Towards Rigorous Derivation of Quantum Kinetic Equations

We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and by the Cauchy problem of the generalized quantum kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is established in the space of trace class operators. The links of the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.Comment: 25 page

The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear equations is constructed in the form of an expansion over particle clusters whose evolution is described by the corresponding order cumulant (semi-invariant) of evolution operators for the von Neumann equations. For the initial data from the space of sequences of trace class operators the existence of a strong and a weak solution of the Cauchy problem is proved. We discuss the relationships of this solution both with the $s$-particle statistical operators, which are solutions of the BBGKY hierarchy, and with the $s$-particle correlation operators of quantum systems.Comment: 26 page

Bis(dihydrogen norfloxacinium) tri-μ2-chlorido-bis­[trichloridobismuthate(III)] chloride dihydrate

The title compound, {systematic name: (3-carb­oxy-1-ethyl-6-fluoro-7-piperazin-4-ium-1-yl-1H-quinolin-4-yl­idene)oxonium tri-μ2-chlorido-bis­[trichloridobismuthate(III)] chloride dihydrate], (C16H20FN3O3)2[Bi2Cl9]Cl·2H2O, is composed of [Bi2Cl9]3− anions lying on crystallographic twofold rotation axes, Cl− anions also on twofold axes, C16H20FN3O3 2+ cations, and water mol­ecules. The BiIII coordination polyhedron is a distorted octa­hedron and two such octa­hedra share a triangular face to form the complex anion. There are three short terminal Bi—Cl bonds [2.5471 (6)–2.5781(5 Å] and three longer bridging bonds [2.8599 (5)–2.9984 (6) Å] in each octa­hedron. Anions, cations and water mol­ecules are linked by hydrogen bonds to form a three-dimensional network. There are also π–π stacking inter­actions between quinoline ring systems, with an inter­planar distance of 3.27 (1) Å

Tetra­potassium dianti­mony(III) tin(IV) tetra­deca­fluoride

The title compound, K4Sb2SnF14, is built from anionic layers, with an overall composition of [Sb2SnF14]4− extending parallel to the ac plane, and K+ cations. The layers are made up from vertex-sharing centrosymmetric SnF6 octa­hedra and Sb2F12 dimers. The Sn—F distances are in the range 1.9581 (14)–1.9611 (17) Å. The Sb polyhedra contain three short terminal Sb—F bonds [1.9380 (14)–2.0696 (15) Å], one short bridging bond [2.0609 (17) Å], one bridging bond of medium length [2.7516 (15) Å], and two longer bridging bonds [3.0471 (18) and 3.117 (2) Å]. The K+ ions are coordinated by F atoms with coordination numbers 10 and 8, and K—F bond lengths are in the range 2.6235 (16)–3.122 (2) Å

The efficiency of using case-method for training staff of the higher qualification

В статье отмечено значение применения кейс-технологий для подготовки инженерных кадров высшей квалификации. Обозначено, что кейсовые чемпионаты являются эффективным инструментом для передачи будущим специалистам-инженерам практических знаний, опыта и новых компетенций. Приведены доказательства, что метод с использованием кейсов, имеет актуальность, эффективность и востребованность по сравнению с традиционными методами обучения, так как реализует главные образовательные аспекты: практическую направленность, интерактивный формат и конкретные навыки.The article notes the importance of using case technologies for the training of highly qualified engineering personnel. It is indicated that case championships are an effective tool for transferring practical knowledge, experience and new competencies to future engineers. Evidence is given that the method using cases is relevant, effective and in demand in comparison with traditional teaching methods, as it implements the main educational aspects: practical orientation, interactive format and Soft skills

Lab-Scale Study of the Calcium Carbonate Dissolution and Deposition by Marine Cyanobacterium Phormidium subcapitatum

Suggestions that calcification in marine organisms changes in response to global variations in seawater chemistry continue to be advanced (Wilkinson, 1979; Degens et al. 1985; Kazmierczak et al. 1986; R. Riding 1992). However, the effect of [Na+] on calcification in marine cyanobacteria has not been discussed in detail although [Na+] fluctuations reflect both temperature and sea-level fluctuations. The goal of these lab-scale studies therefore was to study the effect of environmental pH and [Na+] on CaCO3 deposition and dissolution by marine cyanobacterium Phormidium subcapitatum. Marine cyanobacterium P. subcapitatum has been cultivated in ASN-III medium. [Ca2+] fluctuations were monitored with Ca(2+) probe. Na(+) concentrations were determined by the initial solution chemistry. It was found that the balance between CaCO3 dissolution and precipitation induced by P. subcapitatum grown in neutral ASN III medium is very close to zero. No CaCO3 precipitation induced by cyanobacterial growth occurred. Growth of P. subcapitatum in alkaline ASN III medium, however, was accompanied by significant oscillations in free Ca(2+) concentration within a Na(+) concentration range of 50-400 mM. Calcium carbonate precipitation occurred during the log phase of P. subcapitatum growth while carbonate dissolution was typical for the stationary phase of P. subcapitatum growth. The highest CaCO3 deposition was observed in the range of Na(+) concentrations between 200-400 mM. Alkaline pH also induced the clamping of P. subcapitatum filaments, which appeared to have a strong affinity to envelop particles of chemically deposited CaCO3 followed by enlargement of those particles size. EDS analysis revealed the presence of Mg-rich carbonate (or magnesium calcite) in the solution containing 10-100 mM Na(+); calcite in the solution containing 200 mM Na(+); and aragonite in the solution containing with 400 mM Na(+). Typical present-day seawater contains xxmM Na(+). Early (Archean) seawater was likely less saline. The division of marine cyanobacterium P. subcapitatum is associated with periodic deposition and dissolution of CaCO3, the rhythms and intensity of which are dependent on concentrations of both OH(-) and Na(+). Thus, the role of present-day marine cyanobacteria in the global carbonate cycle might be reduced to aggregation and recrystallization of available CaCO3 particles in marine water rather than long-term precipitation and accumulation of CaCO3 deposits. For lower Na(+) concentrations, precipitation of carbonates by cyanobacteria would be even less significant. These results suggest that the lack of calcified cyanobacteria in stromatalite-bearing Precambrian sequences can be explained not only by high dissolved inorganic carbon concentrations but also by lower salinity, as well as possible lower pH compared to present-day oceans

ВЫДЕЛЕНИЕ ИЗ ПРОДУКТОВ ОБОГАЩЕНИЯ РОССЫПЕЙ ШЛИХОВОГО ЗОЛОТА МЕТОДОМ МАГНИТОЖИДКОСТНОЙ СЕПАРАЦИИ

The process of separation in a ferrofluid is recommended for gold separation from placer beneficiation products. The process of magnetic fluid separation is based on the ponderomotive force of the inhomogeneous magnetic field appeared in ferrofluids in addition to the pushing gravity force. The horizontal component of this force in a separation medium participates in the movement of bodies along an equipotential surface across the working area – to the separation cell walls and towards the central plane of the pole gap, and the longitudinal component participates in the movement along the working area. In order to improve the technological parameters of the process, it is recommended to limit the transverse displacements of the bodies by vertical partitions installed in the separation medium along the separator pole gap. The theoretical study results regarding particle motion in the separator working area suggest that the wall effect is manifested in the appearance of a flow opposite to the direction of particle motion. This increases the hydrodynamic drag force and reduces the speed of particle movement. It is shown that the decrease in the time of light concentrate fraction presence in the separator working area with vertical walls promotes an increase in the productivity of the process with respect to the initial feed and heavy fraction productivity (gold extraction into the heavy fraction). The mathematical methods of experimental design were used to perform investigation tests of competing methods of separation on artificial mineral mixtures and heavy gold-bearing concentrates isolated from placer sands. It has been proved that the transition from ferrofluid volume separation to separation using the developed method increases the unit productivity by 9 %, and the gold extraction into the heavy fraction from 84,34 to 91,77 % due to light fraction losses reduced from 15,46 to 7,96 %. Heavy fraction yield lowered by 11,6 rel.% made it possible to obtain a material containing over 800 kg per ton of gold.Для выделения золота из продуктов обогащения россыпей рекомендуется процесс сепарации в ферромагнитной жидкости (ФМЖ). Процесс магнитожидкостной сепарации основан на появлении в ФМЖ дополнительной к гравитационной выталкивающей силе пондеромоторной силы неоднородного магнитного поля. В объеме среды разделения горизонтальная составляющая этой силы участвует в перемещении тел по эквипотенциальной поверхности поперек рабочей зоны – к стенкам сепарационной кюветы и в сторону центральной плоскости межполюсного зазора, а продольная составляющая – вдоль. С целью повышения технологических показателей процесса рекомендуется ограничить поперечные перемещения тел вертикальными перегородками, установленными в среде разделения вдоль межполюсного зазора сепаратора. Из результатов теоретического исследования движения частиц в рабочей зоне сепаратора следует, что влияние стенок проявляется в возникновении встречного направлению движения частиц потока, который является причиной роста гидродинамической силы сопротивления и снижения скорости движения частиц. Показано, что при наличии вертикальных стенок уменьшение времени нахождения легкой фракции шлиха в рабочей зоне сепаратора способствует росту производительности процесса по исходному питанию и производительности по тяжелой фракции (извлечению золота в тяжелую фракцию). С использованием методов математического планирования эксперимента выполнены исследовательские испытания конкурирующих способов сепарации на искусственных смесях минералов и на тяжелых золотосодержащих шлихах, выделенных из песков россыпи. Доказано, что при переходе от сепарации в объеме ФМЖ к сепарации разработанным способом производительность аппарата увеличивается на 9 %, а извлечение золота в тяжелую фракцию – с 84,34 до 91,77 % за счет уменьшения потерь с легкой фракцией с 15,46 до 7,96 %. При снижении выхода тяжелой фракции на 11,6 отн.% получен материал, содержащий более 800 кг/т золота

Комбинированная гравитационно-флотационная технология обогащения техногенных россыпей золота

Gold recovery from placer washing waste was carried out using a flotation method where circulating rough concentrate is used to increase the recovered metal content in the rougher flotation operation. Moreover, flotation is carried out with a mixture of air with hot steam. Pressure in bubbles drops and their sizes decrease as a result of vapor condensation at the first moment of time under conditions of vapor-air flotation. Heat exchange between the phases worsens when the bubble is compressed, and mass transfer stops at the minimum bubble size, while temperature and vapor pressure in the bubble reach their maximum. As the bubble grows in size, superheated steam becomes saturated and pressure in the bubble decreases resulting in resumed condensation. The bubble surface undergoes damped oscillations. When the bubble surface vibrates, the motion of a slowly developing concentration-capillary Marangoni flow to the center of the interphase film cannot compensate for its thinning by the counter thermocapillary flow with a high hydrodynamic stability potential from the film center to its periphery. The vapor-air flotation results obtained can be interpreted in the context of this mechanism of wetting film stability changes during the vapor-liquid phase transition. Pilot tests of gravity and gravity-flotation technologies for gold extraction from a technogenic placer of gold have been carried out. It has been proved that the main effect of using the developed configuration of the scheme and the mode of flotation with a vapor-air mixture is a decrease in the concentrate yield by ~ 25% rel. while maintaining the achieved level of recovery and concentrate quality. When using the combined technology, the added value of marketable products provides an increase in the value of net discounted income and the return on investment index, and a decrease in their payback period.При извлечении золота из отходов промывки россыпей использован способ флотации, при котором для повышения содержания извлекаемого металла в операции основной флотации используют оборотный черновой концентрат. Причем флотацию выполняют смесью воздуха с горячим водяным паром. В условиях паровоздушной флотации в первый момент времени в результате конденсации пара давление в пузырьках падает и их размер уменьшается. При сжатии пузырька теплообмен между фазами ухудшается, и при минимальном размере пузырька массообмен прекращается, а температура и давление пара в пузырьке достигают своего максимума. С ростом размера пузырька перегретый пар становится насыщенным, и давление в пузырьке уменьшается, что ведет к возобновлению конденсации. Поверхность пузырька совершает затухающие колебания. При этом движение медленно развивающегося концентрационно-капиллярного потока Марангони к центру межфазной пленки не может компенсировать ее утончение встречным термокапиллярным потоком с большим потенциалом гидродинамической устойчивости от центра к периферии пленки. Полученные результаты флотации паровоздушной смесью могут быть интерпретированы в рамках этого механизма изменения устойчивости смачивающих пленок при фазовом переходе пар–жидкость. В работе проведены опытно-промышленные испытания гравитационной и гравитационно-флотационной технологий извлечения золота из его техногенной россыпи. Доказано, что основным эффектом от применения разработанной конфигурации схемы и режима флотации паровоздушной смесью является уменьшение выхода концентрата на ~25 % при сохранении достигнутого уровня извлечения и качества концентрата. При использовании комбинированной технологии добавленная стоимость товарной продукции обеспечивает повышение величины чистого дисконтированного дохода и индекса рентабельности инвестиций, а также снижение срока их окупаемости

КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ ТЕРМООБРАБОТКИ В БАРАБАННОЙ ВРАЩАЮЩЕЙСЯ ПЕЧИ

Algorithms for the calculation of convective exchange coefficients and construction of zonal heat balance equations for computer modeling of calcination of carbon-base materials in a rotary-drum furnace are developed. The possibility to find adequate results in the course of the computing experimental investigation into this process using its complex mathematical model implemented as a computer program is shown.Разработаны алгоритмы расчета коэффициентов конвективного обмена и построения зональных уравнений теплового баланса для компьютерного моделирования процесса прокалки углеродных материалов в барабанной вращающейся печи. Показана возможность получения адекватных результатов при вычислительном экспериментальном исследовании этого процесса с использованием его комплексной математической модели, реализованной в виде компьютерной программы

A single-mode quantum transport in serial-structure geometric scatterers

We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit $N\to\infty$. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. A detailed discussion is presented for a finite-periodic "comb"; we show how the resonance poles can be computed within the Krein formula approach. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart of the resonances coming from the decoupled-surface eigenvalues such scatterers exhibit the high-energy behavior typical for the delta' interaction for the physically interesting couplings.Comment: 36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg figures attache