Related papers: Noncommutative Geometry and Fluid Dynamics
In this work we explore the consequences that a non-minimal coupling between geometry and matter can have on the dynamics of perfect fluids. It is argued that the presence of a static, axially symmetric pressureless fluid does not imply a…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
The $f(R, T)$ theory of gravity extends general relativity (GR) by allowing the gravitational Lagrangian to depend on both the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$. The resulting matter-geometry coupling…
Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…
We study the potential effects of spacetime non-metricity in cosmology. In the spirit of Einstein-Cartan gravity, but with non-metricity replacing torsion, we consider the Einstein-Hilbert action and assume zero torsion. Adopting certain…
We propose new ideal hydrodynamics in the function space which describes a fluid composed of the 1+1 dimensional real scalar field in the framework of the stochastic variational method (SVM). In the derivation, the thermal equilibrium is…
The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether's conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this…
Lagrangian reduction by stages is used to derive the Euler-Poincar\'e equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect complex fluids (PCFs) whose order parameters are continuous…
We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics…
In this paper, we investigate a class of perfect-fluid "anti-Newtonian" cosmological models in the context of f(R) gravity. In particular, we study the integrability conditions of such gravity models using covariant consistency analysis…
In these lecture notes I review the theory of the non--linear evolution of cosmological perturbations in a self--gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the…
When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed…
In this paper we consider the problem of obtaining a general port-Hamiltonian formulation of Newtonian fluids. We propose the port-Hamiltonian models to describe the energy flux of rotational three-dimensional isentropic and non-isentropic…
We investigate the global dynamics of the field equations of (pure) quadratic theories of gravity which generalise Einstein's theory in spatially flat homogeneous and isotropic cosmological models with a perfect fluid. We introduce global…
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the scalar-metric gravity. Using the Schutz' representation for the perfect fluid, we show that, under…
In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have positive constant…
A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The…
We show that a holographic description of four-dimensional asymptotically locally flat spacetimes is reached smoothly from the zero-cosmological-constant limit of anti-de Sitter holography. To this end, we use the derivative expansion of…