相关论文: Tube Volumes via Functional Equations
In this article, we define a class of special zonotopes generated by a matrix pair with finite-interval parameters. We discuss the relationship between the volume of these zonotopes and the controllability of one aspect (the volume of the…
We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by…
A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence…
Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…
We state a conjecture about the volume of symplectically self-polar convex bodies and show that it is equivalent to Mahler's conjecture concerning the volume of a convex body and its Euclidean polar. We also establish lower and upper bounds…
A problem on propagation of waves in deformable shells with flowing liquid is very urgent in connection with wide use of liquid transportation systems in living organisms and technology. It is necessary to consider shell motion equations…
A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…
In these notes, we explain residue formulae for volumes of convex polytopes, and for Ehrahrt polynomials based on the notion of total residue. We apply this method to the computation of the volume of the Chan-Robbins polytope. The final…
We study the dynamics of capillary filling in tubes of regular polygon cross-section. Using Onsager variational principle, we derive a coupled ordinary differential equation and partial differential equation, which respectively describe…
We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore…
We describe a new computational method for the numerically stable particle-based simulation of open-boundary flows, including volume conserving chemical reactions. The novel method is validated for the case of heterogeneous catalysis…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
In this note, we will consider two classical volume problems related to elliptic integrals. The first problem has a neat formula by means of elliptic integrals. We remade it with details. In the second problem, we found a messy formula. On…
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…
We explain an array of basic functional analysis puzzles on the way to general spectral flow formulae and indicate a direction of future topological research for dealing with these puzzles.
We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure.…
The aim of the paper is the study of fluid mixtures in nanotubes by the methods of continuum mechanics. The model starts from a statistical distribution in mean-field molecular theory and uses a density expansion of Taylor series. We get a…
The volume of the unit sphere in every dimension is given a new interpretation as a product of special values of the zeta function of $\mathbb{Z}$, akin to volume formulas of Minkowski and Siegel in the theory of arithmetic groups. A…
We study the moduli spaces of flat surfaces with prescribed conical singularities. Veech showed that these spaces are diffeomorphic to the moduli spaces of marked Riemann surfaces, and endowed with a natural volume form depending on the…
The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…