Multicomponent theory of buoyancy instabilities in magnetized plasmas: The case of magnetic field parallel to gravity

We investigate electromagnetic buoyancy instabilities of the electron-ion plasma with the heat flux based on not the magnetohydrodynamic (MHD) equations, but using the multicomponent plasma approach when the momentum equations are solved for each species. We consider a geometry in which the background magnetic field, gravity, and stratification are directed along one axis. The nonzero background electron thermal flux is taken into account. Collisions between electrons and ions are included in the momentum equations. No simplifications usual for the one-fluid MHD-approach in studying these instabilities are used. We derive a simple dispersion relation, which shows that the thermal flux perturbation generally stabilizes an instability for the geometry under consideration. This result contradicts to conclusion obtained in the MHD-approach. We show that the reason of this contradiction is the simplified assumptions used in the MHD analysis of buoyancy instabilities and the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. Our dispersion relation also shows that the medium with the electron thermal flux can be unstable, if the temperature gradients of ions and electrons have the opposite signs. The results obtained can be applied to the weakly collisional magnetized plasma objects in laboratory and astrophysics.Comment: Accepted for publication in Astrophysics & Space Scienc

Moduli Spaces of Instantons on the Taub-NUT Space

We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.Comment: 26 pages, 7 figure

Instantons in N=2 magnetized D-brane worlds

In a toroidal orbifold of type IIB string theory we study instanton effects in N=2 super Yang-Mills theories engineered with systems of wrapped magnetized D9 branes and Euclidean D5 branes. We analyze the various open string sectors in this brane system and study the 1-loop amplitudes described by annulus diagrams with mixed boundary conditions, explaining their role in the stringy instanton calculus. We show in particular that the non-holomorphic terms in these annulus amplitudes precisely reconstruct the appropriate Kahler metric factors that are needed to write the instanton correlators in terms of purely holomorphic variables. We also explicitly derive the correct holomorphic structure of the instanton induced low energy effective action in the Coulomb branch.Comment: 40 pages, 5 figures, JHEP class. Some footnotes added and typos corrected. Version published in JHE

Orbital state and magnetic properties of LiV_2 O_4

LiV_2 O_4 is one of the most puzzling compounds among transition metal oxides because of its heavy fermion like behavior at low temperatures. In this paper we present results for the orbital state and magnetic properties of LiV_2 O_4 obtained from a combination of density functional theory within the local density approximation and dynamical mean-field theory (DMFT). The DMFT equations are solved by quantum Monte Carlo simulations. The trigonal crystal field splits the V 3d orbitals such that the a_{1g} and e_{g}^{pi} orbitals cross the Fermi level, with the former being slightly lower in energy and narrower in bandwidth. In this situation, the d-d Coulomb interaction leads to an almost localization of one electron per V ion in the a_{1g} orbital, while the e_{g}^{pi} orbitals form relatively broad bands with 1/8 filling. 2The theoretical high-temperature paramagnetic susceptibility chi(T) follows a Curie-Weiss law with an effective paramagnetic moment p_{eff}=1.65 in agreement with the experimental results.Comment: 11 pages, 10 figures, 2 table

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops

We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N=4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N=2 and the N=2* supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N=2 superconformal gauge theory is treated similarly.Comment: 63 pages, 1 figure; v2: correction of mass parameter; v3: typos correcte

Fluctuations of quantities averaged over time in the course of measurements

The averaging effect of measuring instruments in the course of measurements of physical quantities is considered. Formulas are obtained for the calculation of the fluctuations and time correlations, taking into account the effect of the measuring equipment for classical and quantum systems. © 1978 Plenum Publishing Corporation

Fluctuations of quantities averaged over time in the course of measurements

The averaging effect of measuring instruments in the course of measurements of physical quantities is considered. Formulas are obtained for the calculation of the fluctuations and time correlations, taking into account the effect of the measuring equipment for classical and quantum systems. © 1978 Plenum Publishing Corporation

Estimation of the Rate of Turbulent Liquid Flow in the Pipeline Based on Surface Measurements of Flow Noise

Некрасов Сергей Геннадьевич, доктор технических наук, профессор кафедры «Информационно-измерительная техника», Южно-Уральский государственный университет, г. Челябинск, [email protected]. Фомченко Сергей Андреевич, аспирант кафедры «Информационно-измерительная техника», Южно-Уральский государственный университет, г. Челябинск, [email protected]. S.G. Nekrasov, [email protected], S.A. Fomchenko, [email protected] South Ural State University, Chelyabinsk, Russian FederationВ работе приводятся результаты численного и экспериментального исследования, которое направлено на повышение точности неинтрузивных измерений температуры жидкой среды в трубопроводах, являющихся обязательными элементами гидросистем машин и механизмов. Решается вспомогательная задача оценки скорости потока жидкости путем измерения интенсивности шума на поверхности трубопровода. Источником шума в трубопроводе являются флуктуации скорости жидкости в турбулентном потоке, которые мы воспринимаем в виде флуктуаций давления и звука, при этом для больших скоростей потока распределение средней скорости в поперечном сечении трубы достаточно равномерно и имеет логарифмический характер, а общая температура потока близка к температуре в центре трубы. Однако при малых и умеренных скоростях потока распределение температур неравномерно и составляющая от неравномерности может давать существенный вклад в общую погрешность измерений, особенно при измерениях с помощью сравнительно точных термометров сопротивления. Поэтому, для повышения точности неинтрузивных измерений температуры необходимо вводить поправку, являющуюся функцией средней скорости потока и способную компенсировать погрешность измерений от недостаточной степени однородности потока. В работе проведен обоснованный выбор среды численного моделирования, подходящей для требований данной задачи, и рассчитана величина плотности энергии турбулентности в трубопроводе с двумя коленами (термокомпенсаторами), а также порождающей ее диссипацией энергии турбулентности, представлены распределения энергии турбулентности в поперечном сечении потока в районе одного из колен. Это исследование позволяет сказать, что максимальные величины плотности энергии турбулентности возникают на боковых стенках колен в пограничном слое потока, а зависимость энергии от скорости описывается полиномом третьей степени, что согласуется с результатами других авторов. Кроме того, введение логарифмической шкалы для зависимости энергии турбулентности от скорости позволяет линеаризовать эту зависимость и построить тем самым линейную шкалу измерений для диапазона умеренных и больших чисел Рейнольдса. Экспериментальное исследование проведено на проливном стенде в диапазоне расходов до 0,1 кг/с на трубопроводе ДУ50 и температурах 20 и 80 °С, при этом в качестве датчика акустического сигнала использованы пьезопленочные датчики, обладающие равномерной полосой пропускания от единиц герц до мегагерцовых частот. Определены спектральные характеристики сигналов на поверхности трубопровода и, в частности, выявлено, что для поверхностного шума, как и для шума в центре трубопровода, свойственно наличие трех характерных зон спектра, причем первая зона (энергонесущая) является информационной и должна являться объектом измерений. Ширина этой зоны пропорциональна скорости потока и может определяться методами частотного детектирования. Для определения интенсивности энергии шумового сигнала в энергонесущей полосе частот спектра можно использовать квадратичный амплитудный детектор. The article presents the results of numerical and experimental studies, which are aimed at improving the accuracy of non-intrusive measurements of the temperature of a liquid flow in pipelines, which are elements of hydraulic systems of machines and mechanisms. The auxiliary problem of estimating the fluid flow rate by measuring the intensity of noise on the surface of the pipeline is being solved. The noise source in the pipeline is the fluid velocity fluctuations in the turbulent flow, which we perceive as pressure and sound fluctuations, while for high flow velocities the distribution of the average velocity in the pipe cross section is quite uniform and has a logarithmic character, and the total flow temperature is close to the center of the pipe. However, at low and moderate flow rates, the temperature distribution is uneven and the error from the un-evenness can make a significant contribution to the overall measurement error, especially with measurement using relatively accurate resistance thermometers. Therefore, it is necessary to introduce a correction function of the average flow rate and compensate the measurement error due to not-enough flow uniformity, to increase the accuracy of non-intrusive temperature measurements. A reasonable choice is made of a numerical simulation environment suitable for the requirements of this problem: the turbulence energy density in a pipeline with two bends (temperature compensator), the turbulence energy dissipation, the distribution of turbulence energy in the flow cross section at one of the bends were calculated. This allows us to say that the maximum values of the energy density of turbulence arise on the side walls of the pipeline bend in the boundary layer of the flow, and the dependence of energy on speed is described by a polynomial of the third degree, that is consistent with the results of other authors. In addition, the insertion of a logarithmic scale for the dependence of turbulence energy on speed allows to linearize this depen dence and, thus, construct a linear measurement function for the moderate and large Reynolds numbers range. An experimental study was conducted on a flowstand in a flow range of up to 0.1 kg/s with DN50 pipeline and temperatures of 20 and 80 °С. The spectral characteristics of the signals on the pipeline surface were determined. Was revealed that for surface noise, as well as for noise in the center of the pipeline, there are three characteristic spectral zones are characteristic, and the first zone (energy-bearing) is informational and should be the object of measurements. The width of this zone is proportional to the flow rate and can be determined by frequency detection methods. A quadratic amplitude detector can be used to determine the energy intensity of the noise signal in the energy-carrying band of the spectrum