Sectorial Region Research Articles

Sloshing cold fronts in galaxy cluster Abell 2566

This paper presents properties of the intracluster medium (ICM) in the environment of a cool core cluster Abell 2566 (redshift z= 0.08247) based on the analysis of 20 ks Chandra X-ray data. 2D imaging analysis of the Chandra data from this cluster revealed spiral structures in the morphology of X-ray emission from within the central 109 kpc formed due to gas sloshing. This analysis also witness sharp edges in the surface brightness distribution along the south-east and north-west of the X-ray peaks at 41.6 kpc and 77.4 kpc, respectively. Spectral analysis of 0.5 – 7 keV X-ray photons along these discontinuities exhibited sharp temperature jumps from 2.3 to 3.1 keV and 1.8 to 2.8 keV, respectively, with consistency in the pressure profiles, implying their association with cold fronts due to gas sloshing of the gas. Further confirmation for such an association was provided by the deprojected broken power-law density function fit to the surface brightness distribution along these wedge shaped sectorial regions. This study also witness an offset of 4.6′′(6.8 kpc) between the BCG and the X-ray peak, and interaction of the BCG with a sub-system in the central region, pointing towards the origin of the spiral structure due to a minor merger.

Symplectic solutions of the plane annular sectors in micropolar elasticity

The symplectic approach is utilized to derive the solutions of the plane annular sector in micropolar elasticity. According to the Hellinger-Reissner variational principle, the Hamiltonian canonical equations are obtained for the plane problem in an annular sectorial region. Through the method of separation of variables, we obtain an eigenvalue equation of the Hamiltonian operator matrix which is a system of linear differential equations with variable coefficients. By the method of series solutions, its general solutions can be expressed as the linear combination of Bessel functions and power functions. The corresponding eigensolutions for three types of homogeneous boundary conditions are derived. According to the adjoint symplectic orthogonality of the eigensolutions, the solution of the micropolar plane annular sector is expressed as a series expansion of eigensolutions. Numerical analyses are presented to demonstrate the validity of the proposed method and confirm its ability to accurately capture the size effect.

Mathematical model of magnetic field for a sectorial ferromagnetic cylinder

The solution of the boundary-value problem of magnetostatics for a circular ferromagnetic cylinder with a longitudinal sectorial cutout is described. The external primary magnetic field is orthogonal to the cylinder and directed at arbitrary azimuth relative to the cutout. A system of algebraic equations for finding the amplitudes of azimuthal expansions of the spatial distribution of the secondary field of the outer and sectorial partial regions of the cylinder is obtained by the method of rearrangement of functions.

Global solutions of a two-dimensional Riemann problem for the pressure gradient system

<p style="text-indent:20px;">We are concerned with a two-dimensional Riemann problem for the pressure gradient system that is a hyperbolic system of conservation laws. The Riemann initial data consist of four constant states in four sectorial regions such that two shocks and two vortex sheets are generated between the adjacent states. The solutions keep the four constant states and four planar waves outside the outer sonic circle in the self-similar coordinates, while the two shocks keep planar until meeting the outer sonic circle at two different points and then generate a diffracted shock to connect these points, whose location is <em>apriori</em> unknown. Then the problem can be formulated as a free boundary problem, in which the diffracted transonic shock is the one-phase free boundary to connect the two points, while the other part of the sonic circle forms a fixed boundary. We establish the global existence of a solution and the optimal Lipschitz regularity of both the diffracted shock across the two points and the solution across the outer sonic boundary. Then this Riemann problem is solved globally, whose solution contains two vortex sheets and one global shock containing the two originally separated shocks generated by the Riemann data.</p>

Atuação do BNDES e disparidades regionais: evidências da indústria de transformação entre 2000-2018

Este artigo tem como objetivo analisar a dinâmica territorial de desembolso do BNDES sobre a indústria de transformação, a partir dos padrões setoriais de concorrência, regiões e unidades federativas, no período de 2000 a 2018 no Brasil. A abordagem fundamenta-se no arcabouço teórico do desenvolvimento regional e faz o uso do método analítico, descritivo e estatístico, das taxas de crescimento e índices de desigualdade de Theil (interestadual, inter-regional e intra-regional). Os resultados sugerem que a participação dos desembolsos nos grupos setoriais difusoras do progresso técnico/bens duráveis supera a parcela de indústrias de commodities e tradicionais em parte relevante dos últimos 18 anos. Ademais, nota-se que o BNDES alcançou uma distribuição regional mais equilibrada dos desembolsos entre o período de 2010-2015 influenciado, sobretudo, via o Programa de Sustentação do Investimento e fortalecimento da atuação no território. Contudo, a partir de 2015 a forte retração dos desembolsos refletiu veemente na ampliação das disparidades regionais.

Prediction of Eight Earings in Deep Drawing of 5754O Aluminum Alloy Sheet

Earings appear easily during deep drawing of cylindrical parts owing to the anisotropic properties of materials. However, current methods cannot fully utilize the mechanical properties of material, and the number of earings obtained differ with the simulation methods. In order to predict the eight-earing problem in the cylindrical deep drawing of 5754O aluminum alloy sheet, a new method of combining the yield stress and anisotropy index (r-value) to solve the parameters of the Hill48 yield function is proposed. The general formula for the yield stress and r-value in any direction is presented. Taking a 5754O aluminum alloy sheet as an example in this study, the deformation area in deep drawing is divided into several equal sectorial regions based on the anisotropy. The parameters of the Hill48 yield function are solved based on the yield stress and r-value simultaneously for the corresponding deformation area. Finite element simulations of deep drawing based on new and existing methods are carried out for comparison with experimental results. This study provides a convenient and reliable way to predict the formation of eight earings in the deep drawing process, which is expected to be useful in industrial applications. The results of this study lay the foundation for the optimization of the cylindrical deep drawing process, including the optimization of the blank shape to eliminate earing defects on the final product, which is of great importance in the actual production process.

$L_p$ regularity theorem for elliptic equations in less smooth domains

We consider a $2m$th-order strongly elliptic operator $A$ subject to Dirichlet boundary conditions in a domain $\Omega$ of $\mathbb{R}^{n}$, and show the $L_{p}$ regularity theorem, assuming that the domain has less smooth boundary. We derive the regularity theorem from the following isomorphism theorems in Sobolev spaces. Let $k$ be a nonnegative integer. When $A$ is a divergence form elliptic operator, $A-\lambda$ has a bounded inverse from the Sobolev space $W^{k-m}_{p}(\Omega)$ into $W^{k+m}_{p}(\Omega)$ for $\lambda$ belonging to a suitable sectorial region of the complex plane, if $\Omega$ is a uniformly $C^{k,1}$ domain. When $A$ is a non-divergence form elliptic operator, $A-\lambda$ has a bounded inverse from $W^{k}_{p}(\Omega)$ into $W^{k+2m}_{p}(\Omega)$, if $\Omega$ is a uniformly $C^{k+m,1}$ domain. Compared with the known results, we weaken the smoothness assumption on the boundary of $\Omega$ by $m-1$.

Eruptive and shallow conduit dynamics during Vulcanian explosions: insights from the Episode IV block field of the 1912 eruption of Novarupta, Alaska

The study of ~1300 juvenile and lithic blocks from a Vulcanian phase of the 1912 eruption of Novarupta provides new insight into the state of the magma as an eruption passes from sustained Plinian to dome growth. Blocks that were predominantly ballistically ejected were measured and sampled within an ~2–3-km radius from vent and supply a picture of a dynamic and complex shallow conduit prior to magma fragmentation in repeated small explosions. Extreme conduit heterogeneity is expressed in the diverse range of dacitic block types, including pumiceous, dense, banded, and variably welded breccia clasts, all with varied degrees of surface breadcrusting. We present new maps of block lithology and size, making Episode IV the most thoroughly mapped Vulcanian deposit to date. Sectorial regions rich in specific lithologies together with the block size data suggest multiple, small explosions. Modeling of block trajectories to reproduce the field data indicates that ejection velocities range from 50 to 124 m/s with a median of ~70 m/s. We propose that individual explosions originated from a heterogeneous shallow conduit characterized both by the juxtaposition of magma domains of contrasting texture and vesiculation state and by the intimate local mingling of different textures on short vertical and horizontal length scales at the contacts between these domains. In our model, each explosion disrupted the conduit to only shallow depths and tapped diverse, localized pockets within the conduit. This contrasts with existing models for repetitive Vulcanian explosions, and suggests that the dynamics of Episode IV were more complex than a simple progressive top-down evacuation of a horizontally stratified conduit.

Distribution of SS and AS and their bifurcations in aggregations of tuna around two FOBs

A number of empirical and theoretical studies shows that the exploitation of fish sources has benefitted a lot from artificial floating objects (abbr. FOBs) on the surface of ocean. In this paper we investigate the dynamical distribution in aggregations of tuna around two FOBs. We abandon the effort of precise computation for steady states and eigenvalues but utilize the monotonic intervals to determine the location of zeros and signs of eigenvalues qualitatively and use the symmetry of AS steady states to simplify the system. Our method enables us to find two more steady states than known results and complete the analysis of all steady states effectively. Furthermore, we display all bifurcations at steady states, including six bifurcations of co-dimension 1 and two bifurcations of co-dimension 2. One of bifurcations is a degenerate pitchfork bifurcation of co-dimension 4 but only a part of co-dimension 2 can be unfolded within the system. We construct sectorial regions to prove the nonexistence of closed orbits. Those results provide long-time prediction of steady numbers of tuna around the two FOBs and critical conditions for transitions of cases.

On the Hardy constant of non-convex planar domains: The case of the quadrilateral

The Hardy constant of a simply connected domain Ω⊂R2 is the best constant for the inequality∫Ω|∇u|2dx⩾c∫Ωu2dist(x,∂Ω)2dx,u∈Cc∞(Ω). After the work of Ancona where the universal lower bound 1/16 was obtained, there has been a substantial interest on computing or estimating the Hardy constant of planar domains. In this work we determine the Hardy constant of an arbitrary quadrilateral in the plane. In particular we show that the Hardy constant is the same as that of a certain infinite sectorial region which has been studied by E.B. Davies.

Propagation of Moreton Waves

Abstract With the Flare-Monitoring Telescope (FMT) and Solar Magnetic Activity Research Telescope (SMART) at Hida observatory of Kyoto University, 13 events of Moreton waves were captured at H$\alpha$ center, H$\alpha$$\pm$0.5 Å, and H$\alpha$$\pm$0.8 Å wavebands since 1997. With such samples, we have studied the statistical properties of the propagation of Moreton waves. Moreton waves were all restricted in sectorial zones with a mean value of 92$^\circ$. However, their accompanying EIT waves, observed simultaneously with SOHO/EIT at extreme-ultraviolet wavelength, were very isotropic with a quite extended scope of 193$^\circ$. The average propagation speeds of the Moreton waves and the corresponding EIT waves were 664 km s$^{-1}$ and 205 km s$^{-1}$, respectively. Moreton waves propagated either under large-scale close magnetic flux loops, or firstly in the sectorial region where two sets of magnetic loops separated from each other and diverged, and then stopped before the open magnetic flux region. The location swept by Moreton waves had a relatively weak magnetic field as compared to the magnetic fields at their sidewalls. The ratio of the magnetic flux density between the sidewall and the path falls in the range of 1.4 to 3.7 at a height of 0.01 solar radii. Additionally, we roughly estimated the distribution of the fast magnetosonic speed between the propagating path and sidewalls in an event on 1997 November 3, and found a relatively low-fast magnetosonic speed in the path. We also found that the propagating direction of Moreton waves coincided with the direction of filament eruption in a few well-observed events. This favors an interpretation of the “Piston” model, although further studies are necessary for any definitive conclusion.

Formations of minimalist mobile robots using local-templates and spatially distributed interactions

In this paper we address the problem of synthesizing simple rules and local interactions at the individual level so that pre-specified complex behavior emerges at the group level of a collection of autonomous mobile agents. Usually, the emergent collective behavior is used to perform certain spatial group-tasks. Specifically, we consider self-assembling of a group of mobile robots into grid, line, and wedge patterns. We introduce the notion of local-templates in which each mobile agent – capable of simple forward/backward movements and a clock-wise/counter clock-wise spin – actively encodes distinctive information into multiple non-overlapping sectorial regions of the surrounding environment in order to form pose-specific virtual links with similar minimalist agents in a local neighborhood. The resulting local patterns around each agent lead to the desired global formation. In order to take mobile robots closer to their biological counterparts, there is a need to further simplify the manner in which they currently perceive their surroundings, communicate with their neighbors, and compute their actions. We have built a robotic platform consisting of four wheeled-mobile robots that are christened as Kinbots. They are similar in principle to Braitenberg Vehicles and use simple perception/interaction/actuation techniques to achieve individual vehicle complexity and produce effective group behavior through cooperation. To validate the proposed approach, we demonstrate a column-formation task in computer simulations and physical experiments. We illustrate an experiment which is representative of various prominent stages in a group-formation task such as formation-achievement, maintenance, and response of formation movement to the presence of obstacles.

Study of chip strength due to backside grinding on wafer

The strength distribution of semiconductor chips on a wafer was studied for this paper using the three‐point bending test method that complies with ASTM standard E855. It was found from thousands of testing results that a weak region in a wafer always exists when the wafer has been thinned by mechanical backside grinding method. This weak region was distributed in two sectorial regions 45 degrees wide and symmetric to the wafer center. The averaged chip strength in the weak region was found to be at least 30% lower than the averaged chip strength of the whole wafer, and was independent of chip aspect ratio, metallization, diameter of the wafer, and the equipment that the backside grinding process used. The existence of the weak region was due to the grinding mark produced by the equipment, and was physically explained by the experimental results in this study. This weak region was able to be eliminated by using either plasma etching or polishing after the mechanical backside grinding.

Borel summability of formal solutions of some first order singular partial differential equations and normal forms of vector fields

Let L = ∑ i = 1 d X i ( z ) ∂ z i be a holomorphic vector field degenerating at z = 0 such that Jacobi matrix ( ( ∂ X i / ∂ z j ) ( 0 ) ) has zero eigenvalues. Consider L u = F ( z , u ) and let u ˜ ( z ) be a formal power series solution. We study the Borel summability of u ˜ ( z ) , which implies the existence of a genuine solution u ( z ) such that u ( z ) ∼ u ˜ ( z ) as z → 0 in some sectorial region. Further we treat singular equations appearing in finding normal forms of singular vector fields and study to simplify L by transformations with Borel summable functions.

Multistep approximation of linear sectorial evolution equations

This paper concerns the linear multistep approximation of a linear sectorial evolution equation u t = Au on a complex Banach space X. Given a strictly A(a)-stable q-step method of order p whose stability region includes a sectorial region containing the spectrum of the operator A, the corresponding evolution semigroup for the method is C n (hA), n ≥ 0, defined on X q , where C(z) ∈ L(C q ) denotes the one-step map associated with the method. It is shown that for appropriately chosen V, Y: C → C q , based on the principal right and left eigenvectors of C(z), C n (hA) approximates the semigroup V(hA)e nhA Y H (hA) with optimal order p.

Existence of Solutions with Asymptotic Expansion of Linear Partial Differential Equations in the Complex Domain

Consider the linear partial differential equation P(z, ∂_z)u(z) = f(z) in ℂ^{d+1} , where f(z) is not holomorphic on K = \{z_0 = 0\} , but it has an asymptotic expansion with respect to z_0 as z_0 → 0 in some sectorial region. We show under some conditions on P(z, ∂_z) that there exists a solution u(z) which has an asymptotic expansion of the same type as that of f(z) .

On the formation of singularities of solutions of nonlinear differential systems in antistokes directions

We determine the position and the type of spontaneous singularities of solutions of generic analytic nonlinear differential systems in the complex plane, arising along antistokes directions towards irregular singular points of the system. Placing the singularity of the system at infinity we look at equations of the form $\mathbf{y}'=\mathbf{f}(x^{-1},\mathbf{y})$ with $\mathbf{f}$ analytic in a neighborhood of $(0,\mathbf{0})$, with genericity assumptions; $x=\infty$ is then a rank one singular point. We analyze the singularities of those solutions $\mathbf{y}(x)$ which tend to zero for $x\to \infty$ in some sectorial region, on the edges of the maximal region (also described) with this property. After standard normalization of the differential system, it is shown that singularities occuring in antistokes directions are grouped in nearly periodical arrays of similar singularities as $x\to\infty$, the location of the array depending on the solution while the (near-) period and type of singularity are determined by the form of the differential system.

Growth property and slowly increasing behaviour of singular solutions of linear partial differential equations in the complex domain

Consider a linear partial differential equation in Cd+1P(z,∂)u(z)=f(z), where u(z) and f(z) admit singularities on the surface {z0=0}. We assume that |f(z)|≤A|z0|c in some sectorial region with respect to z0. We can give an exponent γ*>0 for each operator P(z,∂) and show for those satisfying some conditions that if ∀ϵ>0∃Cϵ such that |u(z)|≤Cϵexp(ϵ|z0|-γ*) in the sectorial region, then |u(z)|≤C|z0|c′ for some constants c′ and C.

A Note on the Removal of Further Breakdowns in Classical Solutions of Laplace"s Equation on Sectorial Regions

This note considers solutions to Laplace"s equation on sectors with varying vertex angles. Under Neumann conditions on the radial boundaries, there are two critical vertex angles for which classical separable solutions break down. These breakdowns have been noted in the literature and resolved. Here Dirichlet and mixed conditions are also treated. For all three boundary conditions in combination, nine further critical angles are identified and valid corresponding solutions found.

A Laurent-type expansion for solutions of Stokes' equation in sectorial regions

We study solutions of Stokes' equation in a regionD (in the complex plane) being the intersection of a sector with vertex at the origin and a ring about the origin, subject to no-slip boundary conditions on the radial boundaries ofD. Using a result of Kratz and Peyerimhoff, we represent solutionsv(z) by means of two analytic functionsv 1(z) andv 2(z), and for these we obtain expansions into infinite series, quite analogous to Laurent series, but in complex powers ofz, the exponents depending upon the angular opening ofD. Forv(z), this leads to an expansion quite analogous to the one stated without proof by Moffat in 1964 in a more special situation.