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NASA NTRS1980

The pulsating white dwarfs

The characteristics of variable white dwarfs are presented through an examination of observational data. The variable white dwarfs are normal, single, DA white dwarfs. The variations are caused by pulsations, but the pulsations are nonradial rather than radial pulsations. The periods are all very long. Excluding harmonics and cross frequencies, the shortest period is 114 sec and the longest period is 1186 sec. Without exception every variable is multiperiodic. The stability of the periods varies from extremely high to very low; the low stability of many of the variables perhaps being due to incomplete data. Finally, there is a strong correlation between the amplitude of the variations and their remaining properties. The higher amplitude variables have more periods in their light curves and the periods are more unstable.

Robinson, E. L.↗

NASA NTRS1984

Two new extremely hot pulsating white dwarfs

High speed photometry of the extremely hot, nearly degenerate stars PG 1707 + 427 and PG 2131 + 066 reveals that they are low-amplitude pulsating variables. Power spectral analysis shows both to be multiperiodic, with dominant periods of 7.5 and 6.4-6.9 minutes, respectively. Together with the known pulsators PG 1159 - 035 and the central star of the planetary nebula Kohoutek 1-16, these objects define a new pulsational instability strip at the hot edge of the H-R diagram. The variations of these objects closely resemble those of the much cooler pulsating ZZ Ceti DA white dwarfs; both groups are probably nonradial g-mode pulsators. Evolutionary contraction of the PG 1159 - 035 variables may lead to period changes that would be detectable in as little as 1 year. The optical and IUE spectra of the PG 1159 - 035 variables are characterized by absorption lines of C IV and other CNO ions, indicating radiative levitation of species heavier than helium. He II is also present in the spectra, but the hydrogen Balmer lines are absent. Effective temperatures near 100,000 K are required, and the He II 4686 A profiles indicate log g greater than 6. These helium-rich pulsators form the hottest known subgroup of the DO white dwarfs.

Bond, H. E.↗

NASA NTRS1993

Radial pulsations in DB white dwarfs?

Theoretical models of DB white dwarfs are unstable against radial pulsation at effective temperatures near 20,000-30,000 K. Many high-overtone modes are unstable, with periods ranging from 12 s down to the acoustic cutoff period of approximately 0.1 s. The blue edge for radial instability lies at slightly higher effective temperatures than for nonradial pulsations, with the temperature of the blue edge dependent on the assumed efficiency of convection. Models with increased convective efficiency have radial blue edges that are increasingly closer to the nonradial blue edge; in all models the instability persists into the nonradial instability strip. Radial pulsations therefore may exist in the hottest DB stars that lie below the DB gap; the greatest chance for detection would be observations in the ultraviolet. These models also explain why searches for radial pulsations in DA white dwarfs have failed: the efficient convection needed to explain the blue edge for nonradial DA pulsation means that the radial instability strip is 1000 K cooler than found in previous investigations. The multiperiodic nature of the expected pulsations can be used to advantage to identify very low amplitude modes using the uniform spacing of the modes in frequency. This frequency spacing is a direct indicator of the mass of the star.

Kawaler, Steven D.↗

NASA NTRS2020

CoCoSim, a Code Generation Framework for Control/command Applications: An Overview of CoCoSim for Multi-Periodic Discrete Simulink Models

We present CoCoSim, a framework to support the design, code generation and analysis of discrete dataflow model expressed in Simulink. In this work, we specifically focus on the analysis and code generation of multi-periodic systems. For that CoCoSim provides two complementary approaches: the first amounts to encode the multiperiodic semantics in a pure-synchronous one – à la Lustre–, enabling the use of model checker for verifying properties. The second provides a faithful code generation into multiple communicating (mono)synchronous components – à la Prelude– that can be then simulated or embedded in the final platform with any real-time scheduler. These approaches have been experimented in various settings.

Bourbouh, Hamza↗

NASA NTRS2022

Rotation of Low-mass Stars in Upper Centaurus-Lupus and Lower Centaurus-Crux with TESS

We present stellar rotation rates derived from Transiting Exoplanet Survey Satellite (TESS) light curves for stars in Upper Centaurus–Lupus (UCL; ∼136 pc, ∼16 Myr) and Lower Centaurus–Crux (LCC; ∼115 pc, ∼17 Myr). We find spot-modulated periods (P) for ∼90% of members. The range of light-curve and periodogram shapes echoes that found for other clusters with K2, but fewer multiperiod stars may be an indication of the different noise characteristics of TESS, or a result of the source selection methods here. The distribution of P as a function of color as a proxy for mass fits nicely in between that for both older and younger clusters observed by K2, with fast rotators being found among both the highest and lowest masses probed here, and a well-organized distribution of M-star rotation rates. About 13% of the stars have an infrared excess, suggesting a circumstellar disk; this is well matched to expectations, given the age of the stars. There is an obvious pileup of disked M stars at P ∼ 2 days, and the pileup may move to shorter P as the mass decreases. There is also a strong concentration of disk-free M stars at P ∼ 2 days, hinting that perhaps these stars have recently freed themselves from their disks. Exploring the rotation rates of stars in UCL/LCC has the potential to help us understand the beginning of the end of the influence of disks on rotation, and the timescale on which stars respond to unlocking.

L M Rebull↗

DOE OSTI2024

Solving the Grid Optimization Competition Challenge 3 Problem

The Grid Optimization Competition Challenge 3 Problem posed a multiperiod security-constrained unit commitment problem with base-case AC power flow. The problem formulation includes binary unit commitment decisions, nonlinear AC power flow and balance, dispatchable loads, and linearized contingency real power flow, among other features. This talk will present a modified consensus ADMM algorithm, which splits the problem into mixed-integer linear and nonlinear components, as a heuristic solution method for this large-scale mixed integer nonlinear program. We will present some computational results from the competition for our implementation and reflect on the challenges of participating the grid optimization competition.

AC power flow↗

DOE OSTI2025

Beyond Price Taker: Optimizing Integrated Energy Systems Considering Market/Grid Interactions

Integrated Energy Systems (IES) combine two or more processes to increase the efficiency, flexibility of operation, and the overall reliability. However, analyzing IESs in volatile electricity markets is challenging, since the volatility in electricity prices makes the conventional levelized cost-type analysis less realistic. This work presents two approaches to address the challenge: price-taker and a surrogates-based approach for incorporating market interactions. The price-taker approach formulates a multiperiod optimization problem that takes the time-varying electricity prices into account, and solves the optimization problem to determine the optimal operational schedule that maximizes the chosen economic metric. This approach is successfully applied to investigate the performance of flexible power and hydrogen co-production systems. The market surrogates approach trains a machine learning model to predict the market behavior as a function of the characteristics of the IES. The trained surrogate model is used to optimize the design and operation of the given IES in an electricity market. This approach is demonstrated on a case study involving a nuclear power plant retrofitted with a low-temperature electrolysis unit to co-produce power and hydrogen.

beyond price taker↗

DOE OSTI2024

ARPA-E Grid Optimization (GO) Competition Challenge 2

The ARPA-E Grid Optimization (GO) Competition Challenge 2, from 2020 to 2021, expanded upon the problem posed in Challenge 1 by adding adjustable transformer tap ratios, phase shifting transformers, switchable shunts, price-responsive demand, ramp rate constrained generators and loads, and fast-start unit commitment. Furthermore, Challenge 2 was a maximization problem while Challenge 1 was a minimization problem. Specifically, the economic surplus, defined as the benefit of serving load minus the cost of generation, is being maximized. It was expected that the objective value of a given solution should be positive, representing economic gain, but negative objectives from poor solutions were possible. The two code submission feature of Challenge 1 was maintained. Additionally, Divisions 3 and 4 within the competition permitted on/off switching of transmission lines (Divisions 1 and 2 did not). After the initial release of the Problem Formulation on 7/20/2020, ARPA-E Director Lane Genatowski announced Challenge 2 on 9/12/2020. The final May 31, 2021, version of the Problem Formulation was 97 pages long with 299 equations. The Challenge proceeded with 2 non-prize Events and 2 prize Events. Teams receiving Challenge 1 FOA awards and prize money were required to use the prize money to fund their Challenge 2 efforts (Georgia Institute of Technology, Global Optimal Technology, Inc., Lawrence Livermore National Laboratory, Lehigh University, Northwestern University, Artelys, Columbia, Pearl Street Technologies, Pennsylvania State University, and University of Colorado Boulder). For more information on the competition and challenge 2 see the "GO Competition Challenge 2 Information" resource below. Challenge 1 and Challenge 3 information can be found in the resources linked below.

ACOPF↗