Related papers: On the dynamic flows
This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field…
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…
The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads…
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier--Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms.…
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
The usable limits of the customary and relaxational filtrational theories are considered. The questions of applicable the locality and local thermodynamical equilibrium principles to depict the nonstationary flows are discussed. The…
Vorticity in turbulent flows is often organized into complex geometries that influence the dynamics. We use a relatively novel approach to describe these geometries: that of obtaining segments of vortex lines embedded in the flow. This…
We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state…
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow,…
Accurate measurements of atmospheric flows at meter-scale resolution are essential for a broad range of sustainability applications, including optimal design of wind and solar farms, safe and efficient urban air mobility, monitoring of…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130,…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
From the Navier-Stokes-Korteweg (NSK) equations, the exact relations between the fundamental surface physical quantities for two-phase viscous flow with diffuse interface are derived, including density gradient, shear stress, vorticity,…
The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in…
The controllability of passive microparticles that are advected with the fluid flow generated by an actively controlled one is studied. The particles are assumed to be suspended in a viscous fluid and well separated so that the far-field…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…