Related papers: Short branch cut approximation in $2$D Hydrodynami…
We analyze a one-component simple fluid in a liquid-vapor coexistence state, which forms an arbitrarily curved interface. By using an approach based on density functional theory, we obtain an exact and simple expression for the grand…
Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about…
The quantitative characterization of the microstructure of random heterogeneous media in $d$-dimensional Euclidean space $\mathbb{R}^d$ via a variety of $n$-point correlation functions is of great importance, since the respective infinite…
The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by…
New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
Hydrodynamic discontinuities in an external potential and incompressible flow are investigated. Using the reaction front as an example in a 2D stream, an overdetermined system of equations is obtained that describes its motion in terms of…
The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as…
We consider the initial value problem for a nonlinear shallow water model in horizontal dimension d = 2 and in the presence of a fixed partially immersed solid body on the water surface. We assume that the bottom of the solid body is the…
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…
In [arXiv:1004.2488], Baumann et al. present a new formalism for studying cosmological systems where the characteristic scale of non-linearities is much smaller than the Hubble scale. By integrating out the short-wavelength modes, it is…
Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate…
We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids $A$ and $B$ of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the…
We consider a system of nonlinear partial differential equations modelling the steady motion of an incompressible non-Newtonian fluid, which is chemically reacting. The governing system consists of a steady convection-diffusion equation for…
We provide a basic method of Smoothed Particle Hydrodynamics (SPH) to simulate liquid droplet with surface tension in three dimensions. Liquid droplet is a simple case for surface tension modeling. Surface tension works only on fluid…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics (MD) we can pick apart the interface structure and understand surface tension. In…