Pole Boundary Research Articles

Inflationary α-attractor from type-IIB/F theory

We derive an potential of slow-roll inflation in the warped D brane set-up featuring three intersecting D7 branes under type of CY 3-compactification within type-IIB/F theory with some near-conifold regions. The underlying quadratic structure of the kinetic poles is found to arise from a correction in the Kähler potential when an extra contribution of open string moduli is turned on. While the closed string sector of the moduli spectrum is completely stabilized via quantum corrections of perturbative and non-perturbative origin, the open string sector plays the lead role in driving the inflationary expansion in the radial direction. A generic asymptotic behaviour of the inflaton field near the pole boundaries manifests itself as the slow-roll plateau in canonical field space, which becomes responsible for giving universal predictions of the cosmological parameters. We find that the presence of the open strings near conifold regions brings the realization of pole inflation in the present set-up. Finally we compare our results with similar models and discuss the importance of exploring precise values of α in the light of ongoing and forthcoming cosmological surveys.

Scenario for the formation of vortexlike structures in a presubstorm arc, taking into account changes in the arc height during its evolution

Activity in a prebreakup auroral arc in the form of vortexlike structures, the appearance/disappearance of which is preceded by an increase/decrease in the brightness of the arc, was studied in the context of a magnetospheric substorm, large-scale ionospheric convection, the situation in the interplanetary medium, and triangulation measurements of the arc height. The structures are observed in the premidnight hours and represent a superposition of two auroral forms: a large-scale bend in the arc that outlines the polar boundary of the diffuse auroras and smaller luminous tongues of luminosity (mini-torches) elongated along the convection on the western slope of the bends. The structures as a whole move against convection, towards substorm activity to the east of the observation area. We attribute the appearance of structures to the propagation of a disturbance deep into the magnetosphere, generated as a result of interaction of the magnetopause with a solar wind inhomogeneity, on the front of which Bz turns southward. The results of triangulation measurements show that the increase in brightness in the prebreakup arc shortly before the appearance of vortexlike structures is accompanied by a decrease in the height of the lower edge of the arc, which we explain by the appearance of a parallel electric field above the arc, which accelerates the precipitating electrons. The role of such a field in the formation of the torchlike structures is discussed in the framework of the interchange instability of the pole boundary of diffuse auroras.

Algebras, traces, and boundary correlators in mathcal{N} = 4 SYM

We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d mathcal{N} = 4 super Yang-Mills with the gauge group G, which are described by associative algebras equipped with twisted traces. Such data are in one-to-one correspondence with an infinite set of defect correlation functions. We identify algebras and traces for known boundary conditions. Ward identities expressing the (twisted) periodicity of the trace highly constrain its structure, in many cases allowing for the complete solution. Our main examples in this paper are: the universal enveloping algebra Uleft(mathfrak{g}right) with the trace describing the Dirichlet boundary conditions; and the finite W-algebra mathcal{W}left(mathfrak{g},{t}_{+}right) with the trace describing the Nahm pole boundary conditions.

INCREASE IN THE ELECTROMAGNETIC MOMENT OF A SUPERMINIATURE ELECTRIC MOTOR EXCITED BY RARE EARTH PERMANENT MAGNETS

The article is devoted to improving the energy and performance characteristics of superminiature electric motors, which are widely used in modern devices of robotics and mechanotronics. With the development of digital and Autonomous robotic systems, the tasks of improving the efficiency of Executive micromechanisms that affect the functionality and duration of work in offline mode have become particularly relevant. Traditional design and technological solutions used in higher-power electric machines are not scalable to the field of superminiature electric machines. Domestic and foreign developers offer various design options and manufacturing technologies. The key design feature of the electric motor under consideration is a glass stator made by polycapillary fiber technology and an excitation system from rare-earth permanent magnets. In the wall of the glass case, holes are evenly distributed around the circumference, in which the control winding is laid. The motor excitation system is a two-pole permanent magnet located on the rotating rotor shaft. The purpose of the research is to determine the effect of changing the design of the excitation system by changing the location of the magnetic poles. The research uses software that simulates the electromagnetic field using the finite element method. In the course of research, it was found that a decrease in the body of a permanent magnet leads to a decrease in the electromagnetic moment, which is not compensated by a decrease in edge effects at the boundary of the poles of the magnet. However, an increase in the value of the maximum magnetic induction in the air gap allows us to conclude that edge effects at the pole boundary have a significant effect on reducing the energy characteristics of superminiature micromachines. Thus, the solutions proposed in this paper are not sufficient to increase the efficiency of the engine, but the data obtained indicate the need to reduce the edge effects of permanent magnets.

The extended Bogomolny equations with generalized Nahm pole boundary conditions, II

We develop a Kobayashi-Hitchin correspondence for the extended Bogomolny equations, i.e., the dimensionally reduced Kapustin-Witten equations, on the product of a compact Riemann surface $\Sigma$ with ${\mathbb R}^+_y$, with generalized Nahm pole boundary conditions at $y=0$. The correspondence is between solutions of these equations satisfying these singular boundary conditions and also limiting to flat connections as $y \to \infty$, and certain holomorphic data consisting of effective triplets $(\mathcal E, \varphi, L)$ where $(\mathcal E, \varphi)$ is a stable $\mathrm{SL}(n+1,\mathbb C)$ Higgs pair and $L \subset \mathcal E$ is a holomorphic line bundle. This corroborates a prediction of Gaiotto and Witten, and is an extension of our earlier paper \cite{HeMazzeo2017} which treats only the $\mathrm{SL}(2,\mathbb R)$ case.

The extended Bogomolny equations and generalized Nahm pole boundary condition

In this paper we develop a Kobayashi-Hitchin type correspondence between solutions of the extended Bogomolny equations on $\Sigma\times \RP$ with Nahm pole singularity at $\Sigma \times \{0\}$ and the Hitchin component of the stable $SL(2,\mathbb{R})$ Higgs bundle; this verifies a conjecture of Gaiotto and Witten. We also develop a partial Kobayashi-Hitchin correspondence for solutions with a knot singularity in this program, corresponding to the non-Hitchin components in the moduli space of stable $SL(2,\mathbb{R})$ Higgs bundles. We also prove existence and uniqueness of solutions with knot singularities on $\mathbb{C}\ti\RP$.

Energy Bound for Kapustin–Witten Solutions on S3 × ℝ+

AbstractWe show that for solutions of Kapustin–Witten equation with Nahm pole boundary condition on $S^{3}\times \mathbb{R}^{+}$, there exists a universal constant bound on its Yang–Mills energy $\|F_{A}\|_{L^{2}}$.

Four-dimensional mathcal{N} = 2 supersymmetric theory with boundary as a two-dimensional complex Toda theory

We perform a series of dimensional reductions of the 6d, mathcal{N} = (2, 0) SCFT on S2 × Σ × I × S1 down to 2d on Σ. The reductions are performed in three steps: (i) a reduction on S1 (accompanied by a topological twist along Σ) leading to a supersymmetric Yang-Mills theory on S2 × Σ × I, (ii) a further reduction on S2 resulting in a complex Chern-Simons theory defined on Σ × I, with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of S2 and S1, and (iii) a final reduction to the boundary modes of complex Chern-Simons theory with the Nahm pole boundary condition at both ends of the interval I, which gives rise to a complex Toda CFT on the Riemann surface Σ. As the reduction of the 6d theory on Σ would give rise to an mathcal{N} = 2 supersymmetric theory on S2 × I × S1, our results imply a 4d-2d duality between four-dimensional mathcal{N} = 2 supersymmetric theory with boundary and two-dimensional complex Toda theory.

An equivalent boundary model for effects of adjacent spans on wind reliability of wood utility poles in overhead distribution lines

Overhead distribution lines in the United States are primarily supported by wood poles. These utility poles are vulnerable to high wind loads from hurricanes which has resulted in a large number of power outages during past hurricanes, especially in coastal areas. Risk management of distribution systems requires development of distribution line models to reliably assess their performance under hurricanes. However, modeling the entire distribution line is not practically feasible as they are very long and consist of a large number of spans. The present study proposes analytical models to capture boundary effects of adjacent spans on the wind response of the pole of interest via equivalent springs and wind-induced forces. The stiffness of conductors (cables) is derived through a simplified solution that considers the shape of the conductors under lateral static gust wind and gravity loadings; this model is shown to be very accurate when compared to the exact analytical as well as Finite Element solutions. Deterministic and probabilistic studies are performed to assess the impact of boundary conditions on the performance of the poles; results indicate that pole boundaries may have a considerable impact on the estimates of failure probabilities especially when the extent of difference in the properties of adjacent spans is not negligible. Specifically, neglecting boundary effects from neighboring spans may result in underestimation of failure probabilities of stronger poles and overestimation of failure probabilities of weaker poles as load sharing effects among the poles are not considered. The proposed boundary model enables more reliable hurricane risk assessment of power distribution systems to effectively manage the risk of outages.

A Numerical Test of Padé Approximation for Some Functions with Singularity

The aim of this study is to examine some numerical tests of Padé approximation for some typical functions with singularities such as simple pole, essential singularity, brunch cut, and natural boundary. As pointed out by Baker, it was shown that the simple pole and the essential singularity can be characterized by the poles of the Padé approximation. However, it was not fully clear how the Padé approximation works for the functions with the branch cut or the natural boundary. In the present paper, it is shown that the poles and zeros of the Padé approximated functions are alternately lined along the branch cut if the test function has branch cut, and poles are also distributed around the natural boundary for some lacunary power series and random power series which rigorously have a natural boundary on the unit circle. On the other hand, Froissart doublets due to numerical errors and/or external noise also appear around the unit circle in the Padé approximation. It is also shown that the residue calculus for the Padé approximated functions can be used to confirm the numerical accuracy of the Padé approximation and quasianalyticity of the random power series.

Investigating the photo-oxidative and heterogeneous chemical production of HCHO in the snowpack at the South Pole, Antarctica

Environmental context Snowpacks present a surprisingly active environment for photochemistry, leading to sunlight-induced oxidation of deposited organic matter and the subsequent emission of a variety of photochemically active trace gases. We seek to address questions regarding the ultimate fate of organic matter deposited onto snow in the remote regions of the world. The work is relevant to atmospheric composition and climate change. Abstract We investigate snowpack fluxes of formaldehyde (HCHO) into the South Pole boundary layer using steady-state photochemical models. We study two chemical sources of HCHO within the snowpack. First, we study chemical production of HCHO from the processing of methyl hydroperoxide (CH3OOH): photolysis, reaction with the hydroxyl radical (OH•), and by an acid catalysed rearrangement. Assuming surface layer concentration effects for acidic solutes, we show that the acid catalysed production of HCHO within ice could contribute a non-negligible source to the snowpack HCHO budget. This novel source of HCHO complements existing explanations of HCHO fluxes based on physical emission of HCHO from snow. Secondly, we investigate HCHO production from the oxidation of organic matter (OM) by OH• within snow to explain observed fluxes of photochemical origin from the South Pole snowpack. This work shows that laboratory-derived photochemical production rates of HCHO and our standard model are inconsistent with field observations, which has implications for the distribution of OM relative to oxidants within ice particles. We resolve this inconsistency using new laboratory measurements of the molecular dynamics of the OH• photofragment from hydrogen peroxide (H2O2) and nitrate (NO3–) photolysis, which show that only OH produced in the outermost monolayers can contribute to gas phase and surface layer chemistry. Using these new measurements in conjunction with realistic treatments of ice grain size, H2O2 and NO3– distribution within ice grains, diffusion of gas species within solid ice, and observed OM particle size distributions yields snowpack HCHO photochemical production rates more consistent with observations.

Analysis and experiment of eddy current loss in Homopolar magnetic bearings with laminated rotor cores

This paper analyses the eddy current loss in Homopolar magnetic bearings with laminated rotor cores produced by the high speed rotation in order to reduce the power loss for the aerospace applications. The analytical model of rotational power loss is proposed in Homopolar magnetic bearings with laminated rotor cores considering the magnetic circuit difference between Homopolar and Heteropolar magnetic bearings. Therefore, the eddy current power loss can be calculated accurately using the analytical model by magnetic field solutions according to the distribution of magnetic fields around the pole surface and boundary conditions at the surface of the rotor cores. The measurement method of rotational power loss in Homopolar magnetic bearing is proposed, and the results of the theoretical analysis are verified by experiments in the prototype MSCMG. The experimental results show the correctness of calculation results.

Volumetry of the human amygdala — An anatomical study

A striking feature of the studies that have addressed the measurement of the amygdala is the wide range of volumes encountered, with reports of volumes ranging from 1 to almost 4 cm 3. Another striking feature is the number of discrepancies in the landmarks adopted for manual tracing in magnetic resonance imaging (MRI). The goal of our study was to assess the anatomical volume of the amygdala on the basis of its cytoarchitecture while comparing the differences in age and sex. This study was performed on 21 normal male brains (mean age of 56.8 years) and 9 normal female brains (mean age of 61.2 years). The volume of the amygdala was measured by planimetry of Nissl-stained serial sections using ImageJ software. To address the complexity of the amygdala, we elected to use two types of amygdalar measurement that differ mainly in the definition of anterior pole boundaries. The average size of the classic amygdala was 1.24 cm 3 (S.D. = 0.14), while the average size of the amygdala with wider borders was 1.63 cm 3 (S.D. = 0.2). No interhemispheric or intersexual differences were observed for either type of amygdalar measurement. Neither sex revealed any statistically important relationship between volume of the amygdala and age. Our study was concerned exclusively with the anatomical volume of the amygdala rather than the MRI volume. Nevertheless, our results may have important implications for MRI studies because as of yet there is no gold standard for manual volumetry of the amygdala.

Shape optimization of double-chamber side mufflers with extended tube by using four-pole matrix, boundary element method and genetic algorithm

As the excellent noise reduction in dealing with most of the industrial venting noise in lower frequencies, reactive silencer has been prevailing and widely discussed, according. Most researchers explored the noise reduction effects due to flowing rate and temperature gradient based on pure plane wave theory; however, the effect of high degree wave was rarely addressed. Moreover, the maximum of silencer noise reduction under space constraint, in which frequently occurred in engineering problem, are hardly mentioned. Most of the optimal assessments were oriented with a slower optimizer, the mathematic gradient method. An issue by using a precise and quick optimizer to access the optimal noise reduction of a complicated silencer under limited space becomes essential and obligatory. In this paper, the optimal design of a double–chamber side muffler connected with internal extended tube under limited space is presented; in addition, the genetic algorithm is selected as the optimizer in searching for the best design set. In theoretical derivation, on the basis of one–dimensional plane wave theory, the system four-pole matrices under flowing effect have been established and furthermore deduced to a scalar noise reduction function. To verify the accuracy of four–pole transfer matrices, one set of silencer shape parameter has been used to construct and further acoustic test in laboratory and noise simulated in boundary element method (high degree of sound wave) have be performed individually. The results reveal that all of the four–pole matrix theory, experimental data and boundary element method are in agreement. To verify the accuracy of GA solution during optimization, an optimal design of noise reduction onto pure tone with 300 Hz is pre–run. The result reveals that the maximized STL is precisely located at 300 Hz. Consequently, a numerical case of optimal noise reduction to broadband noise source under space constraint is exemplified.

Modelling the impact of possible snowpack emissions of O(3P) and NO2 on photochemistry in the South Pole boundary layer

Environmental context. The study of surface photochemical ozone production on the Antarctic continent has direct relevance to climate change and general air quality and is scientifically noteworthy given the otherwise pristine nature of this environmental region. The identification of possible direct ozone emissions from snow surfaces and their contribution to the already active photochemical pollution present there represents a unique physical phenomenon. This process could have wider global significance for other snow-covered regions and therefore for global climate change. Abstract. O(3P) emissions due to photolysis of nitrate were recently identified from ice surfaces doped with nitric acid. O(3P) atoms react directly with molecular oxygen to yield ozone. Therefore, these results may have direct bearing on photochemical activity monitored at the South Pole, a site already noted for elevated summertime surface ozone concentrations. NO2 is also produced via the photolysis of nitrate and the firn air contains elevated levels of NO2, which will lead to direct emission of NO2. A photochemical box model was used to probe what effect O(3P) and NO2 emissions have on ozone concentrations within the South Pole boundary layer. The results suggest that these emissions could account for a portion of the observed ozone production at the South Pole and may explain the observed upward fluxes of ozone identified there.

Modelling the impact of oxygenated VOC and meteorology upon the boundary layer photochemistry at the South Pole

AbstractA chemistry box model is used to explore implications of recent measurements of methyl hydroperoxide (MHP) across Antarctica and their influence upon high ozone events in the South Pole boundary layer. To reconcile, recent data models suggest that chemistry and meteorology play an important role. Copyright © 2007 Royal Meteorological Society

An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton–Miller formulation

The high solution costs and non-uniqueness difficulties in the boundary element method (BEM) based on the conventional boundary integral equation (CBIE) formulation are two main weaknesses in the BEM for solving exterior acoustic wave problems. To tackle these two weaknesses, an adaptive fast multi- pole boundary element method (FMBEM) based on the Burton-Miller formulation for 3-D acoustics is presented in this paper. In this adaptive FMBEM, the Burton-Miller formulation using a linear combination oftheCBIEandhypersingularBIE(HBIE)isappliedto overcome the non-uniqueness difficulties. The iterative solver generalized minimal residual (GMRES) and fast multipole method (FMM) are adopted to improve the overallcomputationalefficiency.ThisadaptiveFMBEM for acoustics is an extension of the adaptive FMBEM for 3-D potential problems developed by the authors recently. Several examples on large-scale acoustic radi- ationandscatteringproblemsarepresentedinthispaper which show that the developed adaptive FMBEM can be several times faster than the non-adaptive FMBEM while maintaining the accuracies of the BEM.

An analysis of the oxidation potential of the South Pole boundary layer and the influence of stratospheric ozone depletion

The summertime atmospheric boundary layer over the South Pole has recently been shown to be highly oxidizing, with greater concentrations of NO and OH than previously expected. The source of NO has been attributed to photolysis of nitrate impurities in the snowpack, with elevated OH from the reaction NO + HO2. However, the Antarctic troposphere is not currently in a “natural” state, being subject nowadays to greatly increased incidences of ultraviolet (UV) radiation each spring. Here we analyze the long‐term record of surface ozone at the South Pole (1975–2001), to look for evidence of a changing oxidation potential. Daily averaged surface ozone concentrations during spring and early summer now regularly exceed the maximum concentration of the previous winter, while in the 1970s and 1980s this was not the case. This suggests that the proposed springtime ozone source is greater nowadays than before. Such a feature is consistent with increases in UV radiation accompanying the springtime stratospheric ozone hole. Model calculations show that the rate of nitrate photolysis in the South Pole snowpack has increased significantly since the onset of the ozone hole, such that production of NO2 in November has increased by 43% between the late 1960s and the late 1990s. It thus appears that the South Pole boundary layer is more highly oxidizing nowadays than under conditions before the onset of the ozone hole.

The injector microtron for the TEUFEL infrared laser

Progress is reported on a 25 MeV injector racetrack microtron for a 10 ?m radiation free electron laser (TEUFEL project). The accelerator exhibits transverse focusing in 180° inhomogeneous two-sector dipole magnets which are slightly rotated with respect to each other in the bending plane. This provides closed orbits, isochronism and a large transverse acceptance. Details on this unconventional microtron focusing system will be given. An analytical treatment, based on conformal mapping, of the field near pole boundaries and at the hill-valley boundaries in the microtron dipole is compared with Poisson calculated results and with field measurements. The design of a model accelerating cavity is presented together with field measurements based on the perturbation ball method.

Dayside aurorae and their relation to other geophysical phenomena

Principal morphological peculiarities of auroral luminosity are investigated on the basis of the data from multi-year aurorae observations in day hours at Spitzbergen and Franz Jozef Land. It is shown that in this region the typical forms of aurorae are moving poleward rayed arcs appearing at the equatorward boundary of the auroral oval and disappearing at its pole boundary. Discrete forms of aurorae are located inside a much broader red luminosity band in its equatorward part. Auroral pulsations with a period of 10–50 s are observed in the prenoon sector in a region of much harder precipitations found more equatorward with respect to the daytime red luminosity band. The influence of a B z IMF component upon daytime aurorae is exercised both directly through an equatorward (poleward) shift of daytime aurorae upon decreasing (increasing) B z and via an increase in a planetary geomagnetic activity related to the appearance of substorms during which the whole region of the daytime luminosity is shifted to much lower latitudes. A decrease of intensity of daytime aurorae with duration of 5–10 min before the beginning of an expansive phase of a substorm on the night side is detected. The peculiarities of the daytime aurorae dynamics during substorms are also investigated. A scheme of the daytime auroral luminosity distribution is presented. Analytical expressions of the dependence of the daytime aurorae position on IMF are provided. Certain physical mechanisms that can explain the peculiarities of daytime aurorae dynamics are also discussed.