Численное моделирование вольт-амперной характеристики биполярного мемристора на основе оксида гафния

A finite element model has been developed that allows calculating the current-voltage characteristic of a bipolar memristor based on hafnium oxide Pt/HfO2/TiN, which reflects both the high-resistance and low-resistance states of the memristor. The mathematical basis of the model was Maxwell's equations for the stationary case. The model allows us to evaluate the relationship between the properties of materials included in the structure of the memristor and its operating current.

Comparing the best-reply strategy and mean-field games: The stationary case

Mean-field games (MFGs) and the best-reply strategy (BRS) are two methods of describing competitive optimisation of systems of interacting agents. The latter can be interpreted as an approximation of the respective MFG system. In this paper, we present an analysis and comparison of the two approaches in the stationary case. We provide novel existence and uniqueness results for the stationary boundary value problems related to the MFG and BRS formulations, and we present an analytical and numerical comparison of the two paradigms in some specific modelling situations.

On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections

A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter class of reciprocal transformations. The class of invariant transformations originally obtained by Bateman in non-relativistic gasdynamics in connection with lift and drag phenomena is retrieved as a reduction in the classical limit. In the general 3+1-dimensional case, it is demonstrated that Synge’s geometric characterization of the pressure being constant along streamlines encapsulates a three-dimensional extension of an integrable Heisenberg spin equation.

Maximum Likelihood Estimation for the Fractional Vasicek Model

This paper estimates the drift parameters in the fractional Vasicek model from a continuous record of observations via maximum likelihood (ML). The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the boundary case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter changes the asymptotic theory for the MLE, including the rate of convergence and the limiting distribution. It is also found that the asymptotic theory depends on the value of the Hurst parameter.

Micromagnetics of curved thin films

In this paper, we aim at a reduced 2d-model describing the observable states of the magnetization in curved thin films. Under some technical assumptions on the geometry of the thin-film, it is well-known that the demagnetizing field behaves like the projection of the magnetization on the normal to the thin film. We remove these assumptions and show that the result holds for a broader class of surfaces; in particular, for compact surfaces. We treat both the stationary case, governed by the micromagnetic energy functional, and the time-dependent case driven by the Landau–Lifshitz–Gilbert equation.

The Relationship between Entropy and the Reliability Function in Application of Physical and Statistical Approach to Nanosystems

The paper considers application of the physical and statistical approach to the issue of nanosystems reliability. A general method of solving the main equation in this approach is suggested and the solution in quadratures is obtained in one-dimensional stationary case. It is used to study the behaviour of entropy and the reliability function under certain assumptions. The cases of constant, linear, and quadratic degradation rates are analysed. In the first two cases the results correspond to physical intuition while in the last case (quadratic rate) the formal solution demonstrates counterintuitive behaviour. Numerical correlations between the distribution entropy dynamics and the reliability function are given.

Drift of the Earth’s Principal Axes of Inertia from GRACE and Satellite Laser Ranging Data

The location of the Earth’s principal axes of inertia is a foundation for all the theories and solutions of its rotation, and thus has a broad effect on many fields, including astronomy, geodesy, and satellite-based positioning and navigation systems. That location is determined by the second-degree Stokes coefficients of the geopotential. Accurate solutions for those coefficients were limited to the stationary case for many years, but the situation improved with the accomplishment of Gravity Recovery and Climate Experiment (GRACE), and nowadays several solutions for the time-varying geopotential have been derived based on gravity and satellite laser ranging data, with time resolutions reaching one month or one week. Although those solutions are already accurate enough to compute the evolution of the Earth’s axes of inertia along more than a decade, such an analysis has never been performed. In this paper, we present the first analysis of this problem, taking advantage of previous analytical derivations to simplify the computations and the estimation of the uncertainty of solutions. The results are rather striking, since the axes of inertia do not move around some mean position fixed to a given terrestrial reference frame in this period, but drift away from their initial location in a slow but clear and not negligible manner.

The non-stationary case of the Maxwell-Garnett theory: growth of nanomaterials (2D gold flakes) in solution

We followed the growth of the gold flakes by the optical spectra. The optical spectra were deconvoluted based on non-stationary case of Maxwell-Garnett. Two regimes were resolved: 0–90 min which driven by the oxidation process and from 90–180 min which driven by thermal process.