Related papers: Cable equation for general geometry
We study a generalized mean curvature flow involving a positive power of the mean curvature and a driving force. In this paper, we first construct all kinds of radially symmetric translating solutions, and then select one of them to satisfy…
This paper presents a detailed modeling and analysis regarding the dispersion characteristics of multilayered open coaxial waveguides. The study is motivated by the need of improved modeling and an increased physical understanding about the…
The thermodynamics of electrowetting is treated. A general equation of electrowetting is derived from the first principles. It is demonstrated that the well-known Lippmann Equation describes a particular case of electrowetting when the…
The present work aims at describing hysteresis behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. Pure bending experiments conducted in previous work show that slender structures such as electric…
For a curve $\boldsymbol{\gamma}:I\to\mathbb{R}^n$ of order $n-1$, we prove that the generalized curvatures $\kappa_1, \ldots, \kappa_{n-1}$ can be expressed in terms of the leading principal minors of the matrix…
Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of…
Deep neural networks have shown many fruitful applications in this decade. A network can get the generalized function through training with a finite dataset. The degree of generalization is a realization of the proximity scale in the data…
A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression…
The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a…
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a $\delta$…
The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…
We revisit the well-known Curve Shortening Flow for immersed curves in the $d$-dimensional Euclidean space. We exploit a fundamental structure of the problem to derive a new global construction of a solution, that is, a construction that is…
We present a generic solution to the fundamental problem of how to connect two points in a plane by a smooth curve that goes through these points with a given slope. The smoothness of any curve depends both on its curvature and its length.…
Phase diagrams are essential tools of the materials scientist, showing which phases are at equilibrium under a set of applied thermodynamic conditions. Essentially all phase diagrams today are two dimensional, typically constructed with…
A generalized Young's equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid-vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from…
Different magnet applications require compact high current cables. Among the proposed solutions, the Twisted Stacked Tape Cable (TSTC) is easy to manufacture and has very high tape length usage efficiency. In this kind of cables the tapes…
The General Curve Lemma is a tool of Infinite-Dimensional Analysis, which enables refined studies of differentiability properties of mappings between real locally convex spaces. In this article, we generalize the General Curve Lemma in two…
Determining the positions of lattice defects on elastic surfaces with Gaussian curvature is a non-trivial task of mechanical energy optimization, particularly for surfaces with boundaries. We introduce a simple way to predict the onset of…
The traditional method of finding the average value of a physical quantity often gives wrong results. Another formula of averaging is derived which gives correct results. It is applied to calculation of the average radius of tapering tube…
Marine cables under low tension and torsion on the sea floor can form highly contorted three-dimensional geometries that include loops (e.g. hockles) and tangles. These geometries arise from the conversion of torsional strain energy to…