Shock-waves and commutation speed of memristors

Progress of silicon based technology is nearing its physical limit, as minimum feature size of components is reaching a mere 10 nm. The resistive switching behaviour of transition metal oxides and the associated memristor device is emerging as a competitive technology for next generation electronics. Significant progress has already been made in the past decade and devices are beginning to hit the market; however, it has been mainly the result of empirical trial and error. Hence, gaining theoretical insight is of essence. In the present work we report the striking result of a connection between the resistive switching and {\em shock wave} formation, a classic topic of non-linear dynamics. We argue that the profile of oxygen vacancies that migrate during the commutation forms a shock wave that propagates through a highly resistive region of the device. We validate the scenario by means of model simulations and experiments in a manganese-oxide based memristor device. The shock wave scenario brings unprecedented physical insight and enables to rationalize the process of oxygen-vacancy-driven resistive change with direct implications for a key technological aspect -- the commutation speed.Comment: Featured in Physics Synopsis: "Waves that Shock Resistance" (Mar. 15, 2016). http://physics.aps.org/synopsis-for/10.1103/PhysRevX.6.01102

On a problem of dynamical input reconstruction for a system of special type under conditions of uncertainty

From the viewpoint of the approach of the theory of dynamic inversion, an input reconstruction problem in a differential system of special type is under investigation. The first equation of the system is a linear stochastic Ito equation, whereas the second is a linear ordinary equation containing an unknown disturbance. The statement when the reconstruction is performed from the discrete information on several realizations of the stochastic process being a solution of the first equation is considered. The problem is reduced to an inverse problem for the system of ordinary differential equations, which includes, instead of the stochastic equation, the equation describing the dynamics of the mathematical expectation of the desired process. A finite-step software-oriented solving algorithm based on the method of auxiliary feedback controlled models is designed; an estimate for its convergence rate with respect to the number of measurable realizations is obtained. An illustrating example is given, for which the calibration of algorithm’s parameters is discussed. © 2020 the Author(s), licensee AIMS Press

A Guaranteed Control Problem for a Linear Stochastic Differential Equation

A problem of guaranteed closed-loop control under incomplete information is considered for a linear stochastic differential equation (SDE) from the viewpoint of the method of open-loop control packages worked out earlier for the guidance of a linear control system of ordinary differential equations (ODEs) to a convex target set. The problem consists in designing a deterministic open-loop control providing (irrespective of a realized initial state from a given finite set) prescribed properties of the solution (being a random process) at a terminal point in time. It is assumed that a linear signal on some number of realizations is observed. By the equations of the method of moments, the problem for the SDE is reduced to an equivalent problem for systems of ODEs describing the mathematical expectation and covariance matrix of the original process. Solvability conditions for the problems in question are written.This work was supported by the Russian Science Foundation (project no. 14-11-00539)

К задаче динамического восстановления возмущения при дефиците информации

The problem of reconstructing an unknown external influence in a system of linear ordinary differential equations is investigated on the basis of the approach of the theory of dynamic inversion. A statement is considered in which the disturbance is reconstructed synchronously with the process from incomplete discrete information on a part of coordinates of the phase trajectory. A finite-step software-oriented solution algorithm based on the method of auxiliary closed-loop models is proposed, and its error is estimated. The novelty of the paper is that we consider the inverse problem for a dynamic system in which the disturbance to be reconstructed is subject to geometric constraints and is not included in the measured component. © 2019 Krasovskii Institute of Mathematics and Mechanics. All Rights Reserved

One dynamical input reconstruction problem: Tuning of solving algorithm via numerical experiments

The input reconstruction problem for a stochastic differential equation is investigated by means of the approach of the theory of dynamic inversion. The statement when the simultaneous reconstruction of disturbances in both the deterministic and stochastic terms of the equation is performed from the discrete information on several realizations of the stochastic process is considered. A finite-step software-oriented solving algorithm based on the method of auxiliary feedback controlled models is designed; an estimate for its convergence rate with respect to the number of measurable realizations is obtained. An empirical procedure for the automatic tuning of algorithm’s parameters in order to get best approximation results for a specific dynamical system is proposed. To optimize this time-taking process, the parallelization of calculations is applied. A model example illustrating the method proposed is given. © 2019 the Author(s), licensee AIMS Press.The authors would like to thank the generous support from the Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

Integration of the problem of medical ecology on the level of the highly urbanized region

The urgency of the analyzed issue is due to the study of the basic issues of medical ecology: the dynamics of demographic indicators, the correlation of somatic and reproductive public health, depending on the influence of physical factors of the urban environment on public health on the basis of medical and geographic mapping. The article aims at the analysis of the environmentally determined disorder of the urbanized territory. The leading approach to the study of the issue of medical ecology is a medical and geographical mapping, which allows identifying the most affordable and common areas of multi-component medical and environmental maps. While analyzing the impact of various aspects of the environment on human health, the priority is given to risk factors that directly lead to the emergence of diseases. The contents of the article may be useful to justify the choice of the rational approach to public health as a redistribution mechanism to reallocate the space of ecological niches. © 2016 Rozenberg et al