Helical configurations of inhomogeneous symmetric rods with non-constant bending and twisting stiffness are studied within the framework of the Kirchhoff rod model. From the static Kirchhoff equations, we obtain a set of differential equations for the curvature and torsion of the centerline of the rod and the Lancret’s theorem is used to find helical solutions. We obtain a free standing helical...

Here we consider a class of generalized linear chains; that is, the ladder–like chains as a perturbation of a 2n–path by adding consecutive weighted edges between opposite vertices. This class of chains in particular includes a big family of networks that goes from the cycle, unicycle chains up to ladder networks. In this paper, we obtain the Green function, the effective resistance and the Kir...

This article concerns the existence of sign-changing solutions to nonlocal Kirchhoff type problems of the form

Through the formulation of his law of thermal emission, Kirchhoff conferred upon blackbody radiation the quality of universality [G. Kirchhoff, Annalen der Physik, 1860, v. 109, 275]. Consequently, modern physics holds that such radiation is independent of the nature and shape of the emitting object. Recently, Kirchhoff’s experimental work and theoretical conclusions have been reconsidered [P. ...

Euler-Kirchhoff filaments are solutions of the static Kirchhoff equations for elastic rods with circular cross-sections. These equations are known to be formally equivalent to the Euler equations for spinning tops. This equivalence is used to provide a classification of the different shapes a filament can assume. Explicit formulas for the different possible configurations and specific results f...

The present paper deals with a Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R^{N}. The problem studied is a stationary version of the orig inal Kirchhoff equation, involving the p(x)-Lap lacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Appl...

the k-th semi total point graph of a graph g, , ‎is a graph‎ obtained from g by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎in this paper‎, a formula for laplacian polynomial of in terms of‎ characteristic and laplacian polynomials of g is computed‎, ‎where is a connected regular graph‎.the kirchhoff index of is also computed‎.