Theoretical astrophysics, neutrino physics, computational methods
The EML, continuous Sheffer operator eml(x,y) = exp(x) - ln(y), together with the constant 1, generates all elementary functions (integers, fraction, radicals, rational functions, arithmetic, exponentials, logarithms, trigonometry), enabling efficient gradient-based symbolic regression.
Self-gravitating elastic bodies in hydrostatic equilibrium with logarithmic equation of state and constant bulk modulus. Universal scaling properties allow all solutions from a single special function defined by Lane-Emden type ODE. The mass-radius relation reveals oscillatory patterns with maximum mass and radius limits. Analytical approximations for moment of inertia, binding energy, and gravitational potential, with applications to asteroids and moons (ApJ 2025, with B. Zbik).
Efficient numerical evaluation of generalized Fermi-Dirac integrals and their derivatives for moderate and large values of parameters (Computer Physics Communications, with A. Gil, J. Segura, N.M. Temme). These integrals are essential in astrophysics (neutrino processes, stellar structure) and solid-state physics.
Exact analytical and Monte Carlo solutions for accretion of collisionless matter (relativistic Vlasov gas) onto moving Schwarzschild and Kerr black holes. The key result (Phys. Rev. Lett. 2021, with P. Mach): the mass accretion rate is a non-monotonic function of the black hole velocity. Follow-up work with A. Cieslik extends the methods to Kerr geometry and planar configurations.
Classification of extrasolar planets by density reveals three distinct populations: ice/gas giants (~0.7 g/cc), iron/rock super-Earths (~7 g/cc), and objects consistent with brown dwarfs supported by electron degeneracy (~30 g/cc). Several extreme density planetary objects are also identified (Acta Phys. Pol. B, 2018, with J. Rafelski).
"How to Build the Perfect Igloo" — optimal discretization of a hemisphere into flat panels (Eureka, Cambridge, 2014). The problem of approximating curved surfaces with flat elements connects to geodesic dome construction, computational geometry, and practical architecture.
Neutrino emission from massive stars in the final stages of nuclear burning, hours to days before core-collapse supernova explosion. Calculated spectra from thermal pair annihilation, plasmon decay, and photo-neutrino processes provide signatures detectable by next-generation neutrino observatories — a potential early warning signal before the supernova.
Using neutrinos as probes of thermonuclear (Type Ia) supernova explosions. Neutrino signatures distinguish between explosion mechanisms — pure deflagration produces a single neutrino peak, while delayed detonation yields two — even though these scenarios produce nearly identical electromagnetic signals. Estimated event rates for future large-scale detectors.
Microphysics of neutrino production in hot dense astrophysical plasma. Rates and spectra for pair annihilation, plasmon decay, photo-neutrino and bremsstrahlung processes under nuclear statistical equilibrium (NSE). Published tabulated neutrino spectrum data for use in supernova and proto-neutron star modeling.
Analytical and numerical models of rapidly rotating self-gravitating bodies with barotropic equation of state. From exact solutions for the shape of polytropes with index unity (MNRAS 2017) to general-relativistic self-gravitating fluid tori and disks in motion around black holes (Phys. Rev. D 2018, with Mach, Malec et al.).
Formation and early evolution of proto-neutron stars — hot, neutrino-opaque remnants of core-collapse supernovae. Neutrino cooling mechanisms, equation of state of dense matter, and the Kelvin-Helmholtz contraction phase from a hot proto-neutron star to a cold neutron star.
Three-dimensional hydrodynamic simulations of core-collapse supernova explosions. Collaboration with T. Plewa (Florida State University) on shock revival in a 15 solar mass blue supergiant progenitor with SN 1987A energetics, nucleosynthetic yields, and element distribution (ApJ 2014).
Modeling of cosmological voids as underdensity regions in the static Einstein universe. Analytical solutions of the Tolman-Oppenheimer-Volkov equation with cosmological constant yield density contrast profiles and void radii consistent with observational data. Published in Phys. Rev. D 80, 103515 (2009).