We describe the dynamics of the Kirchhoff ellipse by formulating a nonlinear equation for the boundary of a perturbed vortex patch in elliptical coordinates. We demonstrate that in the regime for which the linearized equation of motion is unstable, the nonlinear dynamics of a rather general initial perturbation of the Kirchhoff ellipse are determined by the fastest growing mode for the correspo...

In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the help of Kirchhoff- Love plate theory. The thermoelastic damping of micro-beam resonators is analyzed by using the normal mode a...

Existence and bifurcation of positive solutions to a Kirchhoff type equation ⎧⎪⎨ ⎪⎩ − ( a + b ∫ Ω |∇u|2 ) u= νf (x,u), in Ω, u= 0, on ∂Ω are considered by using topological degree argument and variational method. Here f is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap of recent research about the Kirchhoff ...

Resistance distance was introduced by Klein and Randić. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by Cat(n; t) the set of connected cacti possessing n vertices and t cycles. In this paper, we give the first three smallest Kirchhoff indices among gra...

Simulations of saturated-unsaturated groundwater flow in heterogeneous soil can be carried out by considering non-overlapping domain decomposition problems for the Richards equation in subdomains with homogeneous soil. By the application of different Kirchhoff transformations in the different subdomains local convex minimization problems can be obtained which are coupled via superposition opera...

We develop an a posteriori analysis of C interior penalty methods for the displacement obstacle problem of clamped Kirchhoff plates. We show that a residual based error estimator originally designed for C interior penalty methods for the boundary value problem of clamped Kirchhoff plates can also be used for the obstacle problem. We obtain reliability and efficiency estimates for the error esti...

We show the presence of a dense pure point spectrum on quantum graphs with Maryland-type quasiperiodic Kirchhoff coupling constants at the vertices.

We apply iterative resolution estimation to least-squares Kirchhoff migration. Resolution plots reveal low illumination areas on seismic images and provide information about image uncertainties.

In this paper we study the existence, multiplicity, and regularity of positive weak solutions for following Kirchhoff–Choquard problem: M ∬ ℝ 2 N | u ( x ) − y + s d Δ = λ γ ∫ Ω μ , ∗ in 0 \ where is open bounded domain with C2 boundary, > 2s ∈ (0, 1). models Kirchhoff-type coefficient particular, degenerate case Kirchhoff zero at zero. (− Δ)s fractional Laplace operator, a real parameter, 1) c...