1. Recovering 3D Magnetic Turbulence from Single-Frequency Faraday Screens

arXiv:2602.22204 (Submitted to The Astrophysical Journal)

Authors: Aliaksandr Melnichenka, Alex Lazarian, Dmitri Pogosyan

We demonstrate that three-dimensional magnetic turbulence statistics can be recovered from single-frequency radio polarimetry through a novel directional spectrum estimator. This method, validated against high-resolution magnetohydrodynamic simulations and controlled synthetic models, reliably extracts inertial-range scaling properties of turbulent magnetic fields. Comparative analysis with multi-frequency techniques establishes the conditions under which single-band observations suffice, providing observers with a practical framework for determining optimal frequency coverage requirements.

2. Turing Instability and Electronic Self-Oscillatory Dynamics in Dirac Fluids

arXiv:2512.16571 (In Review at Physical Review Letters)

Authors: Aliaksandr Melnichenka*, Prayoga Liong*, Anton Bukhtatyi, Albert Bilous, Leonid Levitov (*equal contribution)

We demonstrate that ultra-clean electronic materials, such as graphene, exhibit hydrodynamic instabilities analogous to thin fluid films: above a critical drive, the flow becomes unstable and develops self-sustained traveling waves. These waves manifest as coupled oscillations of electron density and current, producing both a non-analytic transition in the average current and a narrow-band, tunable high-frequency signal. This work establishes a new mechanism for generating and controlling high-frequency electronic oscillations through collective fluid-like behavior, distinct from conventional circuit-based approaches.

3. Phase-Space Diffusion Coefficients for Self-Interacting Dark Matter near Supermassive Black Holes

In Preparation (2026)

Authors: Aliaksandr Melnichenka, Xuejian Shen, Vinh Tran, Mark Vogelsberger

We derive and validate first- through third-order velocity diffusion coefficients for self-interacting dark matter particles undergoing gravitational and short-range collisions near a supermassive black hole. Using Monte Carlo orbit-averaged simulations, we identify the regime where the standard Fokker-Planck truncation at second order fails and higher-order corrections become essential. This framework provides the transport theory needed to predict whether dark matter cores surrounding galactic nuclei collapse or grow, a question central to constraining dark matter self-interaction cross sections from observations.

1. American Astronomical Society Meeting 247 (AAS 2026)

New Measure to Study Synchrotron Polarization

Presentation on the directional spectrum diagnostic for recovering three-dimensional magnetic turbulence statistics from single-frequency polarization maps.

2. The Magnetized Turbulent Universe (Invited Talk)

Recovering 3D Magnetic Turbulence from a Single Polarization Map (November 2025, Playa del Carmen, Mexico)

Invited 30-minute talk at an international conference honoring Prof. Alex Lazarian. I presented the directional spectrum diagnostic and crossover scaling analysis, covering synthetic validation tests and MHD simulation results. I was one of the only undergraduates presenting alongside faculty and postdocs.

3. American Physical Society Division of Plasma Physics (APS DPP 2025)

Measuring 3-D Magnetic Turbulence from a Single Polarization Map (November 2025, Long Beach, CA)

Contributed oral presentation of the first high-resolution magnetohydrodynamic validation of the Lazarian-Pogosyan Faraday turbulence theory, demonstrating how single-band radio polarimetry can constrain inertial-range magnetic turbulence properties.

4. University of Kentucky Society of Physics Students (Invited Talk)

Recovering 3D Magnetic Turbulence from a Single Polarization Map (October 2025, Lexington, KY)

Invited talk on whether a single polarization image at one wavelength can constrain inertial-range magnetic turbulence. Introduced the polarization-angle directional correlation, an observer-ready statistic that recovers turbulence scaling properties and cleanly separates emission-dominated from Faraday-screen structure, with implications for LOFAR, MeerKAT, VLA, and the Square Kilometre Array.