Nonlocal Andreev reflection at high transmissions

We analyze non-local effects in electron transport across three-terminal normal-superconducting-normal (NSN) structures. Subgap electrons entering S-electrode from one N-metal may form Cooper pairs with their counterparts penetrating from another N-metal. This phenomenon of crossed Andreev reflection -- combined with normal scattering at SN interfaces -- yields two different contributions to non-local conductance which we evaluate non-perturbatively at arbitrary interface transmissions. Both these contributions reach their maximum values at fully transmitting interfaces and demonstrate interesting features which can be tested in future experiments.Comment: 4 pages, 4 figure

Crossed Andreev reflection at spin-active interfaces

With the aid of the quasiclassical Eilenberger formalism we develop a theory of non-local electron transport across three-terminal ballistic normal-superconducting-normal (NSN) devices with spin-active NS interfaces. The phenomenon of crossed Andreev reflection (CAR) is known to play the key role in such transport. We demonstrate that CAR is highly sensitive to electron spins and yields a rich variety of properties of non-local conductance which we describe non-perturbatively at arbitrary voltages, temperature, spin-dependent interface transmissions and their polarizations. Our results can be applied to multi-terminal hybrid structures with normal, ferromagnetic and half-metallic electrodes and can be directly tested in future experiments.Comment: 11 pages, 7 figures; figures 6 and 7 are corrected; version published in Phys. Rev.

Mathematical simulation of analog-to-digital converter

Numerical relay protection devices (NRP) are a promising area for the development of protection equipment for electric power systems. For its development, research and, in some cases, setting mathematical models are used. At the same time, the converting part of the NRP, which realizes the analog-to-digital conversion (ADC) of the analog input signal to the digital one, with which the microprocessor of the NRP works directly, is often ignored in models. The purpose of this work is to study the characteristics and parameters of the ADC, as well as to evaluate its impact on the operation of the ADC itself and need to take into account those or other characteristics in the simulation. To develop the ADC model, the C programming language was used. The ADC model is takes into account the cutoff frequency of the analog signal, sampling period, and number of samples required. The characteristics and parameters of the ADC are studied, their effect on the operation of the ADC is estimated. The result of this study – the ADC must be modeled as completely as possible, since its operation depends on the correct functioning of the NRP algorithm

Centre for Discrete Mathematics and Theoretical Computer ScienceNot Every Domain of a Plain Decompressor Contains the Domain of a Prefix-Free One

question about the relation between plain and prefix Kolmogorov complexities (see their paper in DLT 2008 conference proceedings): does the domain of every optimal decompressor contain the domain of some optimal prefix-free decompressor? In this paper we provide a negative answer to this question.

Using methods of non-linear dynamics in historical social research: application of chaos theory in the analysis of the worker's movement in pre revolutionary Russia

"Die Autoren analysieren offizielle Statistiken der Streikbewegung in Rußland während der Jahre 1895 bis 1908 mit Methoden der Chaos-Theorie und entwickeln ein Modell zur Erklärung nicht-linearer Prozesse. Der Verlauf und die Häufigkeit der Streiks werden als Selbstorganisation der Industriearbeiter interpretiert, was der herkömmlichen Meinung nach dem Dominieren äußerer Faktoren widerspricht." (Autorenreferat)"Social conflicts often contain unpredictable peaks of activities and relatively long periods of non-stable behaviour. How could we explain such a non-linear, chaotic behaviour? What is more substantial - internal factors of these effects or external causes? Sometimes historians take into account only external factors as the main causes of the historical phenomena, though they possibly play the 'trigger' role in the processes of the 'social explosives'. Such questions can be asked in the investigation of the strike movement in Russia in the end of 19th and the beginning of the 20th century. One of possible ways to answer these questions is to apply the theory of non-linear systems with dynamically stochastic behaviour (or 'chaos'), developed in the last decades. We used official statistics of industrial strikes in the Russian Empire during the years 1895-1908. Our research demonstrates the possible appearance of 'chaos' (in mathematical sense) in the system behaviour and the existence of a rather long unstable period. To describe the development of strike movement we built the quantitative model. The system of the four non-linear ordinary differential equations was constructed after using advanced mathematical procedures to analyse the time-series. This model had a good predictor feature and for defined values of the coefficients demonstrated a chaotic behaviour. The research reveals the great role of the mechanism of information transfer and the significance of internal factors in the strike movement." (author's abstract

Mathematical simulation of analog-to-digital converter

Numerical relay protection devices (NRP) are a promising area for the development of protection equipment for electric power systems. For its development, research and, in some cases, setting mathematical models are used. At the same time, the converting part of the NRP, which realizes the analog-to-digital conversion (ADC) of the analog input signal to the digital one, with which the microprocessor of the NRP works directly, is often ignored in models. The purpose of this work is to study the characteristics and parameters of the ADC, as well as to evaluate its impact on the operation of the ADC itself and need to take into account those or other characteristics in the simulation. To develop the ADC model, the C programming language was used. The ADC model is takes into account the cutoff frequency of the analog signal, sampling period, and number of samples required. The characteristics and parameters of the ADC are studied, their effect on the operation of the ADC is estimated. The result of this study - the ADC must be modeled as completely as possible, since its operation depends on the correct functioning of the NRP algorithm