Weakly reducible H′-splittings of 3-manifolds

We introduce the [Formula: see text]-splittings for 3-manifolds as follows. For a compact connected surface [Formula: see text] properly embedded in a compact connected orientable 3-manifold [Formula: see text], if [Formula: see text] decomposes [Formula: see text] into two handlebodies [Formula: see text] and [Formula: see text], then [Formula: see text] is called an [Formula: see text]-splitting for [Formula: see text]. Clearly, when [Formula: see text] is closed, this is just the Heegaard splitting for [Formula: see text]; when [Formula: see text] is with boundary, the [Formula: see text]-splitting for [Formula: see text] is different from the Heegaard splitting for [Formula: see text]. In this paper, we first show that any compact connected orientable 3-manifold admits an [Formula: see text]-splitting, then generalize Casson–Gordon theorem on weakly reducible Heegaard splitting to the [Formula: see text]-splitting case in the following version: if [Formula: see text] is a weakly reducible [Formula: see text]-splitting for a compact connected orientable 3-manifold [Formula: see text], then (1) [Formula: see text] contains an incompressible closed surface of positive genus or (2) the [Formula: see text]-splitting [Formula: see text] is reducible or (3) there is an essential 2-sphere [Formula: see text] in [Formula: see text] such that [Formula: see text] is a collection of essential disks in [Formula: see text] and [Formula: see text] is an incompressible and not boundary parallel planar surface in [Formula: see text] with at least two boundary components, where [Formula: see text] or (4) [Formula: see text] is stabilized.

A novel geometry image to accurately represent a surface by preserving mesh topology

Geometry images parameterise a mesh with a square domain and store the information in a single chart. A one-to-one correspondence between the 2D plane and the 3D model is convenient for processing 3D models. However, the parameterised vertices are not all located at the intersection of the gridlines the existing geometry images. Thus, errors are unavoidable when a 3D mesh is reconstructed from the chart. In this paper, we propose parameterise surface onto a novel geometry image that preserves the constraint of topological neighbourhood information at integer coordinate points on a 2D grid and ensures that the shape of the reconstructed 3D mesh does not change from supplemented image data. We find a collection of edges that opens the mesh into simply connected surface with a single boundary. The point distribution with approximate blue noise spectral characteristics is computed by capacity-constrained delaunay triangulation without retriangulation. We move the vertices to the constrained mesh intersection, adjust the degenerate triangles on a regular grid, and fill the blank part by performing a local affine transformation between each triangle in the mesh and image. Unlike other geometry images, the proposed method results in no error in the reconstructed surface model when floating-point data are stored in the image. High reconstruction accuracy is achieved when the xyz positions are in a 16-bit data format in each image channel because only rounding errors exist in the topology-preserving geometry images, there are no sampling errors. This method performs one-to-one mapping between the 3D surface mesh and the points in the 2D image, while foldovers do not appear in the 2D triangular mesh, maintaining the topological structure. This also shows the potential of using a 2D image processing algorithm to process 3D models.

A new type of hollow-shallow steel and concrete composite floor beam

Recently in Vietnam, steel-concrete composite structures especially composite beams are widely constructed in high-rise buildings. To apply broader in construction field mainly in secondary beam systems, the new type of slim-floor composite beam is proposed to aim at reducing the cost, saving the raw material, and decreasing the overall floor depth for sustainable development orientation. This type of floor beam structure consists of built-up hollow-shallow steel beam mandatory connected with cast in situ concrete slab through the openings at both side of web along the beam. The shear connection level of composite beam is depended on not only the friction at the connected surface between hollow steel section and concrete but also the shear resistance of concrete dowels, which go through the openings. The paper deals with an innovative shape of cross-section and design philosophy of composite beam according to EN 1994-1-1.

Common Pool Resource Management: Assessing Water Resources Planning for Hydrologically Connected Surface and Groundwater Systems

Common pool resource (CPR) management has the potential to overcome the collective action dilemma, defined as the tendency for individual users to exploit natural resources and contribute to a tragedy of the commons. Design principles associated with effective CPR management help to ensure that arrangements work to the mutual benefit of water users. This study contributes to current research on CPR management by examining the process of implementing integrated management planning through the lens of CPR design principles. Integrated management plans facilitate the management of a complex common pool resource, ground and surface water resources having a hydrological connection. Water governance structures were evaluated through the use of participatory methods and observed records of interannual changes in rainfall, evapotranspiration, and ground water levels across the Northern High Plains. The findings, documented in statutes, field interviews and observed hydrologic variables, point to the potential for addressing large-scale collective action dilemmas, while building on the strengths of local control and participation. The feasibility of a “bottom up” system to foster groundwater resilience was evidenced by reductions in groundwater depths of 2 m in less than a decade.

Method of finite bodies for determination of the plane stressed state of rectangular plates with a rectangular hole

The paper is devoted to the determination of the stress-deformed state of structurally heterogeneous bearing rectangular plates with a rectangular hole. The new analytical-numerical method (finite bodies) was used, to find the stress state of the plate with a hole. The method of finite bodies uses the conditional partition of the doubly-connected surface of the plate into simpler connected rectangular parts. On the lines of conditional contact, the conditions of ideal contact are taken into account, which ensure the equality of stresses, deformations and displacements. The perturbed stressed state, which is presented in the form of a series of functions, which is rapidly intercepted at a distance from the outline of the hole, is considered. A finite sum of solutions of a plane problem is used and the stress state of a perturbed state is given as a sum of a series for nonorthogonal functions. The components of vector of displacements and stresses are written. The determination of the coefficients of the sum of a series is based on the proposed method of satisfying all boundary conditions and the conditions of ideal contact to find the minimum of a generalized quadratic form. The numerical criterion for the convergence of the method is theoretically established. It is shown that the accuracy of satisfaction of boundary conditions and conditions of ideal contact is estimated by one number – the minimum of a generalized quadratic form.

Stream function formulation of surface Stokes equations

In this paper we present a derivation of the surface Helmholtz decomposition, discuss its relation to the surface Hodge decomposition and derive a well-posed stream function formulation of a class of surface Stokes problems. We consider a $C^2$ connected (not necessarily simply connected) oriented hypersurface $\varGamma \subset \mathbb{R}^3$ without boundary. The surface gradient, divergence, curl and Laplace operators are defined in terms of the standard differential operators of the ambient Euclidean space $\mathbb{R}^3$. These representations are very convenient for the implementation of numerical methods for surface partial differential equations. We introduce surface $\mathbf H({\mathop{\rm div}}_{\varGamma})$ and $\mathbf H({\mathop{\rm curl}}_{\varGamma})$ spaces and derive useful properties of these spaces. A main result of the paper is the derivation of the Helmholtz decomposition, in terms of these surface differential operators, based on elementary differential calculus. As a corollary of this decomposition we obtain that for a simply connected surface to every tangential divergence-free velocity field there corresponds a unique scalar stream function. Using this result the variational form of the surface Stokes equation can be reformulated as a well-posed variational formulation of a fourth-order equation for the stream function. The latter can be rewritten as two coupled second-order equations, which form the basis for a finite element discretization. A particular finite element method is explained and the results of a numerical experiment with this method are presented.

Wetlands inform how climate extremes influence surface water expansion and contraction

Effective monitoring and prediction of flood and drought events requires an improved understanding of how and why surface water expansion and contraction in response to climate varies across space. This paper sought to (1) quantify how interannual patterns of surface water expansion and contraction vary spatially across the Prairie Pothole Region (PPR) and adjacent Northern Prairie (NP) in the United States, and (2) explore how landscape characteristics influence the relationship between climate inputs and surface water dynamics. Due to differences in glacial history, the PPR and NP show distinct patterns in regards to drainage development and wetland density, together providing a diversity of conditions to examine surface water dynamics. We used Landsat imagery to characterize variability in surface water extent across 11 Landsat path/rows representing the PPR and NP (images spanned 1985–2015). The PPR not only experienced a 2.6-fold greater surface water extent under median conditions relative to the NP, but also showed a 3.4-fold greater change in surface water extent between drought and deluge conditions. The relationship between surface water extent and accumulated water availability (precipitation minus potential evapotranspiration) was quantified per watershed and statistically related to variables representing hydrology-related landscape characteristics (e.g., infiltration capacity, surface storage capacity, stream density). To investigate the influence stream connectivity has on the rate at which surface water leaves a given location, we modeled stream-connected and stream-disconnected surface water separately. Stream-connected surface water showed a greater expansion with wetter climatic conditions in landscapes with greater total wetland area, but lower total wetland density. Disconnected surface water showed a greater expansion with wetter climatic conditions in landscapes with higher wetland density, lower infiltration and less anthropogenic drainage. From these findings, we can expect that shifts in precipitation and evaporative demand will have uneven effects on surface water quantity. Accurate predictions regarding the effect of climate change on surface water quantity will require consideration of hydrology-related landscape characteristics including wetland storage and arrangement.

Wetlands inform how climate extremes influence surface water expansion and contraction

Effective monitoring and prediction of flood and drought events requires an improved understanding of how and why surface-water expansion and contraction in response to climate varies across space. This paper sought to (1) quantify how interannual patterns of surface-water expansion and contraction vary spatially across the Prairie Pothole Region (PPR) and adjacent Northern Prairie (NP) in the United States, and (2) explore how landscape characteristics influence the relationship between climate inputs and surface-water dynamics. Due to differences in glacial history, the PPR and NP show distinct patterns in regards to drainage development and wetland density, together providing a diversity of conditions to examine surface-water dynamics. We used Landsat imagery to characterize variability in surface-water extent across eleven Landsat path/rows representing the PPR and NP (images spanned 1985–2015). The PPR not only experienced a 2.6-fold greater surface-water extent under median conditions relative to the NP, but also showed a 3.4-fold greater change in surface-water extent between drought and deluge conditions. The relationship between surface-water extent and accumulated water availability (precipitation minus potential evapotranspiration) was quantified per watershed and statistically related to variables representing hydrology-related landscape characteristics (e.g., infiltration capacity, surface storage capacity, stream density). To investigate the influence stream-connectivity has on the rate at which surface water leaves a given location, we modeled stream-connected and stream-disconnected surface water separately. Stream-connected surface water showed a greater expansion with wetter climatic conditions in landscapes with greater total wetland area. Disconnected surface water showed a greater expansion with wetter climatic conditions in landscapes with higher wetland density, lower infiltration and less anthropogenic drainage. From these findings, we can expect that shifts in precipitation and evaporative demand will have uneven effects on surface-water quantity. Accurate predictions regarding the effect of climate change on surface-water quantity will require consideration of hydrology-related landscape characteristics including wetlands.