Conservation laws for invariant functionals containing compositions

The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions. With the help of the new obtained condition, a Noether-type theorem is proved. An application of our main result is given to a problem appearing in the chaotic setting when one consider maps that are ergodic.Comment: Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South Africa, 22-24 August, 200

Quantized conductance coincides with state instability and excess noise in tantalum oxide memristors

This is an Open Access Article. It is published by Nature Publishing under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0Tantalum oxide memristors can switch continuously from a low-conductance semiconducting to a high-conductance metallic state. At the boundary between these two regimes are quantized conductance states, which indicate the formation of a point contact within the oxide characterized by multistable conductance fluctuations and enlarged electronic noise. Here, we observe diverse conductance-dependent noise spectra, including a transition from 1/f 2 (activated transport) to 1/f (flicker noise) as a function of the frequency f, and a large peak in the noise amplitude at the conductance quantum GQ¼2e2/h, in contrast to suppressed noise at the conductance quantum observed in other systems. We model the stochastic behaviour near the point contact regime using Molecular Dynamics–Langevin simulations and understand the observed frequency-dependent noise behaviour in terms of thermally activated atomic-scale fluctuations that make and break a quantum conductance channel. These results provide insights into switching mechanisms and guidance to device operating ranges for different applications