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DOE OSTI2024

On the Impact of Bus Dwelling on Macroscopic Fundamental Diagrams

Network macroscopic fundamental diagrams (MFDs) have recently been shown to exist in real-world urban traffic networks. When present, MFDs can be used to model traffic dynamics within an urban network by dividing the network into a set of spatially compact homogeneous regions and tracking the average level of congestion in each region. Existing analytical methods to estimate MFD mostly focus on the behavior of a single type of vehicle and do not capture the patterns of mixed traffic (e.g., cars and buses). The existence of buses matters since a bus will block the movements of other vehicles when it dwells at the bus stop. This paper proposes an analytical method to estimate the impact of bus dwelling on a network’s MFD based on the network’s geometric features, traffic control strategies, and bus operation parameters, and validates the performance of the proposed method using simulations based on microscopic traffic models. Comparisons of the analytical and simulation results show that the proposed analytical method can generally provide a good estimate of the lower bound and upper bound of the network’s MFD.

Xu, Guanhao↗

DOE OSTI2024

Optimal load attachment of a deeply embedded ring anchor in clay

A Deeply Embedded Ring Anchor (DERA) system has been developed as a cost-effective solution for mooring arrays of floating offshore wind turbines (FOWTs) to the seabed. The DERA boasts several key features, including its versatility in various soil types, compact size, compatibility with diverse mooring systems, multi-line potential, and robust performance even under unintentional loading conditions. While prior preliminary studies have provided valuable insights into how the DERA can enhance cost-effectiveness by offering a high load capacity, these studies have predominantly focused on optimizing anchor performance under translational horizontal and vertical loading. However, to design the DERA optimally, we must also consider its ability to handle inclined loading conditions in addition to lateral and axial loadings. Due to its shorter length compared to a conventional caisson, the DERA has less resistance to moments, making it more sensitive to horizontal load capacity and the optimal load attachment depth concerning load angle. For this reason, our study introduces an analytical approach to evaluate the effects of inclined loading on anchor performance, utilizing the previously validated upper bound plastic limit analysis (PLA) method. In investigating the optimal load attachment of the DERA, this paper conducts a parametric study to analyze how factors such as load attachment depth, anchor aspect ratio, and load inclination affect the DERA’s load capacity. Our findings indicate that PLA can serve as a valuable analytical tool for assessing the ultimate load capacity of the DERA, particularly under inclined loading conditions.

42 ENGINEERING↗

NASA NTRS1994

Three-dimensional numerical simulation of current collection by a probe in a magnetized plasma

A three-dimensional numerical model for current collection in a magnetized plasma is reported. The model is based on an electrostatic particle-in-cell code. The model yields self-consistent sheath structure including distributions of plasma and the electric potential around the body and the collection of electrons. The analytical theory of current collection by a body in a magnetized plasma yields an upper bound for the collected current determined by the conservation of energy and canonical angular momentum. The theory shows that the collected charged particles come from a cylindrical volume aligned with the magnetic shadow of the body; the maximum radius r(sub o) of this volume is determined by the body size, body potential, and the ambient magnetic field. This theory does not deal with the sheath structure around the body. The condition for the actual current to approach the upper-bound value has been a matter of debate. Our simulations reveal when and why the collected current becomes equal to its upper-bound value. Sheath size in the radial direction perpendicular to the axial ambient magnetic field is determined by the current-limiting radius r(sub o). Our simulation yields time-average current in good agreement with its upper bound. This feature of the current collection is explained as follows: Once electrons enter the sheath, some of them are freely accelerated perpendicular to the magnetic field because they are demagnetized by the large gradients in the perpendicular electric fields. Simulations show a large perpendicular acceleration, producing perpendicular energy as large as that determined by the potential on the body, especially in the region where perpendicular electric fields (E perpendicular) are the strongest. An analysis shows that the demagnetization of electrons occurs above a threshold potential on the body. This threshold condition follows from the breakdown of the adiabaticity of the electron dynamics inside the sheath.

Singh, Nagendra↗

DOE OSTI2024

Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the two-dimensional (2D) Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2004

Conservative Analytical Collision Probability for Design of Orbital Formations

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Carpenter, J. Russell↗

NASA NTRS2004

Conservative Analytical Collision Probabilities for Orbital Formation Flying

Carpenter, J. Russell↗

NASA NTRS1985

Transient and steady state viscoelastic rolling contact

Based on moving total Lagrangian coordinates, a so-called traveling Hughes type contact strategy is developed. Employing the modified contact scheme in conjunction with a traveling finite element strategy, an overall solution methodology is developed to handle transient and steady viscoelastic rolling contact. To verify the scheme, the results of both experimental and analytical benchmarking is presented. The experimental benchmarking includes the handling of rolling tires up to their upper bound behavior, namely the standing wave response.

Padovan, J.↗

NASA NTRS1972

A critical examination of the validity of simplified models for radiant heat transfer analysis.

Examination of the directional effects of the simplified models by comparing the experimental data with the predictions based on simple and more detailed models for the radiation characteristics of surfaces. Analytical results indicate that the constant property diffuse and specular models do not yield the upper and lower bounds on local radiant heat flux. In general, the constant property specular analysis yields higher values of irradiation than the constant property diffuse analysis. A diffuse surface in the enclosure appears to destroy the effect of specularity of the other surfaces. Semigray and gray analyses predict the irradiation reasonably well provided that the directional properties and the specularity of the surfaces are taken into account. The uniform and nonuniform radiosity diffuse models are in satisfactory agreement with each other.

Toor, J. S.↗

NASA NTRS1981

Investigation of geomagnetic field forecasting and fluid dynamics of the core

The magnetic determination of the depth of the core-mantle boundary using MAGSAT data is discussed. Refinements to the approach of using the pole-strength of Earth to evaluate the radius of the Earth's core-mantle boundary are reported. The downward extrapolation through the electrically conducting mantle was reviewed. Estimates of an upper bound for the time required for Earth's liquid core to overturn completely are presented. High order analytic approximations to the unsigned magnetic flux crossing the Earth's surface are also presented.

Benton, E. R.↗

DOE OSTI2021

Analytical solutions of the Arrhenius-Semenov problem for constant volume burn

Analytical solutions to the Semenov thermal ignition problem for constant volume burn governed by Arrhenius reaction kinetics are derived. Specifically, an approximate analytical solution technique for the Arrhenius-Semenov differential equation is derived for reaction orders n ϵ R> 0 and exact solutions are also constructed for reaction orders n ϵ N : n ≤ 3. The approximation technique relies on expansion of the respective nondominant terms in the differential equation at the lower and upper bounds of the reaction progress variable in order to create a pair of integrable series. The two integrated series are then connected to create a single continuous analytical solution. Excellent agreement is observed between the analytical approximation and solutions obtained numerically. The presented approximation constitutes a simple and robust strategy for solving the Arrhenius-Semenov problem analytically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1984

Software reliability: Additional investigations into modeling with replicated experiments

The effects of programmer experience level, different program usage distributions, and programming languages are explored. All these factors affect performance, and some tentative relational hypotheses are presented. An analytic framework for replicated and non-replicated (traditional) software experiments is presented. A method of obtaining an upper bound on the error rate of the next error is proposed. The method was validated empirically by comparing forecasts with actual data. In all 14 cases the bound exceeded the observed parameter, albeit somewhat conservatively. Two other forecasting methods are proposed and compared to observed results. Although demonstrated relative to this framework that stages are neither independent nor exponentially distributed, empirical estimates show that the exponential assumption is nearly valid for all but the extreme tails of the distribution. Except for the dependence in the stage probabilities, Cox's model approximates to a degree what is being observed.

Nagel, P. M.↗

NASA NTRS1987

More on the decoder error probability for Reed-Solomon codes

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occurs. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub e (u) for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Cheung, K.-M.↗

NASA NTRS1989

More on the decoder error probability for Reed-Solomon codes

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occur. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub E (u) for the (255,223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Cheung, Kar-Ming↗

DOE OSTI2024

Semiclassical theory of bipolaronic superconductivity in a bond-modulated electron-phonon model

We analyze the transition temperature T c of bipolaronic superconductivity in a bond Su-Schrieffer-Heeger (bond-SSH) model—also known as a bond Peierls model—where the electron hoppings are modulated by bond phonons. Using a semiclassical instanton approximation justifiable in the adiabatic limit of slow phonons, we find that the bipolaron mass is only weakly enhanced, in contrast to the typical large mass enhancement found in standard (Holstein) electron-phonon models. Specifically, in the strong coupling limit, the bipolarons can freely slide within a degenerate manifold rather than become self-trapped. A gas of these bipolarons can undergo a superfluid transition at a critical temperature for which we obtain an upper bound. We find that this bound is exponentially larger than that in the Holstein model. In conclusion, our study provides an analytical understanding of the mechanism behind the high-T c bipolaronic superconductivity numerically observed in [Phys. Rev. X 13, 011010 (2023)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Connecting Material Properties and Redox Flow Cell Cycling Performance through Zero-Dimensional Models

Improvements in redox flow battery (RFB) performance and durability can be achieved through the development of new active materials, electrolytes, and membranes. While a rich design space exists for emerging materials, complex tradeoffs challenge the articulation of unambiguous target criteria, as the relationships between component selection and cycling performance are multifaceted. Here, we derive zero-dimensional, analytical expressions for mass balances and cell voltages under galvanostatic cycling, enabling direct connections between material/electrolyte properties, cell operating conditions, and resulting performance metrics (e.g., energy efficiency, capacity fade). To demonstrate the utility of this modeling framework, we highlight several considerations for RFB design, including upper bound estimation, active species decay, and membrane/separator conductivity-selectivity tradeoffs. Furthermore, we also discuss modalities for extending this framework to incorporate kinetic losses, distributed ohmic losses, and multiple spatial domains. Importantly, because the mass balances are solved analytically, hundreds of cycles can be simulated in seconds, potentially facilitating detailed parametric sweeps, system optimization, and parameter estimation from cycling experiments. More broadly, this approach provides a means for assessing the impact of cell components that simultaneously influence multiple performance-defining processes, aiding in the elucidation of key descriptors and the identification of favorable materials combinations for specific applications.

25 ENERGY STORAGE↗

NASA NTRS1974

Inelastic scattering in atom-diatomic molecule collisions. I - Rotational transitions in the sudden approximation

The impact parameter method and the sudden approximation are applied to determine the total probability of inelastic rotational transitions arising from a collision of an atom and a homonuclear diatomic molecule at large impact parameters. An analytical approximation to this probability is found for conditions where the electron exchange or overlap forces dominate the scattering. An approximate upper bound to the range of impact parameters for which rotational scattering can be important is determined. In addition, an estimate of the total inelastic cross section is found at conditions for which a statistical model describes the scattering well. The results of this analysis are applied to Ar-O2 collisions and may be readily applied to other combinations of atoms and molecules.

Stallcop, J. R.↗

NASA NTRS1988

The undetected error probability for Reed-Solomon codes

McEliece and Swanson (1986) offered an upper bound on P(E)u, the decoder error probability given u symbol errors occur. In the present study, by using a combinatoric technique such as the principle of inclusion and exclusion, an exact formula for P(E)u is derived. The P(E)u of a maximum distance separable code is observed to approach Q rapidly as u gets large, where Q is the probability that a completely random error pattern will cause decoder error. An upper bound for the expansion P(E)u/Q - 1 is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P(E)u indeed approaches Q as u becomes large, and that some laws of large number come into play.

Cheung, Kar-Ming↗

DOE OSTI2023

Nuclear-Level Effective Theory of 𝜇 → 𝑒 Conversion

The Mu2e and COMET 𝜇 → 𝑒 conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation. Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a 𝜇 → 𝑒 conversion rate with six response functions, each of which, in principle, is observable by varying nuclear properties of targets. We construct a nucleon-level nonrelativistic effective theory (NRET) to clarify the microscopic origin of these response functions and to relate rate measurements in different targets. This exercise identifies three operators and their small parameters that control the NRET operator expansion. We note inconsistencies in past treatments of these parameters. The NRET is technically challenging, involving 16 operators, several distorted electron partial waves, bound muon upper and lower components, and an exclusive nuclear matrix element. We introduce a trick for treating the electron Coulomb effects accurately, which enables us to include all of these effects while producing transition densities whose one-body matrix elements can be evaluated analytically, greatly simplifying the nuclear physics. We derive bounds on operator coefficients from existing and anticipated 𝜇 → 𝑒 conversion experiments. We discuss how similar NRET formulations have impacted dark matter phenomenology, noting that the tools this community has developed could be adapted for charged lepton flavor violation studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗