相关论文: A closed-form solution for the flat-state geometry…

The study of vortex flows in the vicinity of multiple solid obstacles is of considerable theoretical interest and practical importance. In particular, the case of flows past a circular cylinder placed above a plane wall has attracted a lot…

We use ODEs and symmetry arguments to construct closed constant curvature space curves, first on cylinders, next on tori, at last with the Frenet-Serret equations.

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.

This article reports the spherical coordinate form of three-dimensional generalized dynamics of soft-matter quasicrystals with 12-fold symmetry which provides a basis for solving initial-boundary value problems of the equations under some…

We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.

The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…

In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…

Any pair of intersecting cylinders on a translation surface is "coherent," in that the geometric and algebraic intersection numbers of their core curves are equal (up to sign). In this paper, we investigate when a pair of multicurves can be…

We present the theory of liquid bridges between two axisymmetric solids, sphere and plane, with prescribed contact angles in a general setup, when the solids are non-touching, touching or intersecting, We give a detailed derivation of…

A contractible simplicial complex is constructed that parametrizes different ways of representing a fixed one-dimensional homology class in a closed orientable surface by isotopy classes of systems of disjoint oriented simple closed curves.…

The intersection matrix of a finite simplicial complex has as each of its entries the rank of the intersection of its respective simplices. We prove that such matrix defines the triangulation of a closed connected surface up to isomorphism.

We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…

We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We announce…

We are interested in an anisotropic singular diffusion equation in the plane and in its regularization. We establish existence, uniqueness and basic regularity of solutions to both equations. We construct explicit solutions showing the…

We show that any complete, immersed self-expander to the inverse mean curvature flow, which has one end asymptotic to a cylinder, or has two ends asymptotic to two coaxial cylinders, must be rotationally symmetric.

We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…

For piecewise-linear maps, the phenomenon that a branch of a one-dimensional unstable manifold of a periodic solution is completely contained in its stable manifold is codimension-two. Unlike codimension-one homoclinic corners, such…

A surface S in R^3 has the central plane oval property (cpo) if (i) S meets at least one affine plane transversally along a strictly convex oval, and (ii) Every such transverse oval on S has central symmetry. We show that a complete,…

Planetary orbits, being conic sections, may be obtained as the locus of intersection of planes and cones. The planes involved are familiar to anyone who has studied the classical Kepler problem. We focus here on the cones.

We observe that numerous symplectic resolutions can be expressed as intersections of twisted cotangent bundles. Additionally, their dual symplectic resolutions can be derived from intersections of dual twisted cotangent bundles. We…