相关论文: Kinetic formulation of vortex vector fields

We present a novel discrete velocity kinetic framework to consistently recover the viscous shallow water equations. The proposed model has the following fundamental advantages and novelties: (a) A novel interpretation and general framework…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

By using the Onsager variational principle as an approximation tool, we develop a new diffusion generated motion method for wetting problems. The method uses a signed distance function to represent the interface between the liquid and vapor…

We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g. the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The…

Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting…

Physical vacuum is a special superfluid medium populated by enormous amount of virtual particle-antiparticle pairs. Its motion is described by the modified Navier-Stokes equation: (a)~the pressure gradient divided by the mass density is…

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…

In order to investigate possible topological vortex structures in generalized models, we developed a perturbative generation approach for scalar-vector theories. We demonstrate explicitly that the dielectric permeability functions must have…

Over the last decade, substantial progress has been made in understanding the topology of quasi-2D non-equilibrium fluid flows driven by ATP-powered microtubules and microorganisms. By contrast, the topology of 3D active fluid flows still…

We review and extend a technique for recovering a smooth function from its averages over a wide class of curves in a general region of Euclidean space. The method is based on complexification of the underlying vector fields defining the…

Vortices represent a class of topological solitons arising in gauge theories coupled with complex scalar fields, holding significant importance across various domains of modern physics. In this paper we establish the existence of vortex…

The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic…

In many theories with flat directions of scalar potential, static vortex solutions do not exist for a generic choice of vacuum. In two Euclidean dimensions, we find their substitutes --- constrained instantons consisting of compact core…

We apply kinetic field theory to non-linear cosmic structure formation. Kinetic field theory decomposes the cosmic density field into particles and follows their trajectories through phase space. We assume that initial particle momenta are…

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…

The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…

By exploiting the convexity of the two-particle-irreducible (2PI) effective action, we describe a procedure for extracting n-point vertex functions. This procedure is developed within the context of a zero-dimensional "quantum field theory"…

Surface tension in drops has been investigated mainly from a thermodynamic standpoint, more rarely with kinetic methods. In the present work, this problem is studied in the framework of kinetic theory, starting from Sutherland's…

We propose a novel differentiable vortex particle (DVP) method to infer and predict fluid dynamics from a single video. Lying at its core is a particle-based latent space to encapsulate the hidden, Lagrangian vortical evolution underpinning…