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

Potential of sub-THz-wave generation in Li2B4O7 nonlinear crystal at room and cryogenic temperatures

Due to their high optical damage threshold, borate crystals can be used for the efficient nonlinear down-conversion of terawatt laser radiation into the terahertz (THz) frequency range of the electromagnetic spectrum. In this work, we carried out a thorough study of the terahertz optical properties of the lithium tetraborate crystal (Li2B4O7; LB4) at 295 and 77 K. Approximating the terahertz refractive index in the form of Sellmeier’s equations, we assessed the possibility of converting the radiation of widespread high-power laser sources with wavelengths of 1064 and 800 nm, as well as their second and third harmonics, into the THz range. It was found that four out of eight types of three-wave mixing processes are possible. The conditions for collinear phase matching were fulfilled only for the o - e -o type of interaction, while cooling the crystal to 77 K did not practically affect the phase-matching curves. However, a noticeable increase of birefringence in the THz range with cooling (from 0.12 to 0.16) led to an increase in the coherence length for o-o-e and e-e-e types of interaction, which are potentially attractive for the down-conversion of ultrashort laser pulses

AWAKE: A proton-driven plasma wakefield acceleration experiment at CERN

The AWAKE Collaboration has been formed in order to demonstrate proton-driven plasma wakefield acceleration for the first time. This acceleration technique could lead to future colliders of high energy but of a much reduced length when compared to proposed linear accelerators. The CERN SPS proton beam in the CNGS facility will be injected into a 10 m plasma cell where the long proton bunches will be modulated into significantly shorter micro bunches. These micro-bunches will then initiate a strong wakefield in the plasma with peak fields above 1 GV/m that will be harnessed to accelerate a bunch of electrons from about 20 MeV to the GeV scale within a few meters. The experimental program is based on detailed numerical simulations of beam and plasma interactions. The main accelerator components, the experimental area and infrastructure required as well as the plasma cell and the diagnostic equipment are discussed in detail. First protons to the experiment are expected at the end of 2016 and this will be followed by an initial three-four years experimental program. The experiment will inform future larger-scale tests of proton-driven plasma wakefield acceleration and applications to high energy colliders.info:eu-repo/semantics/publishedVersio

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: A Proton-Driven Plasma Wakefield Acceleration Experiment at CERN

The AWAKE Collaboration has been formed in order to demonstrate proton-driven plasma wakefield acceleration for the first time. This acceleration technique could lead to future colliders of high energy but of a much reduced length when compared to proposed linear accelerators. The CERN SPS proton beam in the CNGS facility will be injected into a 10 m plasma cell where the long proton bunches will be modulated into significantly shorter micro-bunches. These micro-bunches will then initiate a strong wakefield in the plasma with peak fields above 1 GV/m that will be harnessed to accelerate a bunch of electrons from about 20 MeV to the GeV scale within a few meters. The experimental program is based on detailed numerical simulations of beam and plasma interactions. The main accelerator components, the experimental area and infrastructure required as well as the plasma cell and the diagnostic equipment are discussed in detail. First protons to the experiment are expected at the end of 2016 and this will be followed by an initial three-four years experimental program. The experiment will inform future larger-scale tests of proton-driven plasma wakefield acceleration and applications to high energy colliders