Multi-dimensional boundary effects and regional economic integration: Evidence from the Yangtze River Economic Belt

While the challenges posed by multi-dimensional boundary effects to global economic integration are studied widely, regional economic integration within a sovereign country requires additional analysis. The Yangtze River Economic Belt (YREB), a super-scale interprovincial area including three nested urban alliances, is a meaningful vision of regional economic integration in China. After building the producer services-based urban corporate network, this study investigates the influence of multi-dimensional boundary effects on regional economic integration by social network analysis and the exponential random graph model. The findings show that the fragmented reality of YREB’s economy is significantly different from the vision of the Chinese central government. More specifically, although the natural boundary restraints represented by distance have disappeared, multi-dimensional barriers to regional economic integration are still posed by administrative, policy, economic, and cultural boundaries. The estimation results pass the robustness test of the grouping sample of producer services. Therefore, we confirm that the multi-dimensional boundary effects, particularly the intangible ones, significantly impact regional economic integration even within a country with a top-down ‘strong’ governance.

Boundary conductance in macroscopic bismuth crystals

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

Dynamics of eddying abyssal mixing layers over rough topography

The abyssal overturning circulation is thought to be primarily driven by small-scale turbulent mixing. Diagnosed watermass transformations are dominated by rough topography "hotspots", where the bottom-enhancement of mixing causes the diffusive buoyancy flux to diverge, driving widespread downwelling in the interior—only to be overwhelmed by an even stronger upwelling in a thin Bottom Boundary Layer (BBL). These watermass transformations are significantly underestimated by one-dimensional sloping boundary layer solutions, suggesting the importance of three-dimensional physics. Here, we use a hierarchy of models to generalize this one-dimensional boundary layer approach to three-dimensional eddying flows over realistically rough topography. When applied to the Mid-Atlantic Ridge in the Brazil Basin, the idealized simulation results are roughly consistent with available observations. Integral buoyancy budgets isolate the physical processes that contribute to realistically strong BBL upwelling. The downwards diffusion of buoyancy is primarily balanced by upwelling along the canyon flanks and the surrounding abyssal hills. These flows are strengthened by the restratifying effects of submesoscale baroclinic eddies on the canyon flanks and by the blocking of along-ridge thermal wind within the canyon. Major topographic sills block along-thalweg flows from restratifying the canyon trough, resulting in the continual erosion of the trough's stratification. We propose simple modifications to the one-dimensional boundary layer model which approximate each of these three-dimensional effects. These results provide \textit{local} dynamical insights into mixing-driven abyssal overturning, but a complete theory will also require the non-local coupling to the basin-scale circulation.

On the minimal residual methods for solving diffusion-convection SLAEs

The objective of this research is to develop and to study iterative methods in the Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approximation of multi-dimensional boundary value problems on the unstructured grids. These methods are also relevant in many applications, including diffusion-convection equations. The considered algorithms are based on constructing ATA — orthogonal direction vectors calculated using short recursions and providing global minimization of a residual at each iteration. Methods based on the Lanczos orthogonalization, AT — preconditioned conjugate residuals algorithm, as well as the left Gauss transform for the original SLAEs are implemented. In addition, the efficiency of these iterative processes is investigated when solving algebraic preconditioned systems using an approximate factorization of the original matrix in the Eisenstat modification. The results of a set of computational experiments for various grids and values of convective coefficients are presented, which demonstrate a sufficiently high efficiency of the approaches under consideration.

A COMPLEX POTENTIAL APPROACH TO MICROMECHANICS OF UNIDIRECTIONAL COMPOSITES

Complex potential methods for the solution of two-dimensional boundary value problems in linear elasticity are used to perform micromechanics analysis of unidirectional composites. The composite microstructure is idealized as a square array of unit cells subjected to prescribed strains. Unit cell analyses are performed for plane strain and anti-plane strain conditions to study the interaction of the fiber and matrix materials. The unit cell solutions are used to derive predictions for the ply moduli, Poisson’s ratios and coefficients of thermal expansion, which are shown to agree with the results of other methods. Applications to strength prediction are briefly discussed, and the detailed stress field results that can be generated using the approach are illustrated.

ПРИНЦИП ВОЗМОЖНЫХ ПЕРЕМЕЩЕНИЙ В МОМЕНТНОМЕМБРАННОЙ ДИНАМИЧЕСКОЙ ТЕОРИИ УПРУГИХ ТОНКИХ ОБОЛОЧЕК / The Principle of Possible Displacments in the Moment-Membrane Dynamic Theory of Elastic Thin Shells

В работе излагается моментно-мембранная динамическая теория упругих тонких оболочек на основе метода гипотез, который соответствует качественной стороне результата интегрирования трехмерной граничной задачи моментной теории упругости в тонкой области оболочки. На основе принципа возможных перемещений трехмерной моментной динамической теории упругости с независимыми полями перемещений и вращений и основных соотношений моментномембранной динамической теории упругих тонких оболочек, устанавливается принцип возможных перемещений для моментномембранной динамической теории упругих тонких оболочек./ In the present paper the moment-membrane dynamic theory of elastic thin shells is presented based on the hypotheses method, which corresponds to the qualitative side of the result of integration of the three-dimensional boundary-value problem of the moment theory of elasticity in a thin region of the shell. On the basis of the principle of possible displacements of the threedimensional moment dynamic theory of elasticity with independent fields of displacements and rotations and the basic relations of the moment-membrane dynamic theory of elastic thin shells, the principle of possible displacements for the moment-membrane dynamic theory of elastic thin shells is established.