Negative inductor effects in nonlinear two-dimensional systems: Oscillatory neurons and memristors

Two-Dimensional Inductor-Capacitor Lattice Synthesis

We consider a general class of two-dimensional passive propagation media, represented as a planar graph where nodes are capacitors connected to a common ground and edges are inductors. Capacitances and inductances are fixed in time but vary in space. Kirchhoff’s laws give the time dynamics of voltage and current in the system. By harmonically forcing input nodes and collecting the resulting ste...

On oscillatory behavior of two-dimensional time scale systems

where a,b ∈ Crd([t0,∞)T,R+), and f and g are nondecreasing functions such that uf (u) > 0 and ug(u) > 0 for u = 0. The time scale theory is initiated by the German mathematician S. Hilger in his PhD thesis in 1988. His purpose was to unify continuous and discrete analysis and extend the results in one theory. A time scale, denoted by T, is a nonempty closed subset of real numbers, and some exam...

Oscillatory instability in two-dimensional dynamic fracture.

The stability of a rapid dynamic crack in a two-dimensional infinite strip is studied in the framework of linear elastic fracture mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack becomes unstable by a finite wavelength oscillatory mode at a velocity vc, 0.8cR<vc<0.85cR, where cR is the Rayleigh wave speed. The relevance of this theoretical ...

Two-dimensional effects in nonlinear Kronig-Penney models

Oscillatory curie temperature of two-dimensional ferromagnets.

The effective exchange interactions of magnetic overlayers Fe/Cu(001) and Co/Cu(001) covered by a Cu-cap layer of varying thickness were calculated in real space from first principles. The effective two-dimensional Heisenberg Hamiltonian was constructed and used to estimate magnon dispersion laws, spin-wave stiffness constants, and overlayer Curie temperatures within the mean-field and random-p...