Linear "ship waves" generated in stationary flow of a Bose-Einstein condensate past an obstacle

Using stationary solutions of the linearized two-dimensional Gross-Pitaevskii equation, we describe the ``ship wave'' pattern occurring in the supersonic flow of a Bose-Einstein condensate past an obstacle. It is shown that these ``ship waves'' are generated outside the Mach cone. The developed analytical theory is confirmed by numerical simulations of the flow past body problem in the frame of the full non-stationary Gross-Pitaevskii equation.Comment: 5 pages, 4 figure

On dissipationless shock waves in a discrete nonlinear Schr\"odinger equation

It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless limit these equations lead to wave breaking phenomenon for general enough initial conditions, and, after taking into account small dispersion effects, result in formation of dissipationless shock waves. The Whitham theory of modulations of nonlinear waves is used for analytical description of such waves.Comment: 15 pages, 9 figure

Matter sound waves in two-component Bose-Einstein condensates

The creation and propagation of sound waves in two-component Bose-Einstein condensates (BEC) are investigated and a new method of wave generation in binary BEC mixtures is proposed. The method is based on a fast change of the inter-species interaction constant and is illustrated for two experimental settings: a drop-like condensate immersed into a second large repulsive condensate, and a binary mixture of two homogeneous repulsive BEC's. A mathematical model based on the linearized coupled Gross-Pitaevskii equations is developed and explicit formulae for the space and time dependence of sound waves are provided. Comparison of the analytical and numerical results shows excellent agreement, confirming the validity of the proposed approach.Comment: 16 pages, 9 figure

Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate

Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.Comment: 7 pages, 3 figure

Lagrangian and Hamiltonian two-scale reduction

Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave-length motion or describe the macroscopic modulation of an oscillatory microstructure.Comment: 40 page

Generation of linear waves in the flow of Bose-Einstein condensate past an obstacle

The theory of linear wave structures generated in Bose-Einstein condensate flow past an obstacle is developed. The shape of wave crests and dependence of amplitude on coordinates far enough from the obstacle are calculated. The results are in good agreement with the results of numerical simulations obtained earlier. The theory gives a qualitative description of experiments with Bose-Einstein condensate flow past an obstacle after condensate's release from a trap.Comment: 11 pages, 3 figures, to be published in Zh. Eksp. Teor. Fi

Management of a patient with low back pain: the problems of efficiency and safety

Low back pain (LBP) is a common condition occurring in the population in different age groups; it is characterized by a tendency to relapse.Acute pain may transform to chronic pain, causing patient disability. The goal of LBP treatment is to timely relieve painful sensations so that the patient can return to his/her normal life as soon as possible. The patient is required to participate in the therapeutic process. Ketonal that shows high efficacy and good tolerability is widely used to treat patients with LBP. The medication is available in different dosage forms, which makes it possible to individualize the therapeutic process and to reduce drug load due to its possible topical application

Применение кетонала при поясничной боли

Lumbago is one of the most common musculoskeletal pain syndromes. The course of lumbago shows a tendency towards frequent relapses and is associated with the significant material costs of medical care. A wide range of analgesics, nonsteroidal anti-inflammatory drugs in particular, whose administration may be linked with an increased risk for adverse visceral reactions, is used to treat patient with lumbago. The risk of their side effects may be reduced by the extensive use of non-drug treatments and the early expansion of a motor regimen in a patient. Therapeutic effectiveness in reducing the likelihood of adverse reactions may be provided by short-term treatment with effective drugs. The advantages of using ketoprofen (ketonal) formulations in patients with lumbago are considered.Поясничная боль (ПБ) – один из наиболее распространенных скелетно-мышечных болевых синдромов. Течение ПБ характеризуется склонностью к частому рецидивированию и связано со значительными материальными затратами на оказание медицинской помощи. При лечении пациентов с ПБ применяется широкий спектр противоболевых лекарственных средств, в частности нестероидных противовоспалительных препаратов. Назначение последних может быть связано с повышением риска развития нежелательных побочных эффектов со стороны внутренних органов. Снижение риска развития нежелательных эффектов возможно при широком использовании немедикаментозных методов лечения и раннем расширении двигательного режима больного. Обеспечение эффективности терапии при снижении вероятности развития побочных эффектов возможно при проведении относительно коротких курсов лечения эффективными препаратами. Рассматриваются преимущества применения лекарственных форм кетопрофена (кетонал) у пациентов с ПБ

Generation of dispersive shock waves by the flow of a Bose-Einstein condensate past a narrow obstacle

We study the flow of a quasi-one-dimensional Bose-Einstein condensate incident onto a narrow obstacle. We consider a configuration in which a dispersive shock is formed and propagates upstream away from the obstacle while the downstream flow reaches a supersonic velocity, generating a sonic horizon. Conditions for obtaining this regime are explicitly derived and the accuracy of our analytical results is confirmed by numerical simulations

Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.Comment: 6 pages, 4 figure