1 Optimum Decoding Performance on the Basis of Multithreshold Algorithms

Abstract: The iterative majority improved decoders are described. They are called multithreshold decoders (MTD). These decoders have a property of convergence to the solution of the optimum decoder with keeping linear complexity of implementation, which one is a property of usual threshold procedures. Different decoding applications are discussed. Experimental results are submitted. Decoder for non-binary MTD considered also

Evacuation of SR power from the CLIC damping ring

Absorption of synchrotron radiation (SR) power generated by wigglers of damping rings is a difficult technical task. The CLIC damping ring operates with electron (or positron) beams with energy 2.424 GeV, average beam current is up to 150 mA. The 38 wigglers installed in one straight section of the CLIC damping ring produce radiation with a total power of about 122 kW. Power density at the end of the straight sections is about 75 W per square mm. Such a power density can destroy vacuum chambers, therefore a careful design and placement of appropriate radiation collimators and absorbers is required. In this paper we describe an algorithm to compute SR power density as well as options for safe absorption of SR power. All the calculations were performed for the current design of the CLIC damping ring and wigglers. Some related problems for absorption of high SR power are described

An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and $$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}}$$ are proved for the uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution function $\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta^3$. The first of these inequalities sharpens the best known version of the classical Berry--Esseen inequality since $0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the absolute constant in the classical Berry--Esseen inequality. The second inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051 which is strictly less than the least possible value of the absolute constant in the classical Berry--Esseen inequality. As a corollary, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined.Comment: 33 page

Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.Comment: 15 pages, LaTeX, 5 figures PostScrip

Phase transitions driven by L\'evy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of L\'evy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with L\'evy noise have attracted much attention and behaviors of systems with double-well potential subjected to L\'evy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an {\it analytically solvable model} to study the occurrence of phase transitions driven by L\'evy stable noise.Comment: submitted to EP

Enhancing the Approach to Forecasting the Dynamics of Socio-Economic Development during the COVID-19 Pandemic

This study reveals the approach to scaling socio-economic indicators to ensure economic security through regional budget expenditures to the GRP ratio example. Indicator choice is conditioned by the necessity to determine the degree of the federal center's rational influence on the regional strategic goals of sustainable development. The study aims to develop and test the system for assessing the dynamics of Russian socio-economic development based on the authors' interpretation of the scaling factor values. The main research method is scaling, which provides additional perspectives reflected by preserving proportions when changing the target parameters. The new method's effectiveness is confirmed by calculating the scaling factor. Its value interpretation gives a tool for assessing the effectiveness of the strategy development system and its economic security. The study's relevance is due to adaptation to global transformations based on the management system's capability to act under various crisis scenarios and make anti-crisis decisions important for the Russian economy. The findings improve the basis for implementing a sustainable strategic planning system and strengthening national security in the COVID-19 pandemic. The findings make it possible to predict the further evolution of the relationships between indicator groups in order to increase the role of per capita budgetary expenditures in GRP. Doi: 10.28991/esj-2022-SPER-08 Full Text: PD

Excitation of surface plasmon-polaritons in metal films with double periodic modulation: anomalous optical effects

We perform a thorough theoretical analysis of resonance effects when an arbitrarily polarized plane monochromatic wave is incident onto a double periodically modulated metal film sandwiched by two different transparent media. The proposed theory offers a generalization of the theory that had been build in our recent papers for the simplest case of one-dimensional structures to two-dimensional ones. A special emphasis is placed on the films with the modulation caused by cylindrical inclusions, hence, the results obtained are applicable to the films used in the experiments. We discuss a spectral composition of modulated films and highlight the principal role of ``resonance'' and ``coupling'' modulation harmonics. All the originating multiple resonances are examined in detail. The transformation coefficients corresponding to different diffraction orders are investigated in the vicinity of each resonance. We make a comparison between our theory and recent experiments concerning enhanced light transmittance and show the ways of increasing the efficiency of these phenomena. In the appendix we demonstrate a close analogy between ELT effect and peculiarities of a forced motion of two coupled classical oscillators.Comment: 24 pages, 17 figure

Theory of Systematic Computational Error in Free Energy Differences

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important examples of such averages in physical, chemical and biological settings. Previous work has demonstrated, empirically, that the ``finite-sampling error'' can be very large -- many times kT -- in DF estimates for simple molecular systems. Here, we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of 1/N for large N, the identification of universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems, and thus a role is played by stable (Levy) probability distributions.Comment: 5 pages, 4 figure