相关论文: Tube Volumes via Functional Equations

We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium the local pressure is a functional of the shape of the walls. It…

We propose a specific scaling that formally derives the Euler-Vlasov model for thick sprays which is widely adopted in engineering from the Boltzmann-Enskog model. Beyond validating the kinetic-fluid equations underlying this model, we also…

We discuss and illustrate through numerical examples the relations between generating functionals, thermodynamic consistency (in particular the virial-free energy one), and uniqueness of the solution, in the integral equation theory of…

Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow…

The self-similar potentials are formulated in terms of the shape-invariance. Based on it, a coherent state associated with the shape-invariant potentials is calculated in case of the self-similar potentials. It is shown that it reduces to…

We derived the geometrical parameters on the tube connections that homogenize the pressure drop in a multi-chamber vacuum system, where each chamber has a distinct volume and all are connected to the same vacuum pump. We start deriving the…

We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…

A novel proposal is outlined to determine scattering amplitudes from finite-volume spectral functions. The method requires extracting smeared spectral functions from finite-volume Euclidean correlation functions, with a particular complex…

From a scalar field defined at the corner of a cube, an isosurface can be extracted using the Marching Cube algorithm. The isosurface separates the cell into two or more partial cells. A similar situation arises when an material interface…

In this paper, we construct the transport equation and the wave equation with specular derivatives and solve these equations in one-dimension. To solve these equations, we introduce new function spaces, which we term specular spaces,…

The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…

The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…

In this article we investigate the pressure function and affinity dimension for iterated function systems associated to the "box-like" self-affine fractals investigated by D.-J. Feng, Y. Wang and J.M. Fraser. Combining previous results of…

We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic…

We provide a formula to compute the volume of the intersection of a generalized cylinder with a hyperplane. Then we prove an integral inequality involving Bessel functions similar to Keith Ball's well-known inequality. Using this inequality…

The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the Rational Function Approximation method for the structural…

The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear…

In the context of the density functional theory we consider the single particle excitation spectra of electron systems. As a result, we have related the single particle excitations with the eigenvalues of the corresponding Kohn-Sham…

Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that…

The solution of self-similar shock dynamics satisfying the inviscid Burgers equation are provided in closed form for planar, cylindrical and spherical problems. The approach follows Lee's method for obtaining self-similar solutions for the…