Dispersive Shock Wave, Generalized Laguerre Polynomials and Asymptotic Solitons of the Focusing Nonlinear Schr\"odinger Equation

We consider dispersive shock wave to the focusing nonlinear Schr\"odinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi-axis and zero on the right semi-axis. As an initial function we use a finite-gap potential of the Dirac operator given in an explicit form through hyper-elliptic theta-functions. The paper aim is to study the long-time asymptotics of the solution of this problem in a vicinity of the leading edge, where a train of asymptotic solitons are generated. Such a problem was studied in \cite{KK86} and \cite{K91} using Marchenko's inverse scattering technics. We investigate this problem exceptionally using the Riemann-Hilbert problems technics that allow us to obtain explicit formulas for the asymptotic solitons themselves that in contrast with the cited papers where asymptotic formulas are obtained only for the square of absolute value of solution. Using transformations of the main RH problems we arrive to a model problem corresponding to the parametrix at the end points of continuous spectrum of the Zakharov-Shabat spectral problem. The parametrix problem is effectively solved in terms of the generalized Laguerre polynomials which are naturally appeared after appropriate scaling of the Riemann-Hilbert problem in a small neighborhoods of the end points of continuous spectrum. Further asymptotic analysis give an explicit formula for solitons at the edge of dispersive wave. Thus, we give the complete description of the train of asymptotic solitons: not only bearing envelope of each asymptotic soliton, but its oscillating structure are found explicitly. Besides the second term of asymptotics describing an interaction between these solitons and oscillating background is also found. This gives the fine structure of the edge of dispersive shock wave.Comment: 36 pages, 5 figure

On the origin of membrane potential in membranes with polarizable nanopores

We report a new mechanism for the generation of membrane potential in polarizable nanoporous membranes separating electrolytes with different concentrations. The electric field generated by diffusion of ions with different mobilities induces a non–uniform surface charge, which results in charge separation inside the nanopore. The corresponding Donnan potentials appear at the pore entrance and exit leading to a dramatic enhancement of membrane potential in comparison with an uncharged non–polarizable membrane. At high concentration contrast, the interaction between electric field and uncompensated charge at a low concentration side results in the development of electrokinetic vortices. The theoretical predictions are based on the Space–Charge model, which is extended to nanopores with polarizable conductive surface for the first time. This model is validated against full Navier–Stokes, Nernst–Planck, and Poisson equations, which are solved in a high aspect ratio nanopore connecting two reservoirs. The experimental measurements of membrane potential of dielectric and conductive membranes in KCl and NaCl aqueous solutions confirm the theoretical results. The membranes are prepared from Nafen nanofibers with ∼10nm in diameter and modified by depositing a conductive carbon layer. It is shown theoretically that the membrane potential enhancement becomes greater with decreasing the electrolyte concentration and pore radius. A high sensitivity of membrane potential to the ratio of ion diffusion coefficients is demonstrated. The described phenomenon may find applications in precise determination of ion mobilities, electrochemical and bio–sensing, as well as design of nanofluidic and bioelectronic devices. © 2017 Elsevier B.V

Study of Colloidal Stability and Viscosity of Concentrated Aqueous Silicasols

Проведено исследование коллоидной устойчивости наносуспензий, полученных разбавлением концентрированных силиказолей. Рассмотрен широкий диапазон массовых концентраций наночастиц (от 1 до 50 масс.%) и средних размеров первичных частиц (от 10 до 35 нм). Анализ седиментационных экспериментов показал, что рассмотренные образцы обладают очень высокой коллоидной устойчивостью. Проведена характеризация размеров наночастиц с помощью электронной микроскопии, получены распределения частиц по размерам в суспензии методом акустической спектроскопии. В результате было показано, что почти все рассматриваемые силиказоли имеют очень узкое распределение частиц по размеру. Получены зависимости динамической вязкости наносуспензий от концентрации и размера наночастиц. На их основе построены эмпирические корреляции в широком диапазоне концентраций частицA study of the colloidal stability of nanosuspensions obtained by diluting concentrated silicasols was carried out. A wide range of mass concentrations of nanoparticles (from 1 to 50 wt.%) and average sizes of primary particles (from 10 to 35 nm) were considered. The analysis of sedimentation experiments showed that the considered samples have a very high colloidal stability. The characterization of the nanoparticle sizes by electron microscopy was carried out. The particle size distributions in the suspension were obtained by acoustic spectroscopy. Almost all of the considered silica sols have been shown to have a very narrow particle size distribution. The dependences of the dynamic viscosity of nanosuspensions on the concentration and size of nanoparticles are obtained. Based on the dependences, empirical correlations in a wide range of particle concentrations were obtaine

Study of Colloidal Stability and Rheological Properties of Invert Emulsion with Vegetable Oil as the Base for Drilling Fluid

Работа посвящена проведению комплексных исследований коллоидной устойчивости и реологических свойств обратных эмульсий на основе технического рапсового масла и разработке на их основе рекомендаций использования данных экологически чистых компонентов в качестве основы для создания буровых растворов. Исследование свойств эмульсий производилось в зависимости от концентрации масла (от 50 до 90 об.%), концентрации эмульгатора (от 1 до 3 об.%) и температуры (от 20 до 80 оС). Были получены устойчивые инвертные эмульсии, которые сохраняют свои свойства с ростом температуры, что говорит о возможности их практического применения в качестве компонентов для создания экологически более безопасных буровых растворовThe paper is devoted to comprehensive studies of the colloidal stability and rheological properties of inverse emulsions based on technical rapeseed oil and developing on their base recommendations for using these environmentally friendly components as the base for synthesis drilling fluids. The study of the properties of emulsions was carried out depending on the concentration of oil (from 50 to 90 vol.%), the concentration of the emulsifier (from 1 to 3 vol.%) and temperature (from 20 to 80 °C). Stable invert emulsions were obtained, which retain their properties with increasing temperature, which indicates the possibility of their practical application as components for synthesis environmentally safer drilling fluid

ВЛИЯНИЕ ОБРАБОТКИ ПОВЕРХНОСТИ ПОРИСТОГО КРЕМНИЯ В РАСТВОРЕ ПОЛИАКРИЛОВОЙ КИСЛОТЫ НА ЕГО ФОТОЛЮМИНЕСЦЕНТНЫЕ СВОЙСТВА

Porous silicon (por-Si) has a unique set of physic−chemical properties of characteristics — well-developed surface and consequently, a high sorption activity. In a dependence of the fabrication technique it is possible to form pores and clusters of nanometer size that makes this material rather prospective for elaborations in optoelectronics and sensors production. However, high surface activity stipulates porous silicon instability in the atmosphere. The work is concerned with the study of the influence of por-Si surface treatment in the aqueous solution of polyacrylic acid on the composition and photoluminescence of this material. It was found that this treatment can either enhance and stabilize PL of the material or change spectral position of PL band and also enhance its total intensity in a dependence of the fabrication technique.Пористый кремний обладает уникальным набором физико-химических характеристик — развитой поверхностью и, как следствие, существенной сорбционной активностью. В зависимости от технологии изготовления в нем можно сформировать поры и кластеры нанометровых размеров, что делает этот материал перспективным для разработок в области оптоэлектроники и сенсорики. Однако высокая активность поверхности обуславливает нестабильность пористого кремния при его контакте с атмосферой. Исследовано влияние обработки поверхности пористого кремния в водном растворе полиакриловой кислоты на состав и фотолюминесценцию материала. Установлено, что такая обработка, в зависимости от технологии получения пористого кремния, может усиливать и стабилизировать фотолюминесценцию этого материала или изменять положение полосы фотолюминесценции и значительно увеличивать ее интегральную интенсивность

AWAKE, the advanced proton driven plasma wakefield acceleration experiment at CERN

The Advanced Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE) aims at studying plasma wakefield generation and electron acceleration driven by proton bunches. It is a proof-of-principle R&D experiment at CERN and the world׳s first proton driven plasma wakefield acceleration experiment. The AWAKE experiment will be installed in the former CNGS facility and uses the 400 GeV/c proton beam bunches from the SPS. The first experiments will focus on the self-modulation instability of the long (rms ~12 cm) proton bunch in the plasma. These experiments are planned for the end of 2016. Later, in 2017/2018, low energy (~15 MeV) electrons will be externally injected into the sample wakefields and be accelerated beyond 1 GeV. The main goals of the experiment will be summarized. A summary of the AWAKE design and construction status will be presented