Related papers: Hydrostatic-Based Proofs in Geometry
We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…
In this paper we give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We give many examples of how to formulate…
Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian Dynamics simulations and a simple analytical model to demonstrate that the path's curvature…
The swimming trajectories of self-propelled organisms or synthetic devices in a viscous fluid can be altered by hydrodynamic interactions with nearby boundaries. We explore a multipole description of swimming bodies and provide a general…
We introduce a new computationally efficient and accurate classical density-functional theory for water and apply it to hydration of hard spheres and inert gas atoms. We find good agreement with molecular dynamics simulations for the…
The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are…
In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…
The scale factors of an arbitrary orthogonal space are a measure of its content of homogeneous orthogonal space. In the present study, it is shown, that their spatial and temporal rates of variation do not contribute to the differential…
We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches,…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…
We give a geometric approach to proving know regularity and existence theorems for the 2D Navier-Stokes Equations. We feel this point of view is instructive in better understanding the dynamics. The technique is inspired by constructions in…
A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D) hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals in a periodic domain, and with resulting dynamics constrained by an…
We consider the hydrodynamics for the biaxial nematic phase characterized by a field of orthonormal frame, which can be derived from a molecular-theory-based tensor model. In dimension two and three, we establish the local well-posedness…
This article gives an overview of recent theoretical and experimental findings concerning the hydrodynamic interaction between liquid-embedded particles in various confined geometries. A simple unifying description emerges, which accounts…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
We use the adjoint methods to study the static Hamilton-Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of…
We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles --- the Wasserstein geometry --- which allows the deterministic…