Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations

Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational, periodic, elliptic) are found for a wide class of autonomous nonlinear ordinary differential equations

Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy

The Abelian Chern-Simons Gauge Field Theory in 2+1 dimensions and its relation with holomorphic Burgers' Hierarchy is considered. It is shown that the relation between complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics, has meaning of the analytic Cole-Hopf transformation, linearizing the Burgers Hierarchy in terms of the holomorphic Schr\"odinger Hierarchy. Then the motion of planar vortices in Chern-Simons theory, appearing as pole singularities of the gauge field, corresponds to motion of zeroes of the hierarchy. Using boost transformations of the complex Galilean group of the hierarchy, a rich set of exact solutions, describing integrable dynamics of planar vortices and vortex lattices in terms of the generalized Kampe de Feriet and Hermite polynomials is constructed. The results are applied to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing dynamics of magnetic vortices and corresponding lattices in terms of complexified Calogero-Moser models. Corrections on two vortex dynamics from the Moyal space-time non-commutativity in terms of Airy functions are found.Comment: 15 pages, talk presented in Workshop `Nonlinear Physics IV: Theory and Experiment`, 22-30 June 2006, Gallipoli, Ital

A priori estimates for the Hill and Dirac operators

Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps \g_n,n\ge 1 with length |\g_n|\ge 0. We obtain a priori estimates of the gap lengths, effective masses, action variables for the KDV. For example, if \m_n^\pm are the effective masses associated with the gap \g_n=(\l_n^-,\l_n^+), then |\m_n^-+\m_n^+|\le C|\g_n|^2n^{-4} for some constant $C=C(q)$ and any $n\ge 1$. In order prove these results we use the analysis of a conformal mapping corresponding to quasimomentum of the Hill operator. That makes possible to reformulate the problems for the differential operator as the problems of the conformal mapping theory. Then the proof is based on the analysis of the conformal mapping and the identities. Moreover, we obtain the similar estimates for the Dirac operator

A Dipole Vortex Model of Obscuring Tori in Active Galaxy Nuclei

The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here, the situation is discussed when the torus "twisting" by the radiation or wind transforms it into a dipole toroidal vortex which in turn can be a source of matter replenishing the accretion disk. Thus emerging instability which can be responsible for quasar radiation flares accompanied by matter outbursts is also discussed. The "Matreshka" scheme for an obscuring vortex torus structure capable of explaining the AGN variability and evolution is proposed. The model parameters estimated numerically for the luminosity close to the Eddington limit agree well with the observations.Comment: 17 pages, 11 figures, version of this paper is published in Astronomy Report

Can inertial electrostatic confinement work beyond the ion–ion collisional time scale?

Inertial electrostatic confinement systems are predicated on a non-equilibrium ion distribution function. Coulomb collisions between ions cause this distribution to relax to a Maxwellian on the ion-ion collisional time-scale. The power required to prevent this relaxation and maintain the IEC configuration for times beyond the ion-ion collisional time scale is shown to be at least an order of magnitude greater than the fusion power produced. It is concluded that IEC systems show little promise as a basis for the development of commercial electric power plants

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССА ЭКСТРУЗИИ ТЕРМОЭЛЕКТРИЧЕСКОГО МАТЕРИАЛА

We derive a mathematical model for the composite material extrusion process which describes the main features of the resulting material stress−strain state. The extrusion process includes extrusion of a cylindrical billet of pressed powder through a die of desired geometry. Die geometrical parameters and process speed can be preset. The computational model is based on combined elastic−plastic body approximation. The numericaltechnique uses a finite element approximation on Lagrangian grid, which changes over time with changes in sample shape. To perform it we use adaptive grid units generation in areas of sample high stress and strain. The calculations were performed in Crystmo/Marc software package. We study the basic featuresof stress−strain state of the material obtained at different stages of extrusion process.Для процесса экструзии композиционного материала предложена математическаямодель и на ее основе рассмотрены основные особенности напряженно−деформированногосостояния получаемого стержня. Заданы геометрические параметры фильеры и скорость перемещения Пуансона. Расчетная модель основана на совместном использовании приближенийупругопластического тела. Численная методика использует конечно−элементную аппроксимацию на лагранжевой сетке, которая меняется во времени с изменением формы образца. Для этого применена адаптивная генерация сеточных узлов в зонах больших напряжений и деформаций образца. Расчеты проведены с использованием комплекса программ Crystmo/Marc. На примере термоэлектрического композита на основе Bi2Te3 изучены основные особенности напряженно−деформированного состояния материала, полученного на разных стадиях процесса экструзии

The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media

The original publication can be found at www.springerlink.comDeep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid invasion of reservoir production zones, fines migration in oil fields, industrial filtering, bacteria, viruses or contaminants transport in groundwater etc. The basic features of the process are particle capture by the porous medium and consequent permeability reduction. Models for deep bed filtration contain two quantities that represent rock and fluid properties: the filtration function, which is the fraction of particles captured per unit particle path length, and formation damage function, which is the ratio between reduced and initial permeabilities. These quantities cannot be measured directly in the laboratory or in the field; therefore, they must be calculated indirectly by solving inverse problems. The practical petroleum and environmental engineering purpose is to predict injectivity loss and particle penetration depth around wells. Reliable prediction requires precise knowledge of these two coefficients. In this work we determine these quantities from pressure drop and effluent concentration histories measured in one-dimensional laboratory experiments. The recovery method consists of optimizing deviation functionals in appropriate subdomains; if necessary, a Tikhonov regularization term is added to the functional. The filtration function is recovered by optimizing a non-linear functional with box constraints; this functional involves the effluent concentration history. The permeability reduction is recovered likewise, taking into account the filtration function already found, and the functional involves the pressure drop history. In both cases, the functionals are derived from least square formulations of the deviation between experimental data and quantities predicted by the model.Alvarez, A. C., Hime, G., Marchesin, D., Bedrikovetski, P

ОСОБЕННОСТИ ХИРУРГИЧЕСКОГО ЛЕЧЕНИЯ ГИГАНТСКИХ АТЕРОСКЛЕРОТИЧЕСКИХ АНЕВРИЗМ БРЮШНОГО ОТДЕЛА АОРТЫ

The article deals with some aspects of surgical treatment of giant atherosclerotic abdominal aortic aneurysms. Giant aneurysms measuring more than 10 cm in diameter are an extremely rare disorder. A total of 33 observations of surgical treatment of patients with this disorder are described in the English language literature. This article provides epidemiology data based on the publications we studied. Clinical cases described in both domestic and foreign literature are presented and reviewed. A summary table has been created on the basis of the data, which provides comprehensive information on the experience accumulated over the given time in the treatment of gigantic aortic aneurysms. Over 600 surgeries for abdominal aortic aneurysms, of which nine interventions for gigantic aneurysms, have been performed in A.V.Vishnevsky National Medical Research Institute of Surgery. So far, this is the largest experience in surgery of gigantic aortic aneurysms accumulated in one institution. The article presents an analysis of literature data in the context of the results of our own observations. The aspects of choosing the surgical treatment method, the advantages and disadvantages of both open interventions and endovascular operations were considered in detail. The authors described in detail the features of the choice of surgical access, the technique for isolating the aneurysm neck with a detailed analysis of the further course of the operation. Extensive visual material is presented such as CT-, CT angiography scans, intraoperative photographs. The outcomes of interventions are analysed, the mortality rate of post-surgical treatment of giant aneurysms is 0%, there is no significant difference in morbidity in comparison with surgery of smaller aneurysms.Статья посвящена особенностям хирургического лечения гигантских атеросклеротических аневризм брюшного отдела аорты. Гигантские аневризмы диаметром более 10 см являются крайне редкой патологией. В англоязычной литературе описано всего 33 наблюдения хирургического лечения пациентов с данной патологией. В статье приведены данные эпидемиологии на основе изученных нами публикаций. Представлены и проанализированы клинические случаи, описанные как в отечественной, так и в зарубежной литературе. На основе данных создана сводная таблица, в которой представлена исчерпывающая информация по накопленному на данный момент опыту в лечении гигантстких аневризм аорты. В НМИЦ хирургии им. А.В. Вишневского с 1993 по 2019 г. выполнено более 600 операций по поводу аневризм брюшного отдела аорты, из которых девять – вмешательства по поводу гигантских аневризм. На данный момент это является самым большим опытом хирургии гигантских аневризм аорты, накопленным в рамках одного учреждения. В статье представлен анализ данных литературы в контексте результатов собственных наблюдений. Подробно обсуждены аспекты выбора метода хирургического лечения, преимущества и недостатки как открытых вмешательств, так и эндоваскулярных операций. Обсуждены особенности выбора хирургического доступа, подробно изложена техника выделения шейки аневризмы с детальным разбором дальнейшего хода операции. Представлен обширный визуальный материал – данные КТ, КТ-ангиографии, интраоперационных фотографий. Проанализированы исходы вмешательств, летальность послехирургического лечения гигантских аневризм – 0%, существенного отличия в морбидности нет в сравнении с хирургией аневризм меньшего размера