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We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models…
We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation…
Supersolids are theoretically predicted quantum states that break the continuous rotational and translational symmetries of liquids while preserving superfluid transport properties. Over the last decade, much progress has been made in…
We have calculated the pulsations of massive stars using a nonlinear hydrodynamic code including time-dependent convection. The basic structure models are based on a standard grid published by Meynet et al. (1994). Using the basic…
The study of our Solar System -- its formation, evolution, and long-term stability -- has been ongoing for centuries and is now a standard part of scientific education. While the formation of other Solar-like exoplanetary systems is…
Preplanetary nebulae and planetary nebulae are evolved, mass-losing stellar objects that show a wide variety of morphologies. Many of these nebulae consist of outer structures that are nearly spherical (spiral/shell/arc/halo) and inner…
A number of theoretical and simulation results on star and structure formation in galaxy interactions and mergers is reviewed, and recent hydrodynamic simulations are presented. The role of gravity torques and ISM turbulence in galaxy…
The spherically symmetric thin shells of the barotropic fluids with the linear equation of state are considered within the frameworks of general relativity. We study several aspects of the shells as completely relativistic models of stars,…
Using a modified WKB approach, we present a rigorous semi-classical analysis for solutions of nonlinear Schroedinger equations with rotational forcing. This yields a rigorous justification for the hydrodynamical system of rotating…
I describe recent progress in terms of 3D hydrodynamical model atmospheres and 3D line formation and their applications to stellar abundance analyses of late-type stars. Such 3D studies remove the free parameters inherent in classical 1D…
Starting from hydrodynamic equations, we have established a set of hydrodynamic equations for average flow and a set of dynamic equations of auto- and cross-correlations of turbulent velocity and temperature fluctuations, following the…
This paper explores hydrodynamics and hydrostatic of a star in post-Newtonian approximation of massive Bran-Dicke gravity. We study approximated solution of the field equations upto $O(c^{-4})$ and generalize Euler equation of motion. We…
We consider simple hydrodynamical models of galactic dark matter in which the galactic halo is a self-gravitating and self-interacting gas that dominates the dynamics of the galaxy. Modeling this halo as a sphericaly symmetric and static…
Cosmological perturbations of sufficiently long wavelength admit a fluid dynamic description. We consider modes with wavevectors below a scale $k_m$ for which the dynamics is only mildly non-linear. The leading effect of modes above that…
In the general matter composition where the multiple scalar fields and the multiple perfect fluids coexist, in the leading order of the gradient expansion, we construct all of the solutions of the nonlinear evolutions of the locally…
Massive stars can develop into tepid supergiants at several stages of their post main-sequence evolution, prior to core He-burning, on a blue loop, or close to the final supernova explosion. We discuss observational constraints on models of…
We report on numerical results from an independent formalism to describe the quasi-equilibrium structure of nonsynchronous binary neutron stars in general relativity. This is an important independent test of controversial numerical…
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
We study universal spatial features of certain non-equilibrium steady states corresponding to flows of strongly correlated fluids over obstacles. This allows us to predict universal spatial features of far-from-equilibrium systems, which in…
Motivated by recent observations of plateaus and minima in the radial abundance distributions of heavy elements in the Milky Way and some other spiral galaxies, we propose a dynamical mechanism for the formation of such features around…