-enhanced vortical flow cyclone separator

The dehumidification of air is a highly energy-intensive process, typically requiring vapor compression systems to cool the air significantly below its dew point temperature. Here, this study numerically investigates air dehumidification achieved by electrostatic and dielectrophoresis forces in a converging duct and centrifugal principles in cyclone separators. An electrospray was employed to energize water droplets, which then captured water vapor via dielectrophoresis. A novelty of the present study is the inclusion of a cyclone separator positioned downstream of the electrospray. This combination increased the dehumidification efficiency and controlled the flow of the condensate. By integrating electrospray technology and applying an electric field, this study examines the impact of particle separation efficiency, pressure drops, and cyclone performance on air dehumidification. The control parameters for air dehumidification were investigated. Three cyclones were modelled for airflow rates of 5 cubic feet per minute [cfm] (0.0024 m 3 /s), 38 cfm (0.0179 m 3 /s), and 200 cfm (0.094 m 3 /s). The results indicated air dehumidification was up to 5.7 % under environmental conditions, similar to those used to validate the CFD model. The degree of air dehumidification was primarily influenced by the electric charge acquired by the water droplets, their flight trajectory, and the vorticity intensity within the cyclone. Air dehumidification could increase by up to 13 % by increasing the number of droplets injected into the air stream, the flight time, and the electrical charge. The breakdown electric field strength threshold near the electrospray was a limiting factor for further enhancing dehumidification performance. This study examines the optimization of an electro-assisted dehumidification system that includes cyclone-based droplet separation through numerical analysis. The results provide insights into the design of energy-efficient air treatment technologies.

42 ENGINEERING↗
DOE OSTI2024

Lignin - A green material for antibacterial application — A review

Lignin's antibacterial properties have become increasingly relevant due to the rise of microbial infectious diseases and antibiotic resistance. Lignin is capable of interacting electrostatically with bacteria and contains polyphenols that cause damage to their cell walls. These features make lignin a desirable material to exhibit antibacterial behavior. Therefore, lignin in antibacterial applications offers a novel approach to address the growing need for sustainable and effective antibacterial materials. Recent research has explored the incorporation of lignin in various biomedical applications, such as wound dressings, implants, and drug delivery systems, highlighting their potential as a sustainable alternative to synthetic antibacterial agents. Furthermore, the development of lignin-based nanomaterials with enhanced antimicrobial activity is an active area of research that holds great promise for the future. Here, in this review, we have provided a summary of how lignin can be incorporated into different forms, such as composite and non-composite synthesis of antibacterial agents and their performances. The challenges and future considerations are also discussed in this review article.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Lithium promotion of Pt/m-ZrO 2 catalysts for low temperature water-gas shift

Low temperature water-gas shift (LTS) is an important reaction occurring in a fuel processor for producing and purifying hydrogen. Platinum supported on m-ZrO 2 belongs to a family of catalysts consisting of metal nanoparticles and an active partially reducible oxide, with the catalysis proposed to occur at the boundary between metal particles and the support. In this investigation, increasing the loading of lithium dopant increased the LTS rate up to 0.54 wt % lithium, where conversion was 2.4 times that of the unpromoted catalyst at 260°C. Further increases in lithium loading up to 1.5 wt % decreased the rate, although it remained higher than that of the unpromoted catalyst. Infrared spectroscopy and CO 2 temperature programmed desorption experiments showed three effects with increasing lithium loading: (1) lithium promoter weakened the C–H bond of formate, the proposed rate limiting step of the interfacial surface formate mechanism; (2) high levels of lithium suppressed the platinum site capacity required for hydrogen transfer; and (3) high levels of lithium increased catalyst basicity. Aspects (2) and (3) tended to inhibit desorption of product CO 2 , an acidic molecule the removal of which is metal-catalyzed. XANES and XPS experiments revealed that electron transfer to enrich Pt nanoparticles is unlikely the root cause of C–H bond weakening in formate. However, other electronic effects (e.g., electrostatic effects or molecular rearrangement due to enhanced basicity) were not ruled out.

08 HYDROGEN↗
DOE OSTI2020

Hypervelocity impact flash expansion geometry under various spacecraft surface electrical conditions

A more congested space environment due to increasing space activities introduces new threats to spacecraft operators. Among these threats include hypervelocity impacts from microparticles (< 1 µg) in the form of meteoroids and space debris. These microparticles travel at speeds between 11.2 and 72.8 km/s with respect to the Earth and can impact spacecraft forming a small (~1 µm) and dense (~ 10 26 m -3 ) plasma. This plasma can generate a strong optical emission (impact flash) and a radio frequency (RF) emission. These emissions can lead to spacecraft electrical anomalies when the impacted spacecraft surface (target) carries high electrical potential due to various space weather effects. To understand the microparticle hypervelocity impact plasma and its associated threat to spacecraft electronics, we studied the hypervelocity impact flash expansion geometry under various spacecraft surface electrical conditions. Three high-speed broadband photomultiplier tubes (PMT) are used to capture the temporal evolution of the impact flash and the temporal evolution of the angular distribution of the impact flash expansion geometry in a 3 MV electrostatic dust accelerator during a ground-based experiment. Overall, results indicate that the impact surface electrical condition has a statistically significant influence on the impact flash geometry, and a strong similarity between the impact plasma and flash expansion geometry. Thus, this paper provides new experimental support for the impact flash origin from and connection with the impact plasma, and serves as the first impact flash expansion geometry characterization under various impact surface electrical conditions in a collisionless environment (< 10 -5 Torr).

42 ENGINEERING↗
DOE OSTI2020

Silica nanocluster binding rate coefficients from molecular dynamics trajectory calculations

Oxide nanoparticle growth from vapor phase precursors occurs in high temperature aerosol reactors first via the formation of nanoclusters, which are nanometer-scale condensed-phase species composed of 10 1 -10 2 atoms. The binding rate for nanoclusters, defined as the rate at which two nanoclusters collide with and stick to one another, is hence of interest in predicting nanoparticle size distribution functions in an aerosol. We have utilized molecular dynamics (MD) trajectory calculations to determine the homogeneous (equal-sized) and heterogeneous (disparate-sized) binding rate coefficients of SiO2 (silica) nanoclusters composed of 18, 144, and 333 atoms. MD trajectory calculations incorporated all-atom models of nanoclusters using a combined Born–Huggins–Mayer-Lennard-Jones potential model, which accounts for both short range interactions and electrostatic interactions. MD calculations were utilized to determine the binding probability as a function of both initial relative velocity and impact parameter; integration of the binding probability across impact parameter and relative velocity space yields the binding rate coefficient. MD trajectory calculations reveal that the most common type of encounters between nanoclusters leading to binding are grazing collisions, i.e. instances where collision would not occur without induced dipole potential influences. The resulting binding rate coefficients are found to be extremely weakly dependent on system temperature, which is in contrast to the use of rate coefficient models which are the product of a hard-sphere collision rate coefficient and a constant enhancement factor (leading to a rate coefficient proportional to the square root of temperature). Enhancement factors defined from MD trajectory calculations fall in the range of 3–9 as system temperature decreases from 1500 K to 300 K. Furthermore, such large values suggest that potential interactions need to be considered when modeling oxide nanocluster growth in the gas phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling

The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Lastly, potential applications and caveats to the usage of LD are included as a summary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Chemical preintercalation of magnesium ions into ⍺-MoO 3 structure for improved electrochemical stability in Li-ion cells

Chemical preintercalation of layered materials, used as electrodes in intercalation-based energy storage devices, represents a promising strategy to enhance electrochemical stability and extend cycle life. However, standardized synthesis approaches for the chemical preintercalation of diverse ions into various layered materials are lacking, necessitating the development of specific synthesis routes for each ion and layered phase combination. In this study, we present the first successful demonstration of Mg 2+ ion chemical preintercalation into the interlayer region of α-MoO 3 , revealing its stabilizing effect during cycling in non-aqueous Li-ion cells. Using ethanol during hydrothermal treatment facilitated molybdenum reduction, which was critical for Mg 2+ ion preintercalation. Interestingly, we found that Mg preintercalation was accompanied by the incorporation of water. Mg-preintercalated α-MoO 3 exhibited enhanced charge storage capacity, electrochemical stability, and power capability compared to pristine α-MoO 3 electrodes. This improved performance is attributed to the structural stabilization provided by Mg 2+ pillars, which prevent undesirable phase transformations during repeated Li intercalation/deintercalation, and increased Li + ion diffusion due to the shielding of electrostatic interactions between electrochemically cycled ions and the α-MoO 3 lattice, enabled by structural water. In conclusion, our study offers new insights into developing chemical preintercalation synthesis approaches that can be broadly applied to a wide range of pillaring ions and layered material hosts.

25 ENERGY STORAGE↗
DOE OSTI2020

Breakdown of electroneutrality in nanopores

Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to unique physical properties at the nanoscale and the technological advances that allow us to study them. It is tempting to approach this confined regime with the theoretical tools and knowledge developed for membranes and microfluidic devices, and naively apply continuum models, such as the Poisson-Nernst-Planck and Navier-Stokes equations. However, it turns out that some of the most basic principles we take for granted in larger systems, such as the complete screening of surface charge by counter-ions, can break down under extreme confinement. Additionally, we show that in a truly one-dimensional system of ions interacting with three-dimensional electrostatic interactions, the screening length is exponentially large, and can easily exceed the macroscopic length of a nanotube. Without screening, electroneutrality breaks down within the nanotube, with fundamental consequences for ion transport and electrokinetic phenomena. In this work, we build a general theoretical framework for electroneutrality breakdown in nanopores, focusing on the most interesting case of a one-dimensional nanotube, and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Phase diagrams and microstructures of aqueous short alkyl chain polyethylene glycol ether carboxylate and carboxylic acid triblock surfactant solutions

The surfactant C 8 Eo 8 CH 2 COOH (Akypo LF2) and its salts have a small hydrophobic and a significantly longer hydrophilic part. As a consequence, there must be a significant steric constraint, once these surfactant molecules form micelles. In addition, the partially charged headgroups should bring some additional fine-tuning via electrostatic interactions to this "essentially non-ionic" surfactant. Experiments: Phase diagrams of binary mixtures of water and C 8 Eo 8 CH 2 COOH are established over large concentration and temperature ranges, also at different pHs and in the presence of sodium and calcium ions. Surface tensions and osmotic pressures are measured to understand the systems. To evaluate the microstructures, also Dynamic Light Scattering and Small-Angle X-ray Scattering are performed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Molecular-level understanding of gibbsite particle aggregation in water

Using molecular dynamics simulations, we investigate the molecular scale origin of crystal face selectivity when one gibbsite particle attaches to another in water. A comparison of the free energy per unit surface area of particle–particle attachment indicates that particle attachment through edge surfaces, where the edge surfaces are either (1 0 0) or (1 1 0) crystal faces, is more energetically favorable compared to attachment between two basal surfaces (i.e., (0 0 1) crystal faces) or between the basal surface of one particle and the edge surface of another. This result suggests that gibbsite crystals with low basal/edge surface area ratio will preferentially attach through edge surfaces, potentially helping the crystals grow laterally. However, for larger gibbsite particles (high basal/edge surface area ratio) the total free energy, not normalized by surface area, of particle attachment through the basal surfaces is lower (more negative) than attachment through the edge surfaces, indicating that larger gibbsite particles will preferentially aggregate through basal surface attachments. The short-range electrostatic interactions including the interparticle hydrogen bonds from surface –OH groups drive particle attachment, and the dominant contribution to the free energy minimum is enthalpic rather than entropic. However, the enthalpy of basal-edge attachment is significantly offset by the entropy leading to a higher free energy (less negative) compared to that of basal-basal attachment. Study of the free energy for a few imperfect attachments of two particles indicates a higher free energy (i.e., less negative, less stable), compared to a perfect attachment

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Application of community data to surface complexation modeling framework development: Iron oxide protolysis

This study presents a comprehensive community data-driven surface complexation modeling framework for simulating potentiometric titration of mineral surfaces. Compiled community data for ferrihydrite, goethite, hematite, and magnetite are fit to produce representative protolysis constants that can reproduce potentiometric titration data collected from multiple literature sources. Using this framework, the impact of surface complexation model type and surface site density (SSD) on the fit quality and protolysis constants can be readily evaluated. For example, the non-electrostatic model yielded a poor data fit compared to diffuse double layer model and constant capacitance models due to the absence of known surface charge effects. Regardless of the choice of iron oxide mineral, pK a1 decreased with increasing SSD while the opposite tendency was observed for pK a2 . This newly developed framework demonstrates a method to reconcile community data-wide potentiometric titration data using Findable, Accessible, Interoperable, Reusable data principles to produce mineral protolysis constants that improve robustness of surface complexation models for applications in metal sorption and reactive transport modeling. The framework is readily expandable (as community data increase) and extensible (as the number of minerals increase). The framework provides a path forward for developing self-consistent, comprehensive, and updateable surface complexation databases for surface complexation and reactive transport modeling.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Quantitative SANS and multi-model analysis of spacer-dependent micellization of urea-based gemini surfactants

The micellization behavior of urea-based cationic gemini surfactants was investigated using small-angle neutron scattering (SANS) with multi-model form factor analysis. A homologous series of surfactants with urea group included in the hydrophobic tail and polymethylene spacers consisting of two to ten methylene units was analyzed using three form factor models: a core–shell ellipsoid and two variants of homogeneous ellipsoids. The results from all models show a consistent trend of the micelle structures, confirming that the spacer length critically influences micellar geometry, aggregation number, and hydration. The surfactant with four CH 2 groups in the spacer formed the largest micelles with the highest aggregation number, while longer spacers led to progressively smaller, more compact aggregates. The shell hydration—quantified as the volume fraction of heavy water within the hydrophilic region—decreased systematically with increasing spacer length due to enhanced hydrophobicity of the headgroup-spacer region. Intermicellar interactions, modeled as screened Coulomb interaction using the rescaled mean spherical approximation (RMSA), revealed the strongest electrostatic repulsion for the case of four methylene groups in the spacer, corresponding to the highest micellar charge and largest interparticle spacing. The observed spacer-dependent trends were robust across all modeling approaches, demonstrating that the spacer length serves as a key structural determinant of self-assembly in this type of urea-based gemini systems. These findings provide insight into the design of gemini surfactants with tailored aggregation behavior for applications in drug delivery, nanostructure templating, and solubilization technologies.

Core–shell ellipsoid model↗
DOE OSTI2020

An explicit scheme to enforce charge conservation in transient Particle-in-Cell simulations with Maxwell-Boltzmann electrons

The Maxwell-Boltzmann electron model is a very popular approximation of the electronic behavior in electrostatic plasmas, adopted in all cases where the electron dynamics is governed only by a balance between electric and pressure forces. In such a model, the electron dynamics is reduced to solving for a nonlinear Poisson problem together with an additional expression enforcing charge conservation. In this work we derive an expression of charge conservation which can be conveniently applied to explicit schemes to update the reference Boltzmann density, particularly useful when simulating plasma sheaths. The scheme can be equally applied to both steady-state and transient problems. Two examples are shown, a steady-state plasma sheath, and a radio-frequency magnetic presheath. Our proposed scheme allows to enforce global charge conservation locally in time, and can thus be applied to the simulation of transient phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Improved C 1 shape functions for simplex meshes

Using continuously-differentiable (C 1 ) interpolation methods previously developed for computer visualization and other applications, a new class of shape functions is constructed and applied to electrostatic (ES) Particle-In-Cell (PIC) simulations on simplex (triangle or tetrahedral) meshes. The resulting shape functions are non-negative and partition unity,and lead to a reduction of shot noise and aliasing associated with particle interpolation to and from the mesh. For an energy-conserving implementation as chosen, C 1 interpolation of the potential leads to a continuous (C 0 ) electric field, with associated improved fidelity of particle motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm compresses the particle population per spatial cell by constructing a velocity distribution function using GM. Particles are reconstructed at restart time by local resampling of the Gaussians. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction by exactly matching the density profile at restart time. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. Here, we demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗