Economical adjunction of square roots to groups

How large must an overgroup of a given group be in order to contain a square root of any element of the initial group? We give an almost exact answer to this question (the obtained estimate is at most twice worse than the best possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: minor correction

Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and diffeomorphisms relative to which they are generalized Lie groups or topological groups. Among such topologies pairwise incomparable are found as well. Topological perfectness of the diffeomorphism group relative to certain topologies is studied. There are proved theorems about projective limit decompositions of these groups and their compactifications for compact manifolds. Moreover, an existence of one-parameter local subgroups of diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad

Experimental study of extended timescale dynamics of a plasma wakefield driven by a self-modulated proton bunch

Plasma wakefield dynamics over timescales up to 800 ps, approximately 100 plasma periods, are studied experimentally at the Advanced Wakefield Experiment (AWAKE). The development of the longitudinal wakefield amplitude driven by a self-modulated proton bunch is measured using the external injection of witness electrons that sample the fields. In simulation, resonant excitation of the wakefield causes plasma electron trajectory crossing, resulting in the development of a potential outside the plasma boundary as electrons are transversely ejected. Trends consistent with the presence of this potential are experimentally measured and their dependence on wakefield amplitude are studied via seed laser timing scans and electron injection delay scan

Experimental study of wakefields driven by a self-modulating proton bunch in plasma

We study experimentally the longitudinal and transverse wakefields driven by a highly relativistic proton bunch during self-modulation in plasma. We show that the wakefields' growth and amplitude increase with increasing seed amplitude as well as with the proton bunch charge in the plasma. We study transverse wakefields using the maximum radius of the proton bunch distribution measured on a screen downstream from the plasma. We study longitudinal wakefields by externally injecting electrons and measuring their final energy. Measurements agree with trends predicted by theory and numerical simulations and validate our understanding of the development of self-modulation. Experiments were performed in the context of the Advanced Wakefield Experiment (AWAKE)

Transition between Instability and Seeded Self-Modulation of a Relativistic Particle Bunch in Plasma

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufticient initial amplitude [>= (4.1 +/- 0.4) MV/m], the phase of the modulation along the bunch is reproducible from event to event, with 3%-7% (of 2 pi) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated

Proton Bunch Self-Modulation in Plasma with Density Gradient

We study experimentally the effect of linear plasma density gradients on the self-modulation of a 400 GeV proton bunch. Results show that a positive or negative gradient increases or decreases the number of microbunches and the relative charge per microbunch observed after 10 m of plasma. The measured modulation frequency also increases or decreases. With the largest positive gradient we observe two frequencies in the modulation power spectrum. Results are consistent with changes in wakefields' phase velocity due to plasma density gradients adding to the slow wakefields' phase velocity during self-modulation growth predicted by linear theory

Sochi olympic games as viewed by the youth

На основе результатов прикладного социологического исследования среди студентов Астрахани и Волгограда в данной статье рассматривается общее и особенное в оценках Олимпийских игр в Сочи. В целом рейтинг оценок астраханцев и волгоградцев совпадает, но их общий порядок несколько различается: астраханцы в основном интересуются обстановкой всеобщего праздника, процедурами открытия и закрытия Олимпиады, а волгоградцы проявляют себя как приверженцы профессионального спорта «высоких» достижений. Волгоградские студенты более категоричны и прагматичны, нежели чем студенты – астраханцы, которые в большей степени склонны выражать свои положительные эмоции в оценке Олимпиады. Также у волгоградцев (как у носителей городского типа менталитета) индивидуализм и рационализм выражены более ярко, а астраханцы проявляют себя как носители деревенского типа менталитета с присущими ему коллективизмом, эмоциональностью, иррационализмом.This article is based on the data obtained in the course of sociological study of common and specific features of evaluation of Sochi Olympic Games by university students from Astrakhan and Volgograd. The conclusions of the evaluations by students from Astrakhan and Volgograd are generally similar, but the basic structure of their opinions is slightly different. Students from Astrakhan were more interested in the idea of a large holiday, including the opening and closing ceremonies, whereas students from Volgograd were more interested in high-level sports, involving top-flight individual achievement. The students from Volgograd were more flat and pragmatic than their counterparts from Astrakhan, who expressed more emotion in their evaluation of the Olympic Games. Such features as individualism and rationalism are more typical for the students from Volgograd, reflecting a primarily urban mentality, than of the students from Astrakhan, reflecting a more small-town mentality, characterized by inherent collectivism, expression of emotions and irrationality