Повышение точности измерения амплитуды в бесконтактных приборах контроля толщины полимерных пленок

Розглянуто методи вимірювання товщини полімерних плівок та методи підвищення точності вимірювання амплітуди в безконтактних приладах контролю товщини полімерних плівок. Запропоновано використання коефіцієнтів амплітуди та усереднення для визначення значення амплітуди сигналу відомої форми за результатами вимірювання середньовипрямленого та діючого значення в умовах впливу шумів і завад значного рівня. Розроблена структурна схема та проведені дослідження ефективності запропонованого методу.The massive use of polymer films of different types and thickness determines the relevance of measuring their parameters, primarily the thickness, especially in the production process. Methods for measuring the polymer films thickness were analyzed. The most promising ones are acoustic and optical methods, in which one of the main parameters of the output signal of the primary transmitter is an amplitude value. During measuring the thickness of thin and ultrathin polymer films the variation range of signal amplitude decreases, which reduces amplitude measurement accuracy by increasing the impact of noise. The purpose of this work is to analyze and develop methods to improve the accuracy of measuring signals amplitude for control devices of polymer films thickness. The methods to improve the accuracy of measuring amplitude were considered. According to the results of the analysis it is proposed to use the structural method based on the amplitude and averaging coefficients. Their values are known for standard form signal, and can be defined for constant signal shape, typical in measuring the polymer films thickness. In this case, the value of the amplitude is determined by measuring average rectified (ARV) and/or root mean square (RMS) values and related coefficients. It significantly reduces the impact of noise. Structural diagram for the proposed method was developed and model researches on its basis were made. They indicate that when signal/noise ratio is in the range of 100 to 5, amplitude measurement accuracy increases more than 30 times. When signal/noise ratio is less than 5, accuracy decreases, but still 5 times higher than in traditional methods of measuring amplitude. Methods comparison for determining the amplitude by RMS and ARV values shows that when the signal/noise ratio is more than 10 the difference is insignificant. When signal/noise ratio is less than 5, better results can be obtained with ARV values and averaging coefficient. Particularly when the signal/noise ratio is 1, the error is less by almost 7 times. Thus, researches have confirmed the high efficiency of the proposed method under the impact of noise and interference, compared with traditional methods.Рассмотрены методы измерения толщины полимерных пленок и методы повышения точности измерения амплитуды в бесконтактных приборах контроля толщины полимерных пленок. Предложено использование коэффициентов амплитуды и усреднения для определения значения амплитуды сигнала известной формы по результатам измерения средневыпрямленного и действующего значения в условиях воздействия шумов и помех значительного уровня. Разработана структурная схема и проведены исследования эффективности предложенного метода

Two remarks on generalized entropy power inequalities

This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

3D simulations of gas puff effects on edge density and ICRF coupling in ASDEX Upgrade

In recent experiments, a local gas puff was found to be an effective way to tailor the scrape-off layer (SOL) density and improve the ion cyclotron range of frequency (ICRF) power coupling in tokamaks. In order to quantitatively reproduce these experiments, to understand the corresponding physics and to optimize the gas valve positions and rates, simulations were carried out with the 3D edge plasma transport code EMC3-EIRENE in ASDEX Upgrade. An inter-ELM phase of an H-mode discharge with a moderate gas puff rate (1.2 x 10(22) electrons s(-1)) is used in our simulations. We simulated cases with gas puff in the lower divertor, the outer mid-plane and the top of the machine while keeping other conditions the same. Compared with the lower divertor gas puff, the outer mid-plane gas puff can increase the local density in front of the antennas most effectively, while a toroidally uniform but significantly smaller enhancement is found for the top gas puff. Good agreement between our simulations and experiments is obtained. With further simulations, the mechanisms of SOL density tailoring via local gas puffing and the strategies of gas puff optimization are discussed in the paper

Electronic structure of d-wave superconducting quantum wires

We present analytical and numerical results for the electronic spectra of wires of a d-wave superconductor on a square lattice. The spectra of Andreev and other quasiparticle states, as well as the spatial and particle-hole structures of their wave functions, depend on interference effects caused by the presence of the surfaces and are qualitatively different for half-filled wires with even or odd number of chains. For half-filled wires with an odd number of chains N at (110) orientation, spectra consist of N doubly degenerate branches. By contrast, for even N wires, these levels are split, and all quasiparticle states, even the ones lying above the maximal gap, have the characteristic properties of Andreev bound states. These Andreev states above the gap can be interpreted as a consequence of an infinite sequence of Andreev reflections experienced by quasiparticles along their trajectories bounded by the surfaces of the wire. Our microscopic results for the local density of states display atomic-scale Friedel oscillations due to the presence of the surfaces, which should be observable by scanning tunneling microscopy. For narrow wires the self-consistent treatment of the order parameter is found to play a crucial role. In particular, we find that for small wire widths the finite geometry may drive strong fluctuations or even stablilize exotic quasi-1D pair states with spin triplet character.Comment: 21 pages, 20 figures. Slightly modified version as published in PR

Graviton-Scalar Interaction in the PP-Wave Background

We compute the graviton two scalar off-shell interaction vertex at tree level in Type IIB superstring theory on the pp-wave background using the light-cone string field theory formalism. We then show that the tree level vertex vanishes when all particles are on-shell and conservation of p_{+} and p_{-} are imposed. We reinforce our claim by calculating the same vertex starting from the corresponding SUGRA action expanded around the pp-wave background in the light-cone gauge.Comment: 26 pages, harvmac One reference added. A few comments changed in the introduction. The "cyclic perms." term removed from some equations as unnecessary and equations (2.38) and (3.19) are corrected accordingl

Ricci curvature of finite Markov chains via convexity of the entropy

We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry--Emery and Otto--Villani. Furthermore we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.Comment: 39 pages, to appear in Arch. Ration. Mech. Ana