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Nonlinear singularly perturbed optimal control problems with singular arcs

A third order, nonlinear, singularly perturbed optimal control problem is considered under assumptions which assure that the full problem is singular and the reduced problem is nonsingular. The separation between the singular arc of the full problem and the optimal control law of the reduced one, both of which are hypersurfaces in state space, is of the same order as the small parameter of the problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem. A numerical example is included.

Ardema, M. D.

Sound propagation through a subsonic jet due to a source near the duct exit

Matched asymptotic solutions are constructed for the acoustic potentials of a periodic point source located in a two-dimensional subsonic jet near the exit of the duct with the ratio of the duct thickness to the acoustic wave length as the small parameter. The leading term of the far field solution has the same directionality effect as that for an infinite jet without the duct and that when the plane at the duct exit is considered to be a plane of symmetry. However, the intensity is different because of the wave propagation into the duct and is dependent on the location of the source.

Ting, L.

Motion of a curved vortex filament with decaying vortical core and axial velocity

The motion and decay of a curved vortex filament having large axial and circumferential velocity components in a three-dimensional stream are analyzed by using the method of matched asymptotic expansions of the incompressible Navier-Stokes equations. The small parameter is the square root of the ratio of the kinematic viscosity to the circulation. The outer region is analyzed by the classical Biot-Savart law, and its solution is matched to that of the inner region, where viscous effects are important. Equations describing the coupling between the inner vortex structure and the motion of the vortex filament as well as the time evolution of the inner vortex structure are obtained. Equations are derived for the motion of the vortex filament and for the change and decay in time and space of the leading-order circumferential and axial velocity and vorticity components. Solutions are constructed for these components in terms of initial data.

Callegari, A. J.

Influence of a weak gravitational wave on a bound system of two point-masses

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

Turner, M. S.

Application of the Method of Coordinate Perturbation to Unsteady Duct Flow

The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics.

Himmel, Seymour C.

Steam generator model design parameter sensitivity study for small modular reactor system

Here, this study focuses on design parameter sensitivity studies pertaining to several Once-Through Steam Generator (OTSG) model cases both with and without a riser using python and advanced risk assessment and optimization tool, i.e. Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory (INL), to support a Small Modular Reactor (SMR) system. The presented Steam Generator (SG) python-based model is a mathematical representation of a steam-generating unit for a Pressurized Water Reactor (PWR)-type SMR system, including fluid flow and heat transfer equations, models, and correlations. Design studies involve changing the model’s input design parameters (e.g., temperature, pressure, mass flow rate) to observe the resulting effects on the output of the system, such as the Heat Transfer Coefficient (HTC), Reynolds number, Nusselt number, and heat transfer performance. Sensitivity studies analyze the degree to which system output and/or desired parameters (e.g., HTC or heat transfer performance) are sensitive to changes in the input parameters. By using RAVEN, detailed design parametric sensitivity studies. Six input parameters—namely, the pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid) of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (i.e., ±1%, ±5% and ±10 % relative changes) for 600 samples. The analysis results give valuable insights into SG system performance, and provide justification for further research and development such as optimized sensor placement, design verification, validation, and optimization.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

Kinetic theory of a two-dimensional magnetized plasma. II - Balescu-Lenard limit.

The kinetic theory of a two-dimensional one-species plasma in a uniform dc magnetic field is investigated in the small plasma parameter limit. The plasma consists of charged rods interacting through the logarithmic Coulomb potential. Vahala and Montgomery earlier (1971) derived a Fokker-Planck equation for this system, but it contained a divergent integral, which had to be cut off on physical grounds. This cutoff is compared to the standard cutoff introduced in the two-dimensional unmagnetized Fokker-Planck equation. In the small plasma parameter limit, it is shown that the Balescu-Lenard collision term is zero in the long time average limit if only two-body interactions are considered. The energy transfer from a test particle to an equilibrium plasma is discussed and is also shown to be zero in the long time average limit. This supports the unexpected result of zero Balescu-Lenard collision term.

Vahala, G.

Enabling Mission Flexibility to Battery Driven Deep Space Endeavors With Generalized Battery-Health-Monitoring Using Physics-Based and Data-Driven Reduced-Order Models

The needs and requirements for an electrochemical energy storage for deep space exploration is well explored. It is often understood that different mission sites and environmental conditions require different battery chemistries or technologies. Additionally, various engineering solutions are deployed to overcome specific chemical challenges. One often overlooked need is the “health” monitoring of an electrochemical storage system. The term generalized health monitoring, as envisioned in this work, refers to the monitoring of various aspects such as electrode health, electrolyte health, reaction pathway health, cooling system health, sensor health, and BMS health [1]. Generalized health monitoring allows mission leads, engineers, and scientists to incorporate flexibility in mission designs, make on-the-fly mission changes, and extend the duration of science missions. Moreover, it enables automation and data-driven decision-making without compromising safety and performance. Recently, our group developed a hierarchy of thermal reduced-order models (TROM) by combining a physics-based modeling approach and data-driven model reduction techniques applied to flight data [2]. The resulting TROMs were found to be not only accurate but also identifiable from the flight data. Consequently, the coefficient of variance of the model parameters is small over the course of hundreds of flights, allowing for monitoring the parameter evolution trajectories as the battery ages and degrades. These parameters constitute the metrics of the generalized health of a battery. Monitoring their evolution allows such models to be used for anomaly detection and prognostics, improving early detection of abnormal behavior and thus enabling timely maintenance, longer battery life, and enhanced battery safety. For this presentation, the practicality of the thermal model will be validated on a pack of 14cells under various topology configurations such as 1S14P, 2P7S, 7S2P, and 1P14S. It is well known that manufacturing and non-uniform aging lead to variability in the performance of a cell, which is exacerbated by cell balancing during active load. Additionally, in extreme scenarios, the paramount objective is to complete the mission, regardless of the stresses on the battery. Topology-induced balancing issues further stress the battery. The goal of this study is to determine if the noise (identifiability) in the reduced-order thermal model parameters is sensitive to topology, cell spacing, cooling strategy, and manufacturing or age variability. The variability in cells is considered by assuming a multimodal distribution for microscopic parameters of a cell (such as porosity, tortuosity, reaction kinetics, volumetric thermal conductivity, and volumetric heat capacity). The compounded effect of manufacturing variability, topological selection, cooling strategies, and cell balancing ages each cell in a battery differently. The study aims to clarify whether the challenge in extracting maximum information depends on the minimum number of sensors or models used for data extraction.

Automation

Curves of growth for van der Waals broadened spectral lines

Curves of growth are evaluated for a spectral line broadened by the van der Waals interactions during collisions. The growth of the equivalent widths of such lines is shown to be dependent on the product of the perturber density and the 6/10 power of the van der Waals potential coefficient. When the parameter is small, the widths grow as the 1/2 power of the optical depth as they do for the Voigt profile: but when the parameter is large, they grow as 2/3 power and, hence, faster than the Voigt profile. An approximate analytical expression for the computed growth characteristics is given.

Park, C.

Ultrasonic characterization of material heterogeneities in stainless steel components produced by laser powder bed fusion

We introduce pulse-echo ultrasound as a method for characterizing the impact of powder bed fusion parameters on the properties of additively manufactured stainless-steel components, their material anisotropy, and location-dependent heterogeneity. Our results indicate that accurate characterization requires careful selection of ultrasonic propagation paths, which must consider the direction of additive layering, variations in processing parameters, and the component's geometry. We employed two distinct methods to estimate material properties from ultrasonic data: One assumes isotropy, while the other accounts for anisotropic interactions during the propagation of elastic waves. When applied to samples fabricated with laser energy densities ranging from 24 to 42 J/mm³ , these methods revealed transverse isotropy and weak anisotropy (quantified by small Thomsen parameters, ε = 0.0651 and γ = 0.0092) and less than a ∼6 % change in acoustic impedance. The assumption of isotropy, in this case, leads to small errors (less than 4 % or 1 % for Young's modulus in the build or transverse directions) when estimating orthotropic material properties using ultrasonic data measured along just two orthogonal directions, one of which must align with the build direction. By comparing ultrasonic measurements — which aggregate the spatial variability in material properties along the length of elastic wave propagation into a single value — with localized measurements obtained from surface nanoindentation, we uncovered and spatially profiled significant differences between the surface and interior properties. Specifically, the surface Young's modulus decreased from approximately 210 GPa to 180 GPa within a depth of about 3 mm. We attribute this surface-localized heterogeneity in PBF-fabricated components to distinct thermal histories experienced by the surface and interior regions. Collectively, the results of this study establish a framework for the ultrasonic characterization of material heterogeneity and anisotropy in material properties and demonstrate its application in additively manufactured metal components.

36 MATERIALS SCIENCE

Exploring Uncertainty in Moment Estimation for Small Earthquakes in Southern Nevada Using the Coda Envelope Method

Compiling source parameter estimates for small earthquakes is important both for our understanding of earthquake physics and for accurately assessing earthquake hazard. Reliable source parameter estimates are difficult to achieve for small earthquakes, in part due to our inability to accurately model the relevant physical processes at high frequencies. The coda envelope methodology developed by Mayeda and Walter (1996) and Mayeda et al. (2003) can mitigate this concern and estimate the moment of small earthquakes by determining the parameters that control the shape of the S-wave coda envelope while eliminating path effects by minimizing the scatter between seismic stations. Here, we use an open-source implementation of this technique called the Coda Calibration Tool (CCT; Barno, 2017) to calculate CCT-based moment magnitude estimates of small earthquakes (M L 0–3) in the Rock Valley, Nevada, region within the Nevada National Security Site. The Rock Valley data set is of particular interest because it allows us to explore the changes in uncertainties of the coda calibration method with earthquake size and depth. We found that a consistent linear relationship exists between the local magnitude M L and our coda-derived M w estimates for earthquakes as small as M L 0–3, but that current CCT workflows do not accurately characterize very shallow events. We also demonstrate that the epistemic uncertainty in the apparent stress value assumed by the CCT algorithm can influence magnitude estimates of small earthquakes. In conclusion, these results provide valuable insight into the seismicity of this region, and inform future analysis and modeling efforts for nuclear monitoring and seismic hazard.

58 GEOSCIENCES

Quantum chemically calculated Abraham parameters for quantifying and predicting polymer hydrophobicity

The leakage and accumulation of plastic in the environment is a significant and growing problem with numerous detrimental impacts and has led to a push toward the design and development of more environmentally benign materials. To this end, we have developed a quantum chemistry-based model for predicting the mobility of polymer materials from molecular structure. Hydrophobicity is used as a surrogate for mobility given that hydrophobic interactions drive much of the partitioning of contaminants in and out of various environmentally relevant compartments. To model polymer hydrophobicity, we adjusted a previously developed Quantum Chemically Calculated Abraham Parameter model to calculate Abraham parameters of small molecules from molecular structure information. The resulting model predicted the octanol-water partition coefficient (K OW ) of polymer repeating units with a root mean square error (RMSE) of 0.48 (log scale). Additionally, the hydrophobicity of high molecular weight polymer materials was captured through solubility parameters and Nile red staining experiments from the literature and predicted with RMSEs of 1.21 (J/cc) 0.5 and 3.42 nm, respectively. Finally, to test the environmental applicability of the model, the relative adsorption capacity of three polymers was predicted and used to unify sorption isotherms across multiple sorbates and polymer sorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Cryogenic-Refined MOSFET Modeling for Oscillator, Frequency Divider, and Amplifier Designs Below 4 K

Capturing device characteristic changes at cryogenic temperatures is crucial for cryo-CMOS circuit designs. In this work, we present an isothermal cryogenic-refined modeling approach for CMOS transistors that is simple, low overhead, and easy to implement while offering the required accuracy for predicting circuit performance at the designated temperatures. Guided by die-level measurement data and circuit design principles, the model introduces corrections to only five critical parameters: threshold voltage, carrier mobility, elevated low-frequency flicker noise, dominant high-frequency shot noise, and subthreshold swing (SS). These refinements are implemented around the foundry-provided SPICE model, which is typically validated only down to about 200 K. With these adjustments, the proposed cryogenic-refined model achieves less than 5% error in both large-signal metrics (I–V characteristics) and small-signal parameters (e.g., transconductance) when compared with device measurements at deep-cryogenic temperatures. The methodology is validated in two advanced technologies: TSMC 40-nm CMOS and GlobalFoundries (GF) 45-nm RF-SOI. We further demonstrate its applicability in three representative RF circuits: a 30-GHz LC oscillator, a high-speed current-mode-logic (CML) frequency divider (FD), and a subthreshold Gb/s amplifier, all showing close agreement between simulated predictions and measurements performed at 4 and 2.5 K. Finally, we believe that the proposed approach is implementation-friendly and can significantly accelerate the development of cryo-CMOS integrated circuits.

circuit modeling

Controlled expansion for pairing in a polarized band with strong repulsion

Can strong repulsive interactions be shown to give rise to pairing in a controlled way? We find that for a single flavor polarized band, there is a small expansion parameter in the low density limit, once the Bloch wavefunction form factor is taken into account. A perturbative expansion is possible, even if the interaction is much stronger than the Fermi energy ε F . As a matter of principle, our work shows analytically how strong pairing can emerge from strong repulsion. Here, we illustrate our method with two examples: a 2D Dirac model and a 1D tight binding model with two orbitals. In the latter case, using density matrix renormalization group, we show that the analytical theory indeed guided us to discover the parameter regime where p-wave pairing with order-1 strength is dominant.

Ferromagnetic superconductors

Earth-based navigation capabilities for outer planet missions.

The role of new Earth-based radio metric data types and of advanced estimation algorithms in navigating an outer planet spacecraft in the vicinity of Saturn has been analyzed. The data types included in the study consist of conventional range and range-rate measurements taken from a single station and simultaneous and nearly simultaneous measurements obtained from pairs of stations during overlapping viewing periods. The utility of a third data set that is produced by explicitly differencing the simultaneous points has also been investigated. The data was processed with a conventional least squares batch filter and with a sequential filter that estimated parameters describing small stochastic accelerations (process noise) acting on the spacecraft. It was found that process noise can produce large errors in the estimates obtained from batch filtering conventional and simultaneous data, and that the only batch filtered estimates that were reliable were those obtained from differenced data. The performance of the simultaneous data in the presence of process noise is greatly improved by sequential filtering.

Hildebrand, C. E.

A method for estimating both the solubility parameters and molar volumes of liquids

Development of an indirect method of estimating the solubility parameter of high molecular weight polymers. The proposed method of estimating the solubility parameter, like Small's method, is based on group additive constants, but is believed to be superior to Small's method for two reasons: (1) the contribution of a much larger number of functional groups have been evaluated, and (2) the method requires only a knowledge of structural formula of the compound.

Fedors, R. F.