Irreducible complexity of iterated symmetric bimodal maps

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a $\ast$-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the *-product induced on the associated Markov shifts

Nanoscopic processes of Current Induced Switching in thin tunnel junctions

In magnetic nanostructures one usually uses a magnetic field to commute between two resistance (R) states. A less common but technologically more interesting alternative to achieve R-switching is to use an electrical current, preferably of low intensity. Such Current Induced Switching (CIS) was recently observed in thin magnetic tunnel junctions, and attributed to electromigration of atoms into/out of the insulator. Here we study the Current Induced Switching, electrical resistance, and magnetoresistance of thin MnIr/CoFe/AlO$_x$/CoFe tunnel junctions. The CIS effect at room temperature amounts to 6.9% R-change between the high and low states and is attributed to nanostructural rearrangements of metallic ions in the electrode/barrier interfaces. After switching to the low R-state some electro-migrated ions return to their initial sites through two different energy channels. A low (high) energy barrier of $\sim$0.13 eV ($\sim$0.85 eV) was estimated. Ionic electromigration then occurs through two microscopic processes associated with different types of ions sites/defects. Measurements under an external magnetic field showed an additional intermediate R-state due to the simultaneous conjugation of the MR (magnetic) and CIS (structural) effects.Comment: 6 pages, 4 figure

On the Nonlinear Impulsive Ψ\Psi--Hilfer Fractional Differential Equations

In this paper, we consider the nonlinear $\Psi$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are extended to the nonlocal $\Psi$-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we procured. Further, examples are provided in support of the results we got.Comment: 2

Exponential Distributions in a Mechanical Model for Earthquakes

We study statistical distributions in a mechanical model for an earthquake fault introduced by Burridge and Knopoff [R. Burridge and L. Knopoff, {\sl Bull. Seismol. Soc. Am.} {\bf 57}, 341 (1967)]. Our investigations on the size (moment), time duration and number of blocks involved in an event show that exponential distributions are found in a given range of the paramenter space. This occurs when the two kinds of springs present in the model have the same, or approximately the same, value for the elastic constants. Exponential distributions have also been seen recently in an experimental system to model earthquake-like dynamics [M. A. Rubio and J. Galeano, {\sl Phys. Rev. E} {\bf 50}, 1000 (1994)].Comment: 11 pages, uuencoded (submitted to Phys. Rev. E