Analog Electronic Computation of Stellar Structure: Polytropic Benchmarks, Circuit Scaling, and Error-Controlled Verification
Abstract
We present an electronic analog-computing framework for static stellar-structure equations and verify it using polytropic Lane-Emden benchmarks with known or high-accuracy reference solutions. Starting from an exploratory operational-amplifier and multiplier circuit, we identify sign, coefficient, central-regularity, and signal-conditioning problems that complicate direct electronic implementation. We develop dimensionless first-order formulations, derive regular finite-radius initial conditions, and construct voltage-scaled analog architectures with controlled signal headroom. The principal formulation uses a positive derivative state and reproduces the surface locations and dimensionless mass coefficients of the n = 0, 1, and 3 polytropes at the ideal scaled-voltage level. A common circuit architecture accommodates all three benchmarks, while the nonlinear n = 3 case demonstrates how voltage scaling and computation-speed adjustments can preserve the governing equations. Sensitivity analysis and Monte Carlo simulations quantify the propagation of calibration uncertainties into stellar observables. A separate regularized n = 1 circuit, implemented using AD734 and OPAx197 vendor macromodels, passes all 67 deterministic certification cases and three independently seeded Monte Carlo populations of 1000 cases each. All cases satisfy the predefined first-zero error tolerance of 0.020, with no saturation or convergence failures. A stricter 0.1% accuracy threshold is reported for characterization but is not used as the certification criterion. We also demonstrate a dimensionless four-state radiative extension beyond polytropic models. The results establish a reproducible framework for analog computation of stellar-structure benchmarks while explicitly distinguishing ideal calculations, vendor-macromodel verification, and future physical-hardware validation.
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BibTeX
@misc{elahi2026analog,
title = {{Analog Electronic Computation of Stellar Structure: Polytropic Benchmarks, Circuit Scaling, and Error-Controlled Verification}},
author = {Zuhoor Elahi and Wafa Gull and Christopher Sirola},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30230},
eprint = {2610.30230},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30230},
}
RIS
TY - UNPB
TI - Analog Electronic Computation of Stellar Structure: Polytropic Benchmarks, Circuit Scaling, and Error-Controlled Verification
AU - Zuhoor Elahi
AU - Wafa Gull
AU - Christopher Sirola
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30230
UR - https://arxiv.org/abs/2610.30230
AB - We present an electronic analog-computing framework for static stellar-structure equations and verify it using polytropic Lane-Emden benchmarks with known or high-accuracy reference solutions. Starting from an exploratory operational-amplifier and multiplier circuit, we identify sign, coefficient, central-regularity, and signal-conditioning problems that complicate direct electronic implementation. We develop dimensionless first-order formulations, derive regular finite-radius initial conditions, and construct voltage-scaled analog architectures with controlled signal headroom. The principal formulation uses a positive derivative state and reproduces the surface locations and dimensionless mass coefficients of the n = 0, 1, and 3 polytropes at the ideal scaled-voltage level. A common circuit architecture accommodates all three benchmarks, while the nonlinear n = 3 case demonstrates how voltage scaling and computation-speed adjustments can preserve the governing equations. Sensitivity analysis and Monte Carlo simulations quantify the propagation of calibration uncertainties into stellar observables. A separate regularized n = 1 circuit, implemented using AD734 and OPAx197 vendor macromodels, passes all 67 deterministic certification cases and three independently seeded Monte Carlo populations of 1000 cases each. All cases satisfy the predefined first-zero error tolerance of 0.020, with no saturation or convergence failures. A stricter 0.1% accuracy threshold is reported for characterization but is not used as the certification criterion. We also demonstrate a dimensionless four-state radiative extension beyond polytropic models. The results establish a reproducible framework for analog computation of stellar-structure benchmarks while explicitly distinguishing ideal calculations, vendor-macromodel verification, and future physical-hardware validation.
ER -