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Formulations of Eulerian general relativistic ideal hydrodynamics in conservation form are analyzed in some detail, with particular emphasis to geometric source terms. Simple linear transformations of the equations are introduced and the…
Hydrodynamical interactions of active micro-particles are pervasive in our planet's fluid environments. Hence, understanding the interactions of these self-propelled particles is essential for science and engineering. In this paper the…
Extending the Gaussian covariant hydrodynamics approach [1] using torsion as an auxiliary field we formulate a fluctuating hydrodynamics with spin which is covariant with respect to pseudo-gauge transformations as well as generally…
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result…
The application range of perfect spin hydrodynamics is studied in two cases: one based on the classical spin description and the other using a quantum spin density matrix (Wigner function). Different forms of the conditions connecting the…
This thesis is dedicated to analysing the general structure of two- and three-point correlation functions of conserved currents of arbitrary integer or half-integer spins in three- and four-dimensional (super)conformal field theory.
The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the…
We derive equations of motion for dissipative spin hydrodynamics from kinetic theory up to first order in a gradient expansion. Choosing a specific form of the matching conditions, relating the change in the spin potential to the spin…
A complete classification of integrable conservative hydrodynamic chains is presented. These hydrodynamic chains are written via special coordinates -- moments, such that right hand sides of these infinite component systems depend linearly…
It is usually believed that physics in off-equilibrium state characterized by hydrodynamic gradient can be equivalently studied using equilibrium state with suitable metric perturbation. We scrutinize this assumption using chiral kinetic…
We compare two recently developed frameworks of perfect spin hydrodynamics for spin-$1/2$ particles, based respectively on classical kinetic theory and the Wigner function. We show that the conserved currents in both approaches have the…
The detailed analysis of model of the hydrodynamical vortice on a plane is executed. The derivation of the corresponding equation and its simplified variant is given, a partial solutions are constructed. The question on application of…
Event-by-event hydrodynamics (or hydrodynamics with fluctuating initial conditions) has been developed in the past few years. Here we discuss how it may help to understand the various structures observed in two-particle correlations.
We establish the equations which translate a conservation law for the problem of the seismic response of an above-ground structure (e.g., building, hill or mountain) of arbitrary shape and inquire whether both the implicit (formal) and…
We investigate the dynamics of spin-nonequilibrium electron systems for the case when normal electron collisions prevail over the other scattering processes and the "hydrodynamic flow" regime is realized. The hydrodynamic equations for the…
We formulate a relativistic hydrodynamic theory for fluids with spin and intrinsic dilation charges. Using an entropy-current analysis, we derive constitutive relations featuring a bulk viscosity and a dilation conductivity governing the…
Well known biological approximations are universal, i.e. invariant to transformations from one species to another. With no other experimental data, such invariance yields exact conservation (with respect to biological diversity and…
We review basic ingredients of the recently introduced perfect-fluid hydrodynamic equations for particles with spin one-half. For a quasi-realistic setup, first numerical solutions for various hydrodynamic variables including the spin…
This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.
An introduction to spin techniques in particle physics is given. Among the topics covered are: helicity formalism and its applications to the decay and scattering of spin-1/2 and spin-1 particles, techniques for evaluating helicity…