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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High‐Concentration Antibody Formulation via Solvent‐Based Dehydration

Abstract Although subcutaneous (SC) delivery is the preferred administration route for immunotherapies and other biologics for improved patient compliance and lower healthcare costs, it necessitates high‐concentration antibody formulations. However, high‐concentration antibody solutions face significant instabilities and prohibitively high viscosities. Other approaches for high‐concentration formulations have been developed, including non‐aqueous solutions, which can be irritating or painful, and antibody‐laden hydrogel microparticles, which require centrifugation and are limited to concentrations <300 mg mL −1 . This work presents a new formulation process wherein the antibody is concentrated and encapsulated into hydrogel microparticles via solvent‐based dehydration. The final dosage form is an aqueous particle suspension with a formulation concentration of 360 mg mL −1 . In this process, microparticles are synthesized continuously, and antibody precipitation is realized simultaneously to dehydration, which allows for higher antibody concentrations. Antibody phase behavior and precipitation–dehydration kinetics are analyzed. The antibody is structurally and functionally stable in the microparticle post‐processing and after 4 months. Injectability of the suspension meets clinical standards with glide force <20 N. For the first time, an aqueous antibody formulation at high concentrations comparable to non‐aqueous formulations is presented, ideal for subcutaneous administration. The process is envisioned to be generalizable as a platform for SC delivery in multiple clinical applications.

Zheng, Talia [Department of Chemical Engineering M↗
DOE OSTI2024

A mixed formulation of the plane-stress problem to facilitate reuse of constitutive models in finite-element programs

Here, the plane-stress assumption can be challenging to support in a finite element program because it traditionally requires separate implementations of constitutive models than those intended for three-dimensional or two-dimensional plane-strain simulations. As a solution to this issue, this paper presents a method to solve the plane-stress problem using a mixed formulation. In this formulation, the out-of-plane strain is treated as a field variable that is solved for in addition to the standard in-plane displacement variables, in a manner that weakly enforces the condition that the out-of-plane stress is zero. The proposed formulation is non-intrusive, requiring no modifications to the constitutive models in contrast to the conventional plane-stress formulation. The proposed mixed formulation has been benchmarked against analytical solutions and numerical solutions, with good performance and accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Generative Electrolyte Solvent and Formulation Discovery

Molecular mixtures and/or formulations are of great importance in fields ranging from materials science to pharmaceuticals to chemistry. In batteries, electrolytes are complex molecular mixtures consisting of multiple salts and solvents and additives at different concentrations that dictate battery capacity, safety, and cycle life, among others. Unfortunately, due to the complex composition and infinite design space as well as the conflicting property requirements, electrolyte design is the rate-determining step in the design of next generation battery chemistries. In this work, we develop a transformer-based generative AI model − ElectrolyteGPT − capable of generating solvents and electrolyte formulations to satisfy a wide range of desired property requirements. First, we curate an electrolyte-relevant database and develop a new line notation for formulations. Then, we show that ElectrolyteGPT can generate solvents and formulations conditioned on a wide range of important electrolyte properties such as ionic conductivity, oxidative stability, Coulombic efficiency, viscosity, and more. Finally, we experimentally synthesize the generated solvents and fabricate the electrolyte formulations and show that they can meet the desired property requirements and enable longterm cycling in energy-dense anode-free lithium metal batteries. Our work showcases the ability of generative models to address challenges in molecular mixture design for next generation batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Design-driven optimization of low-cost reagent formulations for reproducible and high-yielding cell-free gene expression

Access to recombinant proteins is vital in basic science and biotechnology research. Cell-free gene expression systems provide one approach to address this need, but widespread utilization remains limited by the cost, complexity, and inconsistency of current platforms. To address these limitations, we carry out a multi-dimensional definitive screening design to reduce the number of reagent components and remove costly secondary energy substrates. From 1,231 different reagent formulations, we discover a simple and reproducible system based on 12 components. The optimized reagent formulation can produce 2.4 ± 0.3 g/L of protein product at the 15-µL scale (~$\$60$/gprotein) and 3.7 ± 0.2 g/L (~$\$39$/gprotein) at the 4-mL scale with oxygen supplementation. This provides an average 95% reduction in cost over previous cell-free reagent formulations. We further show that the optimized reagent formulation can produce nucleoside triphosphates from nitrogenous bases and ribose and that it is robust to failure across batches of cell lysates, users/locations, and in the synthesis of more than 20 different proteins. For example, we demonstrate the production of fifteen therapeutically relevant products, including full-length aglycosylated monoclonal antibodies. We anticipate that our optimized reagent formulation will democratize the use of cell-free systems for protein manufacturing and synthetic biology applications.

Biologics↗
DOE OSTI2024

Glass Formulation and Testing with RPP-WTP HLW Simulants (Final Report)

This report presents the results from HLW glass formulation work that was conducted at the Vitreous State Laboratory of The Catholic University of America during Part B1 of the RPP-WTP Project (formally known as TWRS-P) in support of the Privatization contractor, BNFL, Inc. Glass formulation development is required to provide data that are essential for design of the vitrification facility in the near term and for safe and reliable operation of that facility in the longer-term. These data also form the bases from which contractually and technically acceptable immobilized high-level waste (IHLW) products will be devised. Glass formulation therefore impacts many aspects of the vitrification facility design, overall process economics, and contractual compliance. As an integral part of the overall system design, development of glass formulations requires input from many sources including tank waste characterization, pretreatment process definition, flow sheet development, and processing schedules. Accordingly, the glass formulation effort must be responsive to new information as the facility design basis evolves.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Time-domain all-frequency stable formulation for low-frequency electromagnetic simulation with Newmark-β time integration

An implicitly Coulomb-gauged A-ϕ formulation has previously been proposed and validated for finite ele- ment simulations of low-frequency and multiscale electromag- netic problems in the frequency domain. This formulation has demonstrated numerical stability across all frequencies, with its accuracy, efficiency, and iterative convergence established in various frequency-domain scenarios. However, direct time- domain computation is often preferable for wideband electro- magnetic problems and is typically indispensable in nonlinear and multiphysics simulations. In this work, the A-ϕ formulation is extended to the time domain. By incorporating the well-known Newmark-β time integration scheme, the proposed formulation is validated through capacitive and inductive test cases. The results confirm the solution’s accuracy and demonstrate the formulation’s stability in the time domain.

Mekonnen, Minyechil↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A regularized-interface method as a unified formulation for simulations of high-pressure multiphase flows

The injection of multi-species fluids into high-pressure and high-temperature environments beyond the species' critical points is commonly found in engineering applications. At these conditions, for immiscible species, both subcritical interfacial dynamics and supercritical mixing can coexist due to variations in temperature around the mixture critical point. The modeling of these complex transcritical phenomena for large-scale configurations is so far not possible. To address this issue, we propose the Regularized-Interface Method (RIM) as a unified formulation that can describe both sub- and supercritical processes as well as the transition between them. The proposed method is derived via filtering of the nanoscale interface-resolving formulation based on van der Waals' linear gradient theory. Thus, this approach allows for the consistent modeling of interfacial dynamics that vanishes at supercritical conditions, while significantly reducing the temporal and spatial resolution constraints of the original nanoscale formulation. The resulting RIM formulation is examined in interface-capturing simulations of sub-, trans-, and supercritical fuel injection processes, involving droplets and jets. Furthermore, these results highlight the importance of resolving spatio-temporal transitions from subcritical interfacial dynamics to supercritical mixing in high-pressure multiphase simulations, in contrast to commonly employed diffused-interface methods, where interfacial dynamics are often neglected.

Interface capturing↗
DOE OSTI2026

Synergistic cellulase–xylanase formulations for enhanced dewatering and fiber bonding toward energy-efficient and sustainable paper and packaging production

A mechanistic understanding of the synergistic effects of enzymes on cellulosic fibers dewatering and fiber bonding is essential for advancing energy-efficiency and lightweight production of paper and packaging materials. This study investigates the impact of varying cellulase and xylanase formulations on equilibrium moisture content (EMC) after pressing and tensile strength of cellulosic fiber webs using a factorial experimental design. Nine custom enzyme formulations were evaluated at controlled dosages ranging from ∼20 to 76 FPU/mL cellulase and ∼500–1130 IU/mL xylanase. Response surface modeling revealed a significant synergy, particularly at 20–40 FPU/mL cellulase combined with ≥ 1000 IU/mL xylanase. Under these conditions, EMC decreased by up to 3.6% compared with the untreated refined control, while tensile index gains of up to 16% were statistically significant for optimized blends (p < 0.05). The interaction between cellulase and xylanase was also significant for the tensile response (p = 0.010). Protein efficiency analysis showed that optimized formulations containing 30–40% less protein outperformed the commercial benchmark. The nonlinear synergy between cellulase and xylanase is attributed to their complementary substrate specificities. Endoglucanase- and β‑glucosidase‑rich cellulases hydrolyze internal β‑1,4‑glycosidic bonds in amorphous cellulose, loosening fiber walls and increasing flexibility, while xylanases target hemicellulose, primarily xylan-rich domains, enhancing porosity and improve cellulase accessibility. Tailoring enzyme formulations at low loadings overcomes traditional trade-offs between strength and dewatering, enabling cost-effective, energy-efficient, low-carbon solutions for sustainable packaging and hygiene products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Data-Efficient Methods for Determining Flory–Huggins χ Parameters in Multicomponent Polymer Formulations

Polymer formulations are essential in diverse applications including personal care products, coatings, paints, adhesives, and plastic materials. Designing these formulations requires navigating large, complex design spaces, where phase and self-assembly behavior critically impact performance. The Flory–Huggins χ parameter, which quantifies segmental miscibility, is widely used to parametrize the excess free energy of mixing in formulation models. In this work, we introduce two data-efficient, top-down methods for estimating χ parameters using the Random Phase Approximation (RPA): (i) Boundary Nonlinear Regression (Boundary-NLR), which fits theoretical spinodal boundaries to experimental phase boundaries, and (ii) Surrogate Model Inverse Parameter Estimation (SMIPE), which uses a Gaussian Process Classifier to fit sparse phase maps via a surrogate model. Both methods allow rapid parametrization of polymer field-theoretic models without the need for additional experiments. We evaluate these approaches on data sets involving polymer–solvent–nonsolvent ternary mixtures and block copolymer–solvent systems, demonstrating their robustness to experimental noise and their relevance for real-world formulation design.

copolymers↗
DOE OSTI2024

Fragmentation in Collisions of Snow with Graupel/Hail: New Formulation from Field Observations

Abstract Secondary ice production (SIP) has been attributed to the generation of most ice particles observed in precipitating clouds with cloud tops warmer than −36°C, from various aircraft- and ground-based field observations across the globe. One of the known SIP mechanisms is fragmentation during collisions among ice particles. It has been studied with our theoretical formulation, which has been applied in microphysical schemes of atmospheric models in a few studies. These have predicted an extensive impact on cloud glaciation and radiative properties. However, there has been a lack of experimental field studies, especially involving naturally falling snowflakes, to better understand this particular mechanism of SIP. This study reports the first field measurements with modern technology for fragmentation during collisions between naturally falling snowflakes and graupel/hail particles. This was observed with an innovatively designed portable chamber that was deployed outdoors in northern Sweden. Applying the observations from this field-based study, we optimized the existing formulation for predicting numbers of fragments from collisions of snow with graupel/hail. The observations show the average numbers of fragments per collision for dendritic (3–12 mm) and nondendritic (1–3 mm) snow were about 12 and 1, respectively. This represents a boost of predicted fragment numbers relative to our original formulation published in 2017. The updated formulation for breakup in ice–ice collisions can be implemented in the microphysical schemes of atmospheric models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A simplified all-frequency stable formulation with an implicit Coulomb gauge

A potential-based finite element formulation has been developed in the past to circumvent the low-frequency breakdown issues commonly encountered in electromagnetic (EM) simulations of low-frequency and multiscale problems. In this formulation, the magnetic vector and electric scalar potentials have been employed to express the electric field and magnetic flux, leading to a set of two equations that represents all four Maxwell’s equations and the current continuity equation. To enforce the Coulomb gauge, an auxiliary potential has been introduced, which results in a total of three equations to be solved simultaneously. To reduce the number of equations and unknowns needed in a simulation, a simplified formulation is proposed in this paper to enforce the Coulomb gauge implicitly without the need for the auxiliary potential. A numerical example is given to demonstrate the accuracy of the proposed formulation.

Mekonnen, Minyechil↗
DOE OSTI2023

Shear and combustion characterization of printable ammonium perchlorate composite propellant formulations

Seven formulations of ammonium perchlorate composite propellant (APCP) are developed and their properties relevant for successful additive manufacture are characterized. Extrusion in a custom-built 3D printing system and spindle viscometry are used to collect viscosity measurements of curing primary and non-curing secondary versions of the formulations. The formulations that behave similarly to a Bingham plastic, with apparent viscosities between 4 and 8 thousand Pa*s at 30 minutes post-mix, are determined to be most suitable for printing applications. Measurements of one material show a yield stress of 1 kPa. Ambient pressure burn rates of 2.0–2.9 mm/s were measured for the compositions tested. All measured burn rates were comparable to the lower end of typical burn rates for APCP. In conclusion, the results of the characterization demonstrate a propellant suitable for use in a 3D printing system.

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

Note on two formulations of Crank-Nicolson method for Navier-Stokes equations

Here, we consider two formulations of the Crank-Nicolson (CN) method for the Navier-Stokes equations (NSE). The “natural” way of implementing CN for NSE is formally second order accurate in time for both velocity and pressure, whereas another formulation approximates pressure with only first order accuracy in time. Both versions of the method are applied to the benchmark problem of computing drag and lift in the flow around a cylinder. We show that the presumably more accurate version of the CN can create a solution with nonphysical oscillations and give incorrect predictions for the maximal drag coefficient, whereas the other formulation of the method predicts the drag and lift coefficients more accurately and does not introduce nonphysical oscillations. We locate the source of the issue and suggest several remedies.

Crank-Nicolson↗
DOE OSTI2026

Excipient screening by lyophilization provides insights into spray drying formulations for nanoparticle vaccines

Nanoparticles have shown great promise as delivery platforms in the development of tunable and safe vaccines. Nanolipoprotein particles (NLPs), also known as nanodiscs, are discoidal nanoparticles composed of a lipid bilayer stabilized at their periphery by apolipoproteins. Under the right conditions, the NLP self-assembly process is highly customizable in terms of lipids and apolipoprotein constituents, allowing for tunable physical and chemical characteristics. This flexibility allows a wide range of vaccine antigens and adjuvants to be incorporated onto the NLP platform for tailored vaccine design. The stability of NLPs during long term storage is a very important factor in developing a vaccine delivery platform suitable for widespread global use. When stored in a solution for extended periods of time, NLPs dissociate into their corresponding lipids and protein constituents, leading to particle degradation. Proper stabilization of NLPs can often be achieved by lyophilization (i.e. freeze-drying), a method widely used for various applications including pharmaceuticals. This process, however, can be damaging to particles without the presence of lyoprotectants or excipients that help maintain particle stability during lyophilization. Another method used to stabilize vaccines and pharmaceuticals is spray drying, a process that converts liquid formulations into dry powders through controlled heating and airflow. While spray drying is rapid, scalable, and cost-effective, lyophilization is typically a gentler process that better retains biomolecule structure and function. Both processes use excipients for particle stabilization, so lyophilization can be used as a surrogate to test stability of NLPs, to down-select formulations that may withstand the harsher conditions of spray drying. To screen different formulations, NLPs were synthesized and purified to homogeneity by size exclusion chromatography (SEC) and samples were prepared with a wide range of lyoprotectants and/or excipients. To assess the protective effects of excipients on NLPs upon spray drying, both pre- and post-lyophilized samples were analyzed by SEC. To assess the protective effects upon heating (encountered during the spray drying process), NLP samples were incubated at elevated temperatures prior to SEC analysis. The lyoprotectants and excipients evaluated in this study had different efficiencies in protecting NLPs during lyophilization and heating tests. Trehalose, for example, exhibits stabilization on NLPs both upon lyophilization and heating whereas leucine accelerated NLP dissociation. Although some lyoprotectants are effective by themselves, different combinations can decrease the stabilization of NLPs. Shelf-stable vaccines that do not require cold-chain storage are essential for global accessibility and our findings provide fundamental insight into how to advance NLP-based vaccines for these applications.

Serrano, Litzay J [Lawrence Livermore National Lab↗
DOE OSTI2026

Formulation and Performance Evaluation of Epoxy Sealant Systems for Double-Shell Tank Bottom Refurbishment

The performance of epoxy sealants used in the refurbishment of double-shell tank (DST) systems requires balancing processability, thermomechanical stability, and adhesion to cementitious substrates. This study incorporates Heloxy 8 as a reactive diluent into Westlake 862 epoxy to tailor workability and cured-state properties. Rheological time-sweep analysis demonstrates that increasing the diluent content significantly reduces complex viscosity and extends workability, thereby improving pumpability and flow for large-area applications. However, the targeted 2-hour processing window is not fully achieved. Differential scanning calorimetry (DSC) confirms that all formulations cure at room temperature to glass transition temperatures ( T g ) at least 20 °C above the maximum DST operating temperature (27 °C), thereby ensuring service in the glassy regime. Dynamic mechanical analysis (DMA) reveals formulation-dependent reductions in tan delta and increases in storage modulus, indicating increasingly elastic and mechanically stable networks with diluent incorporation. Pull-off adhesion testing shows that modified formulations (70–90% Westlake epoxy) exhibit significantly higher adhesion strengths than the unmodified system. Grout cohesive failure indicates that interfacial bonding exceeds substrate strength. Collectively, these results demonstrate that controlled reactive diluent incorporation enables optimization of processing behavior, interfacial adhesion, and thermomechanical performance, supporting the suitability of the modified epoxy systems as durable sealant layers for cementitious barrier applications in hazardous waste containment infrastructure.

Differential scanning calorimetry↗