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1. Observational Analysis and Numerical Modeling of the Solar Wind Fluctuation Spectra during Intervals of Plasma Instability

   https://doi.org/10.3847/1538-4357/ac9f42  

   Markovskii, S. A.; Vasquez, Bernard J. (December 2022, The Astrophysical Journal)

   Abstract We perform a statistical analysis of observed magnetic spectra in the solar wind at 1 au with localized power elevations above the level of the ambient turbulent fluctuations. We show that the elevations are seen only when the intensity of the ambient fluctuations is sufficiently low. Assuming that the spectral elevations are caused by thermal-ion instabilities, this suggests that on average the effect of the solar wind background is strong enough to suppress the instability or obscure it or both. We then carry out nonlinear numerical simulations with particle ions and an electron fluid to model a thermal-ion instability coexisting with an ambient turbulence. The parameters of the simulation are taken from a known solar wind interval where an instability was assumed to exist based on the linear theory and a bi-Maxwellian fit of the observed distribution with core and secondary-beam protons. The numerical model closely matches the position of the observed spectral elevation in the wavenumber space. This confirms that the thermal-ion instability is responsible for the elevation. At the same time, the magnitude of the elevation turns out to be smaller than in the real solar wind. When higher intensity of the turbulence is used in the simulation, which is typical of solar wind in general, the power elevation is no longer seen. This is in agreement with the reduced observability of the elevations at higher intensities. However, the simulations show that the turbulence does not simply obscure the instability but also lowers its saturation level. 

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2. Towards Scalable Voltage Control in Smart Grid: A Submodular Optimization Approach

   https://doi.org/10.1109/ICCPS.2016.7479120  

   Liu, Zhipeng; Clark, Andrew; Lee, Phillip; Bushnell, Linda; Kirschen, Daniel; Poovendran, Radha (April 2016, 2016 ACM/IEEE 7th International Conference on Cyber-Physical Systems (ICCPS))

   Voltage instability occurs when a power system is unable to meet reactive power demand at one or more buses. Voltage instability events have caused several major outages and promise to become more frequent due to increasing energy demand. The future smart grid may help to ensure voltage stability by enabling rapid detection of possible voltage instability and implementation of corrective action. These corrective actions will only be effective in restoring stability if they are chosen in a timely, scalable manner. Current techniques for selecting control actions, however, rely on exhaustive search, and hence may choose an inefficient control strategy. In this paper, we propose a submodular optimization approach to designing a control strategy to prevent voltage instability at one or more buses. Our key insight is that the deviation from the desired voltage is a supermodular function of the set of reactive power injections that are employed, leading to computationally efficient control algorithms with provable optimality guarantees. Furthermore, we show that the optimality bound of our approach can be improved from 1/3 to 1/2 when the power system operates under heavy loading conditions. We demonstrate our framework through extensive simulation study on the IEEE 30 bus test case. 

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3. Secondary Proton Beam Instability in a Turbulent Solar Wind at 50 R _⊙

   https://doi.org/10.3847/1538-4357/acf656  

   Markovskii, S. A.; Vasquez, Bernard J. (September 2023, The Astrophysical Journal)

   Abstract We investigate a secondary proton beam instability coexisting with the ambient solar wind turbulence at 50R_☉. Three-dimensional hybrid numerical simulations (particle ions and a quasi-neutralizing electron fluid) are carried out with the plasma parameters in the observed range. In the turbulent background, the particle distribution function, in particular the slope of the “bump-on-tail” responsible for the instability, is time-dependent and inhomogeneous. The presence of the turbulence substantially reduces the growth rate and saturation level of the instability. We derive magnetic power spectra from the observational data and perform a statistical analysis to evaluate the average turbulence intensity at 50R_☉. This information is used to link the observed frequency spectrum to the wavenumber spectrum in the simulations. We verify that Taylor’s frozen-in hypothesis is valid for this purpose to a sufficient extent. To reproduce the typical magnetic power spectrum of the instability observed concurrently with the background turbulence, an artificial spacecraft probe is run through the simulation box. The thermal-ion instabilities are often seen as power elevations in the kinetic range of scales above an extrapolation of the turbulence spectrum from larger scales. We show that the elevated power in the simulations is much higher than the background level. Therefore, the turbulence at the average intensity does not obscure the secondary proton beam instability, as opposed to the solar wind at 1 au, in which the ambient turbulence typically obscures thermal-ion instabilities. 

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4. Stability and minimality of the ball for attractive-repulsive energies with perimeter penalization

   https://doi.org/10.4171/IFB/548  

   Bonacini, Marco; Topaloglu, Ihsan (June 2025, Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications)

   We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exist curves in the perturbation-volume parameter space that separate stability/instability and global minimality/nonminimality regions of the ball, and provide a precise description of these curves for certain interaction kernels. In particular, we show that in small perturbation regimes there are (at least) two disconnected regions for the mass parameter in which the ball is stable, separated by an instability region. 

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5. Hybrid Simulations of the Resonant and Non-Resonant Cosmic Ray Streaming Instability

   Haggerty, C.; Caprioli, D.; Zweibel, E. (July 2019, 36th International Cosmic Ray Conference (ICRC2019))

   Using hybrid simulations (kinetic ions--fluid electrons), we test the linear theory predictions of the cosmic ray (CR) streaming instability. We consider two types of CR distribution functions: a "hot" distribution where CRs are represented by a drifting power law in momentum and an anisotropic "beam" of monochromatic particles. Additionally, for each CR distribution we scan over different CR densities to transition from triggering the resonant to the non-resonant (Bell) streaming instability. We determine the growth rates of these instabilities in simulations by fitting an exponential curve during the linear stage, and we show that they agree well with the theoretical predictions as a function of wave number agree. We also examine the magnetic helicity as a function of time and wave number, finding a general good agreement with the predictions, as well as some unexpected non-linear features to the instability development. 

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