Proton beam self-modulation seeded by electron bunch in plasma with density ramp

Seeded self-modulation in a plasma can transform a long proton beam into a train of micro-bunches that can excite a strong wakefield over long distances, but this needs the plasma to have a certain density profile with a short-scale ramp up. For the parameters of the AWAKE experiment at CERN, we numerically study which density profiles are optimal if the self-modulation is seeded by a short electron bunch. With the optimal profiles, it is possible to "freeze" the wakefield at approximately half the wavebreaking level. High-energy electron bunches (160 MeV) are less efficient seeds than low-energy ones (18 MeV), because the wakefield of the former lasts longer than necessary for efficient seeding.Comment: 11 pages, 15 figure

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

Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution

The modified Korteveg{de Vries equation on the line is considered. The initial function is a discontinuous and piece-wise constant step function, i.e. q(x, 0) = cr for x ≥ 0 and q(x, 0) = cl for x cr > 0. The goal of this paper is to study the asymptotic behavior of the solution of the initial-value problem as t → ∞.Рассматривается модифицированное уравнение КдФ на всей прямой с начальным условием типа ступеньки, которая равна константе cl при x 0. При этом выполняется условие cl > cr > 0, что обеспечивает режим "гидродинамической волны сжатия" при t → ∞. Цель статьи - изучение асимптотического поведения решения начально-краевой задачи, когда t → ∞

Spontaneous imbibition experiments for enhanced oil recovery with silica nanosols

Experimental oil displacement as a result of spontaneous imbibition of silica nanosols has been carried out using two types of sandstone as the reservoir rock. The permeability of the cores ranged from 0.34 to 333 mD, while the porosity was 11% and 22%, respectively. During the research, the influence of the concentration and nanoparticle size, as well as the permeability of the rock, on the process of spontaneous imbibition, was studied. Silica nanosols were considered as an object of study. The nanoparticle size ranged from 10 to 35 nm. The mass concentration of nanoparticles varied from 0.01% to 0.25%. It was found that the use of silica nanosols significantly increases the rate of the spontaneous imbibition process. It was established that a silica nanosol with a nanoparticle size of 10 nm and a concentration of 0.25% allows to displace more than six times oil compared to the reservoir water model in the same time. As a result, it was shown that the oil displacement efficiency and the efficiency of spontaneous imbibition increase along with an increase in the nanoparticle concentration and a decrease in the nanoparticle size.Document Type: Original articleCited as: Pryazhnikov, M. I., Zhigarev, V. A., Minakov, A. V., Nemtsev, I. V. Spontaneous imbibition experiments for enhanced oil recovery with silica nanosols. Capillarity, 2024, 10(3): 73-86. https://doi.org/10.46690/capi.2024.03.0

Color Effects Associated with the 1999 Microlensing Brightness Peaks in Gravitationally Lensed Quasar Q2237+0305

Photometry of the Q2237+0305gravitational lens in VRI spectral bands with the 1.5-m telescope of the high-altitude Maidanak observatory in 1995-2000 is presented. Monitoring of Q2237+0305 in July-October 2000, made at nearly daily basis, did not reveal rapid (night-to-night and intranight) variations of brightness of the components during this time period. Rather slow changes of magnitudes of the components were observed, such as 0.08 mag fading of B and C components and 0.05 mag brightening of D in R band during July 23 - October 7, 2000. By good luck three nights in 1999 were almost at the time of the strong brightness peak of image C, and approximately in the middle of the ascending slope of the image A brightness peak. The C component was the most blue one in the system in 1998 and 1999, having changed its (V-I) color from 0.56 mag to 0.12 mag since August 1997, while its brightness increased almost 1.2 mag during this time period. The A component behaved similarly between August 1998 and August 2000, having become 0.47 mag brighter in R, and at the same time, 0.15 mag bluer. A correlation between the color variations and variations of magnitudes of the components is demonstrated to be significant and reaches 0.75, with a regression line slope of 0.33. A color (V-I) vrs color (V-R) plot shows the components settled in a cluster, stretched along a line with a slope of 1.31. Both slopes are noticeably smaller than those expected if a standard galactic interstellar reddening law were responsible for the differences between the colors of images and their variations over time. We attribute the brightness and color changes to microlensing of the quasar's structure, which we conclude is more compact at shorter wavelengths, as predicted by most quasar models featuring an energizing central source.Comment: 14 pages, 7 figures, LaTeX, submitted to A&