A Computational Phase Field Study of Conducting Channel Formation in Dielectric Thin Films: A View Towards the Physical Origins of Resistive Switching

A phase field method is used to computationally study conducting channel morphology of resistive switching thin film structures. Our approach successfully predicts the formation of conducting channels in typical dielectric thin film structures, comparable to a range of resistive switches, offering an alternative computational formulation based on metastable states treated at the atomic scale. In contrast to previous resistive switching thin film models, our formulation makes no a priori assumptions on conducting channel morphology and its fundamental transport mechanisms

An electro-thermal computational study of conducting channels in dielectric thin films using self-consistent phase-field methodology: A view toward the physical origins of resistive switching

A large number of experimental studies suggest two-terminal resistive switching devices made of a dielectric thin film sandwiched by a pair of electrodes exhibit reversible multi-state switching behaviors; however coherent understanding of physical and chemical origins of their electrical properties needs to be further pursued to improve and customize the performance. In this paper, phase-field methodology is used to study the formation and annihilation of conductive channels resulting in reversible resistive switching behaviors that can generally occur in any dielectric thin films. Our focus is on the dynamical evolution of domains made of electrical charges under the influence of spatially varying electric field and temperature resulting in distinctive changes in electrical conductance.Comment: 6 pages, 5 figure

Computational method for obtaining filiform Lie algebras of arbitrary dimension

This paper shows a new computational method to obtain filiform Lie algebras, which is based on the relation between some known invariants of these algebras and the maximal dimension of their abelian ideals. Using this relation, the law of each of these algebras can be completely determined and characterized by means of the triple consisting of its dimension and the invariants z1 and z2. As examples of application, we have included a table showing all valid triples determining filiform Lie algebras for dimension 13

Conductance Quantization and Magnetoresistance in Magnetic Point Contacts

We theoretically study the electron transport through a magnetic point contact (PC) with special attention to the effect of an atomic scale domain wall (DW). The spin precession of a conduction electron is forbidden in such an atomic scale DW and the sequence of quantized conductances depends on the relative orientation of magnetizations between left and right electrodes. The magnetoresistance is strongly enhanced for the narrow PC and oscillates with the conductance.Comment: 4 pages, 4 figures, revised version with new figure

A particular type of non-associative algebras and graph theory

Evolution algebras have many connections with other mathematical fields, like group theory, stochastics processes, dynamical systems and other related ones. The main goal of this paper is to introduce a novel non-usual research on Discrete Mathematics regarding the use of graphs to solve some open problems related to the theory of graphicable algebras, which constitute a subset of those algebras. We show as many our advances in this field as other non solved problems to be tackled in future

Low-dimensional filiform Lie algebras over finite fields

In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/pZ, for p = 2, 3, 5.Plan Andaluz de Investigación (Junta de Andalucía