Related papers: Dual pairs in fluid dynamics
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
Thermodynamics of superfluids is revisited, clarifying two points. First, the density and pressure distribution for given equilibrium velocities is obtained, with the finding that counter heat currents give rise to a pressure depression and…
This paper considers magnetohydrodynamics (MHD) and some of its applications from the perspective of differential geometry, considering the dynamics of an ideal fluid flow and magnetic field on a general three-dimensional manifold, equipped…
We review some of the exactly solvable one dimensional continuum fluid models of equilibrium classical statistical mechanics under the unified setting of functional integration in one dimension. We make some further developments and remarks…
Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface $(M,g)$ isometrically embedded in $\mathbb{R}^3$, we…
Fluid dynamics plays a crucial role in various multiphysics applications, including energy systems, electronics cooling, and biomedical engineering. Developing models for complex coupled systems can be challenging and time-consuming. In…
For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant…
In this article, we aim to study the stability and dynamic transition of an electrically conducting fluid in the presence of an external uniform horizontal magnetic field and rotation based on a Boussinesq approximation model. By analyzing…
We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…
Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for…
We present simple, concrete, two-fermion models that exhibit thermodynamically stable isotropic translationally-invariant gapless superfluid states (breached pair superfluidity). The mass ratio between the components and the momentum…
Perfect fluid equations are formulated which are invariant under the $\ell$-conformal Newton-Hooke group for an arbitrary integer or half-integer value of the parameter $\ell$. For $\ell=\frac32$ the corresponding conserved charges are…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
The theory of ideal Yang-Mills fluids (IYMF; a Yang-Mills field coupled to a fluid in the limit of infinite conductivity) is embedded in symmetric hyperbolic form. This yields both causality and well-posedness of initial value problems in…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
Multipolar order in complex fluids is described by statistical correlations. This paper presents a novel dynamical approach, which accounts for microscopic effects on the order parameter space. Indeed, the order parameter field is replaced…
The Hamiltonian structure of the monodromy preserving deformation equations of Jimbo {\it et al } is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to the dual spaces of two different loop…
The phase space formulation of Double Field Theory (DFT) indicates that statistical matter can be included in terms of (T-)duality multiplets. We propose the inclusion of a perfect fluid in the geometry of DFT through a generalized…
General properties of the effective conductivity sigma_e of planar isotropic randomly inhomogeneous two-phase self-dual systems are investigated. A new approach for finding out sigma_e of random systems based on a duality, a series…
This article characterizes topological duals of spaces of cadlag processes. We obtain extensions of functional analytic results of Dellacherie and Meyer that underlie many fundamental results in stochastic analysis. In particular, we obtain…