Fomenko-Mischenko Theory, Hessenberg Varieties, and Polarizations

The symmetric algebra g (denoted S(\g)) over a Lie algebra \g (frak g) has the structure of a Poisson algebra. Assume \g is complex semi-simple. Then results of Fomenko- Mischenko (translation of invariants) and A.Tarasev construct a polynomial subalgebra \cal H = \bf C[q_1,...,q_b] of S(\g) which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of \g. Let G be the adjoint group of \g and let \ell = rank \g. Identify \g with its dual so that any G-orbit O in \g has the structure (KKS) of a symplectic manifold and S(\g) can be identified with the affine algebra of \g. An element x \in \g is strongly regular if \{(dq_i)_x\}, i=1,...,b, are linearly independent. Then the set \g^{sreg} of all strongly regular elements is Zariski open and dense in \g, and also \g^{sreg \subset \g^{reg} where \g^{reg} is the set of all regular elements in \g. A Hessenberg variety is the b-dimensional affine plane in \g, obtained by translating a Borel subalgebra by a suitable principal nilpotent element. This variety was introduced in [K2]. Defining Hess to be a particular Hessenberg variety, Tarasev has shown that Hess \subset \g^sreg. Let R be the set of all regular G-orbits in \g. Thus if O \in R, then O is a symplectic manifold of dim 2n where n= b-\ell. For any O\in R let O^{sreg} = \g^{sreg}\cap O. We show that O^{sreg} is Zariski open and dense in O so that O^{sreg} is again a symplectic manifold of dim 2n. For any O \in R let Hess (O) = Hess \cap O. We prove that Hess(O) is a Lagrangian submanifold of O^{sreg} and Hess =\sqcup_{O \in R} Hess(O). The main result here shows that there exists, simultaneously over all O \in R, an explicit polarization (i.e., a "fibration" by Lagrangian submanifolds) of O^{sreg} which makes O^{sreg} simulate, in some sense, the cotangent bundle of Hess(O).Comment: 36 pages, plain te

On the feasibility of iron or chromium substitution for aluminium in the Al13-Keggin ion

Al-27 NMR measurements in the liquid and the solid state supplemented with chemical analysis of the mixed salts; unambiguously reveal that neither tetrahedral nor octahedral aluminium can be substituted by either iron or chromium in Al-13-Keggin ion salts prepared by conventional methods

Movement patterns and athletic performance of leopards in the Okavango Delta

Although leopards are the most widespread of all the big cats and are known for their adaptability, they are elusive and little is known in detail about their movement and hunting energetics. We used high-resolution GPS/IMU (inertial measurement unit) collars to record position, activity and the first high-speed movement data on four male leopards in the Okavango Delta, an area with high habitat diversity and habitat fragmentation. Leopards in this study were generally active and conducted more runs during the night, with peaks in activity and number of runs in the morning and evening twilight. Runs were generally short (less than 100 m) and relatively slow (maximum speed 5.3 m s−1, mean of individual medians) compared to other large predators. Average daily travel distance was 11 km and maximum daily travel distance was 29 km. No direct correlation was found between average daily temperature and travel distance or between season and travel distance. Total daily energy requirements based on locomotor cost and basal metabolic rate varied little between individuals and over time. This study provides novel insights into movement patterns and athletic performance of leopards through quantitative high-resolution measurement of the locomotor, energetic, spatial and temporal movement characteristics. The results are unbiased by methodological and observational limitations characteristic of previous studies and demonstrate the utility of applying new technologies to field studies of elusive nocturnal species

Capturing the "Whole Tale" of Computational Research: Reproducibility in Computing Environments

We present an overview of the recently funded "Merging Science and Cyberinfrastructure Pathways: The Whole Tale" project (NSF award #1541450). Our approach has two nested goals: 1) deliver an environment that enables researchers to create a complete narrative of the research process including exposure of the data-to-publication lifecycle, and 2) systematically and persistently link research publications to their associated digital scholarly objects such as the data, code, and workflows. To enable this, Whole Tale will create an environment where researchers can collaborate on data, workspaces, and workflows and then publish them for future adoption or modification. Published data and applications will be consumed either directly by users using the Whole Tale environment or can be integrated into existing or future domain Science Gateways

Ideal MHD theory of low-frequency Alfven waves in the H-1 Heliac

A part analytical, part numerical ideal MHD analysis of low-frequency Alfven wave physics in the H-1 stellarator is given. The three-dimensional, compressible ideal spectrum for H-1 is presented and it is found that despite the low beta (approx. 10^-4) of H-1 plasmas, significant Alfven-acoustic interactions occur at low frequencies. Several quasi-discrete modes are found with the three-dimensional linearised ideal MHD eigenmode solver CAS3D, including beta-induced Alfven eigenmode (BAE)- type modes in beta-induced gaps. The strongly shaped, low-aspect ratio magnetic geometry of H-1 causes CAS3D convergence difficulties requiring the inclusion of many Fourier harmonics for the parallel component of the fluid displacement eigenvector even for shear wave motions. The highest beta-induced gap reproduces large parts of the observed configurational frequency dependencies in the presence of hollow temperature profiles

Модернизация теплообменных аппаратов различной производительности на основе численного моделирования

Выпускная квалификационная работа 104 с., 49 рис., 10 табл., 20 источников, 3 прил. Ключевые слова: математическое моделирование, теплообменник, топливный газ, интенсификаторы теплообмена, принудительная конвекция, турбулентность, расчетная сетка, присоединительный вихрь, тепловой поток, геометрическая модель. Объектом исследования является теплообменный аппарат, применяемый для нагрева топливного газа перед подачей его на горелочные устройства. Цель работы - исследование интенсифицированного теплообмена при турбулентном течении теплоносителя в прямых круглых трубах с итенсификаторами теплообмена и анализ эффективности различных турбулизаторов.Final qualifying work 104 p., 49 fig., 10 tab., 20 sources, 3 application. Keywords: mathematical modeling, heat exchanger, fuel gas, to vary the heat transfer, forced convection, turbulence, computational grid, connecting a whirlwind, heat flow, the geometric model. The object of research is the heat exchanger that is used to heat the fuel gas before it is fed to the burners. Objective - research intensified heat exchange in turbulent flow of coolant in straight circular pipes with itensifikatorami heat exchange and analysis of the effectiveness of different turbulence. The study was carried out mathematical modeling of the object of study with the use of ANSYS package applications, analysis of the results and evaluation of the effectiveness of different types of turbulence

Syringomyelia: A review of the biomechanics

Syringomyelia is a neurological disorder caused by the development of one or more macroscopic fluid-filled cavities in the spinal cord. While the aetiology remains uncertain, hydrodynamics appear to play a role. This has led to the involvement of engineers, who have modelled the system in silico and on the bench. In the process, hypotheses from the neurosurgical literature have been tested, and others generated, while aspects of the system mechanics have been clarified. The spinal cord is surrounded by cerebrospinal fluid (CSF) which is subject both to the periodic excitation of CSF expelled from the head with each heartbeat, and to intermittent larger transients from cough, sneeze, etc., via vertebral veins. The resulting pulsatile flow and pressure wave propagation, and their possible effects on cord cavities and cord stresses, have been elucidated. These engineering contributions are here reviewed for the first time

Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points

In this paper, we derive the virtual structure constants used in mirror computation of degree k hypersurface in CP^{N-1}, by using localization computation applied to moduli space of polynomial maps from CP^{1} to CP^{N-1} with two marked points. We also apply this technique to non-nef local geometry O(1)+O(-3)->CP^{1} and realize mirror computation without using Birkhoff factorization.Comment: 10 pages, latex, a minor change in Section 4, English is refined, Some typing errors in Section 3 are correcte