Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Natural extensions and entropy of α\alpha-continued fractions

We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domain with respect to the density function $(1+xy)^{-2}$. In particular, we show that, for all $0 < \alpha \le 1$, the product of the entropy with the measure of the domain equals $\pi^2/6$. As a key step, we give the explicit relationship between the $\alpha$-expansion of $\alpha-1$ and of $\alpha$

Plasma Enhanced Chemical Vapor Deposited Materials and Organic Semiconductors in Photovoltaic Devices

Introduction. PECVD enables fabrication of wide range of advanced materials with various structure such as amorphous, polymorphous, nano-crystalline, nanostructured, microcrystalline etc. and with various electronic properties. The latter can be also changed by different dopingl. PECVD silicon materials are commercially employed in multi-layered PV structures (including ones on flexible substrates). Combining these materials with crystalline silicon active substrate resulted in significant improvement of PCE in hetero junction technology PV structures. Existence of new organic semiconductors (OS) together with understanding of physical properties resulted in fast development of OC PV devicesAim. To consider both PECVD and OS materials and to present description of fabrication, structure and electronic properties for device application.Materials and methods. Devices based on non-crystalline materials, devices based on OS, hybrid devices. PECVD and Spin coating technique was used to deposit materials with tunable properties enabling device engineering possibilities.Results. PECVD and OS materials were analyzed. These materials have different levels of characterization (data volume, interpretation of the results etc.) and of understanding of physics determining device performance. Some examples of these materials in PV including structures with crystalline silicon were considered.Conclusion. Important advantage of both PECVD and OS materials is that fabrication methods are compatible and allow fabrication of great variety of hybrid device structures on crystalline semiconductors. Advantages of such devices are difficult to predict because of lack of data in scientific literature. However a new area in material science and related devices for further exploring and exploiting has appeared.Introduction. PECVD enables fabrication of wide range of advanced materials with various structure such as amorphous, polymorphous, nano-crystalline, nanostructured, microcrystalline etc. and with various electronic properties. The latter can be also changed by different dopingl. PECVD silicon materials are commercially employed in multi-layered PV structures (including ones on flexible substrates). Combining these materials with crystalline silicon active substrate resulted in significant improvement of PCE in hetero junction technology PV structures. Existence of new organic semiconductors (OS) together with understanding of physical properties resulted in fast development of OC PV devices.Aim. To consider both PECVD and OS materials and to present description of fabrication, structure and electronic properties for device application.Materials and methods. Devices based on non-crystalline materials, devices based on OS, hybrid devices. PECVD and Spin coating technique was used to deposit materials with tunable properties enabling device engineering possibilities.Results. PECVD and OS materials were analyzed. These materials have different levels of characterization (data volume, interpretation of the results etc.) and of understanding of physics determining device performance. Some examples of these materials in PV including structures with crystalline silicon were considered.Conclusion. Important advantage of both PECVD and OS materials is that fabrication methods are compatible and allow fabrication of great variety of hybrid device structures on crystalline semiconductors. Advantages of such devices are difficult to predict because of lack of data in scientific literature. However a new area in material science and related devices for further exploring and exploiting has appeared

Correlative confocal Raman and scanning probe microscopy in the ionically active particles of LiMn 2 O 4 cathodes

In this contribution, a correlative confocal Raman and scanning probe microscopy approach was implemented to find a relation between the composition, lithiation state, and functional electrochemical response in individual micro-scale particles of a LiMn 2 O 4 spinel in a commercial Li battery cathode. Electrochemical strain microscopy (ESM) was implemented both at a low-frequency (3.5 kHz) and in a high-frequency range of excitation (above 400 kHz). It was shown that the high-frequency ESM has a significant cross-talk with topography due to a tip-sample electrostatic interaction, while the low-frequency ESM yields a response correlated with distributions of Li ions and electrochemically inactive phases revealed by the confocal Raman microscopy. Parasitic contributions into the electromechanical response from the local Joule heating and flexoelectric effect were considered as well and found to be negligible. It was concluded that the low-frequency ESM response directly corresponds to the confocal Raman microscopy data. The analysis implemented in this work is an important step towards the quantitative measurement of diffusion coefficients and ion concentration via strain-based scanning probe microscopy methods in a wide range of ionically active materials. © 2019 by the authors

Nash equilibrium design in the interaction model of entities in the customs service system

The urgency of the analyzed issue is due to the importance of the use of economic-mathematical tools in the course of modeling the interaction of the entities in the customs service system that is necessary for the development of foreign economic activity (FEA) of any state. The purpose of the article is to identify effective strategies for the interaction between the participants of foreign trade activities with customs brokers. The leading method to the study of this issue is economic-mathematical modeling, allowing studying the process of making decisions while choosing the strategy of cooperation between the customs broker and his client. Results: the article suggests the mathematical model to optimize the management mechanisms of interaction between enterprises, engaged in foreign trade, and customs dealers. The data of this article may be useful in modeling interaction of the entities in the customs service system using the methods of game theory. The model of “customer - customs broker” is implemented as a bimatrix game. Assuming the noncooperativegame the authors solve the problem of finding Nash equilibrium in mixed strategies. © 2016 Fedorenko et al