Approximate formula for the ground state energy of anyons in 2D parabolic well

We determine approximate formula for the ground state energy of anyons in 2D parabolic well which is valid for the arbitrary anyonic factor \nu and number of particles N in the system. We assume that centre of mass motion energy is not excluded from the energy of the system. Formula for ground state energy calculated by variational principle contains logarithmic divergence at small distances between two anyons which is regularized by cut-off parameter. By equating this variational formula to the analogous formula of Wu near bosonic limit (\nu ~ 0)we determine the value of the cut-off and thus derive the approximate formula for the ground state energy for the any \nu and N. We checked this formula at \nu=1, when anyons become fermions, for the systems containing two to thirty particles. We find that our approximate formula has an accuracy within 6%. It turns out, at the big number N limit the ground state energy has square root dependence on factor \nu.Comment: 7 page

Моделирование рабочей зоны обработки аксиконов на технологическом оборудовании

Annotation. An analytical expression is obtained for engineering calculation of the regularities of removing the allowance from the flat surface of the part (a rectangle in the form of a flat glass plate of considerable thickness with holes for axicon blanks), which participates in relative and portable movement on the surface of a rotating tool (faceplate) and is in a power circuit with it, which provides automatic self-installation of lapping surfaces. A scheme is proposed for dividing the lapping surfaces of a flat tool and part into ring zones and sectors, resulting in the formation of elementary platforms with reference (calculated) points in their center. Analytical expressions are obtained for calculating the coordinates of these points. The kinematics of the relative movement of the tool and the straightener without oscillation of the upper link is considered, while the sliding of the conjugate surfaces takes place due to rotation of the tool and the straightener installed with a certain eccentricity. An expression is obtained for determining the sliding speed at any point of contact of the conjugate surfaces. Modeling when dealing with relative and portable movement of the upper unit, which allowed obtaining a formula for the slip velocity of the straightener relative to the tool that allows calculation the path of friction in a particular zone in different modes of operation of technological equipment. Modeling can be used as the basis for creating a method for controlling the process of forming conical optical parts (axicons) on serial lever grinding and polishing machines with a flat tool under free lapping conditions, which provide the possibility of obtaining axicons with a deviation of the forming cone from the straightness of no more than ±0.00012 mm.Получено аналитическое выражение для инженерного расчета закономерностей съема припуска с плоской поверхности детали (правильника в виде плоской стеклянной пластины значительной толщины с отверстиями для заготовок аксиконов), которая участвует в относительном и переносном движении по поверхности вращающегося инструмента (планшайбы) и находится с ним в силовом замыкании, обеспечивающем автоматическую самоустановку притирающихся поверхностей. Предложена схема разбиения притирающихся поверхностей плоского инструмента и детали на кольцевые зоны и сектора, в результате чего образуются элементарные площадки с опорными (расчетными) точками в их центре. Для расчета координат данных точек получены аналитические выражения. Рассмотрена кинематика относительного движения инструмента и правильника без осцилляции верхнего звена, при этом скольжение сопряженных поверхностей обусловлено вращением инструмента и правильника, установленных с определенным эксцентриситетом. Получено выражение для определения скорости скольжения в любой точке контакта сопряженных поверхностей. Выполнено моделирование при обработке с относительным и переносным движениями верхнего звена, позволившее получить формулу для скорости скольжения правильника относительно инструмента, что дает возможность рассчитать пути трения в той или иной зоне последнего при различных режимах работы технологического оборудования. Моделирование может быть положено в основу создания методики управления процессом формообразования конических оптических деталей (аксиконов) на серийных рычажных шлифовально-полировальных станках плоским инструментом в условиях свободного притирания, обеспечивающей возможность получения аксиконов с отклонением образующей конуса от прямолинейности не более ±0,00012 мм

Кинематический анализ способа, повышающего точность обработки конических поверхностей

A method for processing high-precision conical surfaces under conditions of free grinding on a lever machine is proposed, which allows adjusting the process parameters taking into account the technological heredity of the workpiece from the point of view of the distribution pattern of the allowance to be removed from its surface. The scheme of implementation of the method in which the main links are a tool in the form of a faceplate and a separator for maintaining the required accuracy of its flatness. In order to develop a method of targeted control of the actuation of the working surface of the tool to maintain the required accuracy of its flatness, mathematical modeling of the motion patterns of the links of the actuator of the base machine, on which the proposed device for processing conical parts is installed, was performed. In the process of mathematical simulation structural analysis of the executive mechanism of the lever machine is carried out, connection between the generalized coordinate and provisions of links of the executive mechanism of the lever machine is established, position of the lever and the upper link in the vertical plane is probed, geometrical parameters of reflexive rotational motion of the upper link are considered, the ratio for calculation of length of a crank of the executive mechanism of the machine depending on amplitude of figurative movement of its output link is obtained. An analytical relationship has been established between the input and output links of the machine actuator, which makes it possible to calculate the length of the first of the marked links depending on the required amplitude of the oscillatory motion of the second of them and creates the prerequisites for the development of engineering methods for controlling the process of forming high-precision conical surfaces under conditions of free grinding.Предложен способ получения высокоточных конических поверхностей в условиях свободного притирания, позволяющий регулировать параметры процесса обработки конической детали в зависимости от распределения подлежащего удалению припуска с ее поверхности. Приведена схема реализации способа, в которой основными звеньями являются инструмент с плоской рабочей поверхностью и правильник в виде стеклянной пластины, предназначенный для поддержания необходимой точности обрабатывающей поверхности инструмента. Для разработки методики управления срабатыванием рабочей поверхности инструмента с целью обеспечения необходимой точности ее плоскостности выполнен анализ закономерностей движения звеньев исполнительного механизма базового станка, на котором устанавливается предлагаемое устройство для обработки конических деталей. Рассмотрена структура исполнительного механизма рычажного станка, установлена связь между обобщенной координатой и положениями звеньев этого механизма в процессе обработки с учетом возвратно-вращательного движения деталей относительно инструмента в условиях свободного притирания, исследовано положение рычага и верхнего звена в вертикальной плоскости, рассмотрены геометрические параметры колебательного перемещения верхнего звена. Получено соотношение для расчета длины кривошипа исполнительного механизма станка в зависимости от амплитуды переносного движения его выходного звена. Установлена аналитическая связь между входным и выходным звеньями исполнительного механизма станка, что дает возможность рассчитать длину первого из отмеченных звеньев в зависимости от требуемой величины амплитуды колебательного движения второго из них и создает предпосылки для разработки инженерных методов управления процессом формообразования высокоточных конических поверхностей в условиях свободного притирания

Root morphology and phosphorus uptake by potato cultivars grown under deficient and sufficient phosphorus supply

Information regarding the characteristics that affect P-uptake capacity may assist in the selection of more adapted potato (Solanum tuberosum L.) cultivars and more adequate fertilization management for each cultivar. This study evaluated the P-uptake capacity of potato cultivars (Agata, Asterix, Atlantic, Markies, and Mondial) grown under P-deficient (2 mg L-1) or P-sufficient (31 mg L-1) conditions in nutrient solution and related it to physiological parameters of uptake and morphological root characteristics. When the plants were 24 days old, they were subjected to a P-uptake kinetics study. The length and surface area of roots and the uptake kinetic parameters (I-max, K-m, and C-min) varied among potato cultivars. Phosphorus-deficient potato plants had an approximately 60% smaller root surface area and an increase of 86% in the I-max and net P influx compared with the plants in P-sufficient conditions. However, these modifications in P uptake kinetics can do not influence P acquisition in the soil environment due to very limited P diffusion. The amount of P accumulated by plants grown under P-deficient conditions was directly related to the root length and surface area; a greater root surface, as demonstrated by the Asterix cultivar, is the most important factor for achieving a greater P-uptake capacity. Under P-sufficient conditions, potato cultivars such as Markies and Mondial showed a balance between morphological root characteristics (medium/large length and surface area) and physiological parameters (medium/high I-max values and net P influx) and had a greater P-uptake capacity. However, under field conditions, the responses to P deficiency may be different due to the very limited diffusion of P in the soil and because plants can use additional mechanisms to improve their P uptake from the soil. (C) 2014 Elsevier B.V. All rights reserved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Antibacterial activity of propolis collected in different regions of Brazil

The aim of this study was to investigate the antibacterial activity of propolis samples from Goiás, Paraná and São Paulo States, Brazil, and their flavonoids content. Ethanolic extracts of propolis (EEP) were prepared (30g of propolis in 70% ethanol), and the microorganisms Staphylococcus aureus and Escherichia coli were tested. The methodology employed was agar diffusion using filter paper discs. Ampicillin and tetracycline were used as controls. Antibacterial activity was determined by the reading of inhibition zone diameters (mm) after 24 hours incubation at 37°C. Results demonstrated that EEP inhibited the growth of Staphylococcus aureus but not that of Escherichia coli. Tetracycline and ampicillin showed an efficient action against both bacteria. Flavonoids content was variable, depending on the propolis sample. According to the results, it may be concluded that EEP showed effective action against Gram-positive bacteria, independently on their geographic origin, and a positive correlation between antibacterial activity and flavonoids content

Cyclic polyacetylene

Here we demonstrate the synthesis of cyclic polyacetylene (c-PA), or [∞]annulene, via homogeneous tungsten-catalysed polymerization of acetylene. Unique to the cyclic structure and evidence for its topology, the c-PA contains >99% trans double bonds, even when synthesized at −94 °C. High activity with low catalyst loadings allows for the synthesis of temporarily soluble c-PA, thus opening the opportunity to derivatize the polymer in solution. Absolute evidence for the cyclic topology comes from atomic force microscopy images of bottlebrush derivatives generated from soluble c-PA. Now available in its cyclic form, initial characterization studies are presented to elucidate the topological differences compared with traditionally synthesized linear polyacetylene. One advantage to the synthesis of c-PA is the direct synthesis of the trans–transoid isomer. Low defect concentrations, low soliton concentration, and relatively high conjugation lengths are characteristics of c-PA. Efficient catalysis permits the rapid synthesis of lustrous flexible thin films of c-PA, and when doped with I2, they are highly conductive (398 (±76) Ω−1 cm−1). [Figure not available: see fulltext.