SEARCH · Search NASA

Results for “Nonlinear solution”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

221 records · Page 13

All sources NASA NTRS DOE OSTI

DOE OSTI2025

A Fast Dynamic Internal Predictive Power Scheduling Approach for Power Management in Microgrids: Preprint

This paper presents a Dynamic Internal Predictive Power Scheduling (DIPPS) approach for optimizing power management in microgrids, particularly focusing on external power exchanges among diverse prosumers. DIPPS utilizes a dynamic objective function with a time-varying binary parameter to control the timing of power transfers to the external grid, facilitated by efficient usage of energy storage for surplus renewable power. The microgrid power scheduling problem is modeled as a mixed-integer nonlinear programming (MINLP-PS) and subsequently transformed into a mixed-integer linear programming (MILPPS) optimization through McCormick's relaxation to reduce computational complexity. A predictive window window with 6 data points is solved at an average of 0.92s, a 97.6% improvement over the 38.27s required for the MINLP-PS formulation, implying the numerical feasibility of the DIPPS approach for real-time implementation. Finally, the approach is validated against a static objective using real-world load data across three case studies with different time-varying parameters, demonstrating the ability of DIPPS to optimize power exchanges and efficiently utilize distributed resources while shifting the external power transfers to specified time durations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Shapes of ideal stalagmites

Stalagmites are isolated columns of calcium carbonate growing on a cave floor; their growth is driven by the constant dripping of supersaturated solutions from the roof of the cave. In this paper, we derive a closed-form expression for the shape of a steadily growing stalagmite. Our analysis gives rise to three distinct shapes, all of them observable in nature, with the shape characterized by a single dimensionless parameter. Transitions between different shapes occur at a specific value of this parameter, with additional selection rules determining the shape and size of stalagmites evolving under specific cave conditions. Our theory shows that the stalagmite shape influences the 13 C isotope shifts, which are an important source of paleoclimatic information.

invariant growth↗

DOE OSTI2026

Polarization transmission in the Hadron Storage Ring of the Electron-Ion Collider

The successful operation of the future Electron-Ion Collider is contingent on maintaining high hadron beam polarization up to 275 GeV. The Hadron Storage Ring lattice, however, features a symmetry-breaking interaction region that excites strong, nonsystematic spin resonances, posing a significant threat to polarization preservation. This paper systematically investigates two complementary strategies to ensure high polarization transmission. The first method involves optimizing the vertical betatron phase advance between Siberian snakes to orchestrate a cancellation of depolarizing kicks across the ring. We demonstrate through simulations that both dynamic and fixed-optics solutions based on this principle can successfully preserve polarization through the strongest resonances. The second, more powerful approach involves optimizing the snake rotation axes to suppress resonance driving terms at their source. We revisit established symmetric configurations, such as the Lee-Courant schemes, and introduce a novel, highly symmetric “Doubly Lee-Courant” (DLC) scheme, which enforces a local 𝜋 spin phase advance across every consecutive pair of snakes. Our analysis reveals a clear performance hierarchy, with the DLC configuration providing an exceptionally robust and energy-insensitive baseline for polarization preservation. We conclude that a hybrid strategy, using a DLC snake scheme as a symmetric foundation and betatron phase tuning for fine corrections, offers the most effective path forward for the EIC and future high-energy polarized-beam facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Modeling active nematics via the nematic locking principle

Active nematic systems consist of rod-like internally driven subunits that interact with one another to form large-scale coherent flows. They are important examples of far-from-equilibrium fluids, which exhibit a wealth of nonlinear behavior. This includes active turbulence, in which topological defects in the nematic order braid around one another in a chaotic fashion. One of the most studied examples of active nematics consists of a dense two-dimensional layer of microtubules, crosslinked by kinesin molecular motors that inject extensile deformations into the fluid. Though numerous theoretical studies have modeled microtubule-based active nematics, no consensus has emerged on how to fully and quantitatively capture the features of the experimental system. Here, to better understand the theoretical foundations for modeling this system, we propose a fundamental principle we call the nematic locking principle—individual microtubules cannot rotate without all neighboring microtubules also rotating. Physically, this is justified by the high density of the microtubules, their elongated nature, and their corresponding steric interactions. We assert that the nematic locking principle holds throughout the majority of the material, but breaks down in the neighborhood of topological defects and other regions of low density. We derive the most general nematic transport equation consistent with this principle and also derive the most general term that violates it, introducing fracturing into the material. We then examine the standard Beris–Edwards approach, commonly used to model this system, and show that it violates the nematic locking principle throughout the majority of the material due to fracturing. We then propose a modification to the Beris–Edwards model that enforces nematic locking nearly everywhere. This modification shuts off fracturing except in regions where the order parameter (a proxy for density) is reduced. In these regions fracturing is turned on. The resulting simulations in turn show strong nematic locking throughout the bulk of the material, with narrow bands of fracturing, consistent with experimental observation. One additional advantage of enforcing nematic locking is that nontrivial stationary state solutions, common in Beris–Edwards simulations but not seen in experiments, are eliminated.

Mitchell, Kevin A. [Univ. of California, Merced, C↗

DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗