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Conditionally Active Min-Max Limit Regulators

A conditionally active limit regulator may be used to regulate the performance of engines or other limit regulated systems. A computing system may determine whether a variable to be limited is within a predetermined range of a limit value as a first condition. The computing system may also determine whether a current rate of increase or decrease of the variable to be limited is great enough that the variable will reach the limit within a predetermined period of time with no other changes as a second condition. When both conditions are true, the computing system may activate a simulated or physical limit regulator.

Garg, Sanjay

Cycling phosphorus on the Archean Earth: Part II. Phosphorus limitation on primary production in Archean ecosystems

Several lines of evidence point to low rates of net primary production (NPP) in Archean oceans. However, whether Archean NPP was limited by electron donors or nutrients, particularly phosphorus (P), and how these factors might have changed over a billion years of recorded Archean history, remains contentious. One major challenge is to understand quantitatively the biogeochemical cycling of P on the early Earth. In Part I of this series (Hao et al., 2020), we estimated the weathering flux of P to the oceans as a function of temporally increasing continental emergence and elevation through Archean time. In Part II, we conduct thermodynamic and kinetic simulations to understand key processes of P cycling within the Archean ocean, including seafloor weathering, recycling of organic P, the solubility and precipitation of secondary phosphate minerals, and the burial diagenesis of P precipitates. Our calculations suggest low solubilities of apatite minerals in Archean seawater, primarily due to nearly neutral pH and high levels of Ca. This low solubility, in turn, implies a negligible contribution of apatite dissolution to P bioavailability in Archean seawater. We also simulate the solubility limits of common secondary P-bearing minerals, showing that vivianite would have been the least soluble P mineral in ferruginous Archean seawater (0.1–0.3 µM), even at moderate supersaturation states (Ω = 100 or 1000). If vivianite precipitation was kinetically favorable by microbial activities and mineral adsorption, the sinking flux of P as vivianite in Archean seawater could have reached the modern sinking flux, implying that vivianite precipitation was a potentially major sink for P in Archean oceans. During burial diagenesis, however, vivianite in porewater would have become less stable than Ca-phosphates of lower solubility. At elevated temperatures (>100 °C) associated with burial diagenesis and low-grade metamorphism, vivianite is predicted to react irreversibly with calcite to form apatite. Optimistic assumptions about the recycling efficiency of P on the Archean Earth lead us to estimate that by the end of the eon the total flux of P (continental weathering + recycling) could have supported NPP at levels up to 7% of the modern. The total flux of P would have been much lower on the early and middle Archean Earth, whereas fluxes of electron donors could have been higher, suggesting very low productivity and P-limitation of marine ecosystems during much of the eon. Comparing our estimates of NPP as limited by P supply with the estimate by Ward et al. (2019), in which NPP was limited by electron donors and metabolic efficiency, there could have been a transition between P-limited productivity in the early to middle Archean to electron donor-limitation closer to the eon’s end (assuming no oxygenic photosynthesis). Once oxygenic photosynthesis reached ecological significance, probably near the end of the Archean, our estimated flux of P would allow rapid oxidation of atmosphere.

Vivianite

Small-Signal Analysis of Current-Limiting Grid-Forming Inverters

Grid-forming (GFM) inverters are equipped with a current limiter to protect the device during grid disturbances. Because the intervention of the current limiter can compromise the transient stability of the GFM inverter, various types of current limiter designs and additional frequency-stabilization control methods have been proposed in recent literature to aid in transient GFM inverter stability; however, the small-signal stability implications of adding these additional control blocks during, in particular, off-nominal conditions are not fully understood. To address this challenge, this paper presents a generic small-signal model of a GFM inverter that incorporates various types of current limiters and frequency stability-enhancing controls. With the proposed model, we analyze the root causes of inverter instability, which reveals two critical design trade-offs. First, due to current-limiter engagement caused by a disturbance, the GFM inverter dynamics are altered, which can lead to voltage oscillations. Second, additional frequency-stabilization controls can improve the small-signal stability of the GFM inverter, but at the cost of reduced power and voltage support to the grid. Comprehensive hardware experiments validate the theoretical concept and analysis. The findings in this work underscore the importance of incorporating both transient-response and small-signal dynamics requirements into the design procedure of GFM current limiters and frequency-stabilization controls.

24 POWER TRANSMISSION AND DISTRIBUTION

A scoping study of far-SOL main-wall protection limiters for steady-state operation of compact pilot plant tokamaks

We present a novel method for handling steady-state heat fluxes incident on the main wall of pilot plant-scale magnetic fusion devices, based on the utilization of protection limiters in the far scrape-off layer (SOL). This method helps avoid large plasma-wall gaps, without excessively compromising blanket performance. We present an optimization algorithm for determining the appropriate size and scale of these protection limiters given (1) probability distributions of SOL plasma parameters and (2) assumed risk tolerance. As part of this optimization, we have developed an analytic description of parallel heat fluxes across limiter shadows, and an objective cost function (the ‘Far-SOL Marginal Cost’) to quantify the impact that different main-wall thermal management design choices have on reactor capital cost. Applying the model to a midscale fusion pilot plant concept shows that making use of far-SOL protection limiters can reduce capital costs on the order of $500 M, relative to naively increasing the plasma-wall gap. Our analysis demonstrates that the far-SOL power decay length is the highest-leverage plasma assumption for thermal loading of the first wall, and the primary cost driver for main wall thermal management. The relative cost efficiency of protection limiters increases as assumptions on the far-SOL heat flux become more pessimistic. The concepts described in this paper motivate the further development of far-SOL protection limiters as part of larger efforts to design economical core-edge-wall compatible solutions for a fusion pilot plant.

Design under uncertainty

High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. Further, these solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.

42 ENGINEERING

E-Area Low-Level Waste Facility Inadvertent Human Intruder Limits and Doses in Support of the PA2022

This report documents the inadvertent human intruder (IHI) analysis for the E-Area Low-Level Waste Facility (ELLWF) at the Savannah River Site (SRS), near Aiken, South Carolina. This analysis supports the revised ELLWF Performance Assessment (PA), complying with the Department of Energy standard for operation of low-level waste disposal facilities (USDOE, 2017). The ELLWF is an operating waste disposal facility and is scheduled to continue accepting waste to 2065. One task of the revised PA is to establish waste inventory limits for the various disposal units at ELLWF. This is done by modeling future contaminant release and transport through applicable pathways to human receptors, comparing predicted doses per disposed curie with applicable performance measures, to obtain inventory limits which will assure that doses to receptors do not exceed performance measures. This report documents results of modeling future doses to one class of receptor, the inadvertent human intruder. It is assumed that after site closure, public knowledge of the site is lost, and IHIs will engage in activities on the ELLWF that will disrupt the closure cap, causing dose to the IHI. Following USDOE (2017), six different stylized exposure scenarios are considered, simulating activities by an IHI which could result in a radiological dose. The six scenarios are: • Acute – Basement Construction: IHI constructs a basement and encounters waste during excavation which is inadvertently mixed with clean soil and diluted. • Acute – Well Drilling: IHI drills a water well through waste and is exposed to drill cuttings mixed with clean soil that are brought to the surface. • Acute – Discovery: IHI begins constructing a basement but stops when encountering the riprap in the final closure cap and is exposed to photon radiation from unexcavated material residing in the undisturbed waste zone. • Chronic – Agriculture: Resident IHI is exposed to waste that was excavated for basement construction and mixed with native soil in the intruder’s vegetable garden. • Chronic – Post-Drilling: Resident IHI is exposed to waste from drill cuttings mixed with native soil and scattered in the garden area. • Chronic – Residential: Resident IHI is exposed to external radiation while in home located above waste with shielding provided by the concrete basement floor and any soil or engineered material remaining between the basement and waste. Dose calculations are performed using the SRNL Dose Toolkit (Aleman, 2023), following the approach of Smith et al (2019). Calculations are performed separately for 27 of the 33 disposal units (DUs) at ELLWF and are radionuclide specific. The results of the IHI analysis include: • Dose Factors: mrem per disposed curie (acute) and mrem/yr per disposed curie (chronic) for each parent radionuclide, for each DU. • Inventory Limits: in curies, for each parent radionuclide, for each DU. • Estimated Dose to IHI: mrem (acute) and mrem/yr (chronic), for each DU, given its projected closure inventory without inventory biases applied. Most DU-specific IHI inventory limits are in the range of 10 3 to 10 7 curies per nuclide. The lowest inventory limits are associated with gamma-emitters such as Sn-126, Ra-226, Th-232, and Cm-248. Radionuclides with short half-lives such as Pu-241, and nuclides which are pure beta emitters or which decay by electron capture, such as Ni-59 and Ni-63, have the highest limits. For the 27 evaluated DUs, predicted IHI doses are shown in Table ES-1. The maximum acute dose is 1.18 mrem, at ST23, much less than the DOE performance measure of 500 mrem (USDOE, 2017). The highest chronic dose is 37.2 mrem/yr at ST02, below the DOE performance measure of 100 mrem/yr. Also shown are estimated inventory sums of fractions (SOFs) at closure in 2065, for groundwater (GW) and IHI pathways. For each DU, the inventory is constrained by the GW pathway. For most DUs, the IHI SOFs are approximately 1000 times lower than the GW SOF values, and the IHI pathway does not drive risk for any disposal unit.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W

Limits on Achievable Dimensional and Photon Efficiencies with Intensity-Modulation and Photon-Counting Due to Non-Ideal Photon-Counter Behavior

An ideal intensity-modulated photon-counting channel can achieve unbounded photon information efficiencies (PIEs). However, a number of limitations of a physical system limit the practically achievable PIE. In this paper, we discuss several of these limitations and illustrate their impact on the channel. We show that, for the Poisson channel, noise does not strictly bound PIE, although there is an effective limit, as the dimensional information efficiency goes as e[overline] e PIE beyond a threshold PIE. Since the Holevo limit is bounded in the presence of noise, this illustrates that the Poisson approximation is invalid at large PIE for any number of noise modes. We show that a finite transmitter extinction ratio bounds the achievable PIE to a maximum that is logarithmic in the extinction ratio. We show how detector jitter limits the ability to mitigate noise in the PPM signaling framework. We illustrate a method to model detector blocking when the number of detectors is large, and illustrate mitigation of blocking with spatial spreading and altering. Finally, we illustrate the design of a high photon efficiency system using state-of-the-art photo-detectors and taking all these effects into account.

quantum limited communications

The three-point energy correlator in the coplanar limit

Energy correlators are a type of observables that measure how energy is distributed across multiple detectors as a function of the angles between pairs of detectors. In this paper, we study the three-point energy correlator (EEEC) at lepton colliders in the three-particle near-to-plane (coplanar) limit. The leading-power contribution in this limit is governed by the three-jet (trijet) configuration. We introduce a new approach by projecting the EEEC onto the volume of the parallelepiped formed by the unit vectors aligned with three detected final-state particles. Analogous to the back-to-back limit of the two-point energy correlator probing the dijet configuration, the small-volume limit of the EEEC probes the trijet configuration. We derive a transverse momentum dependent (TMD) based factorization theorem that captures the soft and collinear logarithms in the coplanar limit, which enables us to achieve the next-to-next-to-next-to-leading logarithm (N 3 LL) resummation. To our knowledge, this is the first N 3 LL result for a trijet event shape. Additionally, we demonstrate that a similar factorization theorem can be applied to the fully differential EEEC in the three-particle coplanar limit, which provides a clean environment for studying different coplanar trijet shapes.

Effective Field Theories of QCD

Nutrient Limitation Induces a Productivity Decline From Light‐Controlled Maximum

Abstract Nutrient impacts on productivity in stream ecosystems can be obscured by light limitation imposed by canopy cover and water turbidity, thereby creating uncertainties in linking nutrient and productivity regimes. Evaluations of nutrient limitations are often based on a response ratio (RR) quantifying productivity stimulation above ambient levels given augmented nutrient supply. This metric neglects the primacy of light effects on productivity. We propose an alternative approach to quantify nutrient limitations using a “decline ratio” (DR), which quantifies the productivity decline from the maximum established by light availability. The DR treats light as the first‐order control and nutrient depletion as a disturbance causing productivity decline, allowing separation of nutrient and light influences. We used DR to assess nutrient diffusing substrate (NDS) experiments with three nutrients (nitrogen [N], phosphorus [P], iron [Fe]) from five Greenland streams during summer, where light is not limited due to the lack of canopy and low turbidity. We tested two hypotheses: (a) productivity maximum (i.e., highest chlorophyll‐ a among NDS treatments) is controlled by light and (b) DR depends on both light and nutrients. The productivity maximum was strongly predicted by light ( R 2 = 0.60). The productivity decline induced by N limitation (i.e., DR N ) was best explained by light availability when parameterized with either dissolved inorganic nitrogen concentration ( R 2 = 0.79) or N:Fe ratio ( R 2 = 0.87). These predictions outperformed predictions of RR for which light was not a significant factor. Reversing the perspective on nutrient limitation from “stimulation above ambient” to “decline below maximum” provides insights into both light and nutrient impacts on stream productivity.

Shin, Yuseung [School of Natural Resources and Env

Ansatz-Free Hamiltonian Learning with Heisenberg-Limited Scaling

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.

machine learning

On Rate-Limiting Mechanisms in NMC Cathodes: The Interplay of Low and High Current Constraints

In this study, we investigate the rate performance limits in LiNi 0.6 Mn 0.2 Co 0.2 O 2 cathodes for lithium-ion batteries, focusing on how cathode thickness, porosity, and threshold voltage impact discharge capacity. By conducting galvanostatic discharge experiments across a wide range of current densities using cathodes of varying thicknesses and porosities, we identify two distinct rate-limiting mechanisms: ionic liquid-diffusion and Ohmic/charge-transfer limitations. Our findings show that thick, dense cathodes are primarily limited by lithium diffusion in the electrolyte, while thinner and more porous cathodes are dominated by Ohmic/charge-transfer limitations, particularly at higher lower cutoff voltages. Crucially, these results allow us to identify the rate-limiting mechanisms in different cathode configurations, offering clear insights into how cathode design can be optimized for improved performance. Understanding these mechanisms is essential for designing next-generation batteries with enhanced rate performance, which is critical for applications such as electric vehicles and renewable energy storage systems.

Brischetto, Martin (ORCID:0000000339865813)

Evaluation of Hydrogen Storage Quantity Limits for Safety Requirements

As hydrogen storage facilities increase in size and capacity, it may be necessary to evaluate codes and standards that regulate hydrogen, especially in relation to allowable aggregate quantities. Existing regulations for other substances with comparable hazards such as oxygen, natural gas, and petroleum were reviewed; most fuels do not have aggregate quantity limits despite sometimes having individual tank capacity restrictions or limits for certain non-industrial, indoor, or small-scale applications. This precedent suggests that specifying a hydrogen quantity limit may not be necessary. Several possible methods for identifying an appropriate limit are presented to illustrate different approaches for a limit basis. These methods are based on overall risk, or the specific consequences inflicted by a jet fire or an explosion on people and infrastructure. However, these example metrics tend to require assumptions about potential leak sizes, suggesting that a general aggregate quantity limit would be difficult to justify without more system-specific requirements.

08 HYDROGEN

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Padeapproximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.

Corotation lag limit on mass-loss rate from Io

Considering rapid escape of H2O from Io during an early hot evolutionary epoch, an H2O plasma torus is constructed by balancing dissociation and ionization products against centrifugally driven diffusion, including for the first time the effects of corotation lag resulting from mass loading. Two fundamental limits are found as the mass injection rate increases: (1) an 'ignition' limit of 1.1 x 10 to the 6th kg/s, beyond which the torus cannot ionize itself and photoionization dominates; and (2) the ultimate mass loading limit of 1.3 x 10 to the 7th kg/s, which occurs when neutrals newly created by charge exchange and recombination cannot leave the torus, thereby bringing magnetospherically driven transport to a halt. Connecting this limit with the variations of Io's temperature in its early evolution epoch gives an estimate of the upper limit on the total mass loss from Io, about 3.0 x 10 to the 20th kg (for high-opacity nebula) and about 8.9 x 10 to the 20th kg (for low-opacity nebula). These limits correspond to eroding 8 km and 22 km of H2O from the surface. It is concluded that compared to the other Galilean satellites, Io was created basically dry.

Huang, T. S.

A theoretical analysis of the extinction limits of a methane-air opposed-jet diffusion flame

A theoretical analysis is described for a methane-air diffusion flame stabilized in the forward stagnation region of a porous metal cylinder in a forced convective flow. The analysis includes effects of radiative heat loss from the porous metal surface and finite rate kinetics but neglects the effects of gravity. The theoretically predicted extinction limits compare well with experimentally observed extinction limits from the literature. After the predicted limits compared well with the experimental limits, a parametric study of the effect of fuel surface emissivity and Lewis number was conducted with the numerical model. It was found that the computed blowoff limit is independent of radiative heat loss for high fuel blowing velocities but is a strong function of Lewis number. At low fuel blowing velocities, the extinction limit varies with both radiative heat loss and Lewis number. It is discovered, however, that even if thermal losses from the fuel surface are absent, the flame can extinguish at the fuel surface independently of Lewis number due to excessive reaction zone thinning.

Olson, S. L.

Analysis of exhaustive limited service for token ring networks

Token ring operation is well-understood in the cases of exhaustive, gated, gated limited, and ordinary cyclic service. There is no current data, however, on queueing models for the exhaustive limited service type. This service type differs from the others in that there is a preset maximum (omega) on the number of packets which may be transmitted per token reception, and packets which arrive after token reception may still be transmitted if the preset packet limit has not been reached. Exhaustive limited service is important since it closely approximates a timed token service discipline (the approximation becomes exact if packet lengths are constant). A method for deriving the z-transforms of the distributions of the number of packets present at both token departure and token arrival for a system using exhaustive limited service is presented. This allows for the derivation of a formula for mean queueing delay and queue lengths. The method is theoretically applicable to any omega. Fortunately, as the value of omega becomes large (typically values on the order of omega = 8 are considered large), the exhaustive limited service discipline closely approximates an exhaustive service discipline.

Peden, Jeffery H.

The Lagrangian multiplier method of finding upper and lower limits to critical stresses of clamped plates

The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the true stress, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Rayleigh-Ritz method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz, but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems the Lagrangian multiplier method of finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies.

Budiansky, Bernard