The core idea of the spectral theory mathematical approach is that the relationship between a given interaction potential and the structure and dynamics can be inferred from the spectral properties of the corresponding infinite-dimensional Hamiltonian operator. For a given interaction potential and plasma conditions, a corresponding Hamiltonian can be defined. Then, the time-evolved dynamics of the system evolving under the action of this Hamiltonian depends on the collection of possible energy states, or the spectrum of the Hamiltonian. During a structural or dynamical transition, changes in the structural or dynamical function and the correlation scale lengths within the system also yield changes in the corresponding energy spectrum and related transport properties.
Anomalous diffusion refers to a non-linear or non-Gaussian diffusion process that deviates from classical diffusion models. In plasma physics, anomalous diffusion is often observed in turbulent or nonequilibrium plasmas, where irregular fluctuations or temperature differences may cause more complex transport behavior. Understanding and modeling anomalous diffusion is essential for predicting and controlling transport processes in plasmas, impacting fusion research, and space physics.
Dusty plasmas are a type of complex plasma as they contain micron-sized particles of dust. Dusty plasmas are commonly found in space (planetary rings, comet tails), industry (semiconductor manufacturing, thin-film growth), and laboratory experiments. Understanding dusty plasmas is crucial for explaining phenomena in these environments and developing applications such as dust particle manipulation and self-organization in complex plasmas.
Energetic electrons can be trapped or transported in magnetic islands within fusion devices, such as tokamaks, due to the complex interplay between magnetic fields and particle trajectories. These electrons, with energies significantly higher than the plasma's thermal energy, can contribute to various phenomena, including localized heating, instabilities, and enhanced particle transport, impacting the overall performance and stability of the fusion plasma.
Machine learning can enhance understanding of disruptions in plasma confinement devices by analyzing large datasets to identify complex patterns and correlations that may be difficult to discern using traditional methods. By employing advanced algorithms, machine learning can help predict and mitigate disruptions by recognizing precursor signals and providing insights into the underlying physical processes leading to disruptions.
InProgress: Anisotropic Anomalous Diffusion and Velocity Distributions in Microgravity Dusty Plasma by Bradley Andrew and Evdokiya Kostadinova
Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer by Evdokiya et al.
Magnetized Dusty Plasma : Beckers, Job, et al. "Physics and applications of dusty plasmas: The Perspectives 2023." Physics of Plasmas 30.12 (2023) which Dr. Kostadinova helped in writing. See the magnetized dusty plasmas figure above.
InProgress: Energetic Electron Diffusion and Trapping in Magnetic Island in Fusion Devices by Jessica Eskew, Bradley Andrew, Evdokiya Kostadinova
InProgress: Machine Learning on the PK-4 Experimental System by Brooks Howe and Evdokiya Kostadinova
Heat shield ablation tests done at DIII-D by Chris Mehta and Evdokiya Kostadinova
Delocalization in infinite disordered two-dimensional lattices of different geometry, Physical interpretation of the spectral approach to delocalization in infinite disordered systems, Transport properties of disordered two‐dimensional complex plasma crystal.
Dr. Kostadinova has also authored a Springer book on employing novel mathematical techniques in the study of energy transport in two-dimensional disordered systems.
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