Related papers: A systematic study of exact solutions in second-or…
We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of the curvature tensor. Scattering amplitudes in…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates. Viewing this problem as a quasilinear dispersive…
A method of solving perfect fluid Einstein equations with two commuting spacelike Killing vectors is presented. Given a spacelike 2-dimensional surface in the 3-dimensional nonphysical Minkowski space the field equations reduce to a single…
The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use…
After briefly touching on relativistic hydrodynamics, we provide a detailed description of recent developments in spin hydrodynamics. We discuss the theory of perfect spin hydrodynamics within two different approaches, which lead to…
We propose an alternative formulation for the exact relations in three-dimensional homogeneous turbulence using two-point statistics. Our finding is illustrated with incompressible hydrodynamic, standard and Hall magnetohydrodynamic…
We extend a recent proof of hyperbolicity of the exact (to all orders in Knudsen number) linear hydrodynamic equations [M. Colangeli et al, Phys. Rev. E (2007), in press; arXiv:cond-mat/0703791v2] to the three-dimensional Grad's moment…
High order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution $\Delta x$) with only a moderate increase to computational expense. Significant…
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the…
Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form…
Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen…
We analyze the effect of using the Fermi-Dirac statistics, rather than its Boltzmann approximation, in numerical simulations of perfect spin hydrodynamics of particles with spin 1/2. The system considered is boost invariant, transversely…
In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl…
The Boltzmann equation is solved in the relaxation time approximation using a hierarchy of angular moments of the distribution function. Our solution is obtained for an azimuthally symmetric radially expanding boost-invariant conformal…
We describe the dynamics of two-dimensional relativistic and Carrollian fluids. These are mapped holographically to three-dimensional locally anti-de Sitter and locally Minkowski spacetimes, respectively. To this end, we use…
We study the one-dimensional boost-invariant Boltzmann equation in the relaxation-time approximation using special moments of the distribution function for a system with a finite particle mass. The infinite hierarchy of moments can be…
Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on…
A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperbolic equation is coupled to the Navier-Stokes equation. The…
We derive a new, exact formula for the estimate of the initial energy densities from a new family of finite and exact solution of relativistic perfect fluid hydrodynamics. The new formula depends non-trivially on the speed of sound and on…