PCPATCH

Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems.

Imaging how thermal capillary waves and anisotropic interfacial stiffness shape nanoparticle supracrystals

Development of the surface morphology and shape of crystalline nanostructures governs the functionality of various materials, ranging from phonon transport to biocompatibility. However, the kinetic pathways, following which such development occurs, have been largely unexplored due to the lack of real-space imaging at single particle resolution. Here, we use colloidal nanoparticles assembling into supracrystals as a model system, and pinpoint the key role of surface fluctuation in shaping supracrystals. Utilizing liquid-phase transmission electron microscopy, we map the spatiotemporal surface profiles of supracrystals, which follow a capillary wave theory. Based on this theory, we measure otherwise elusive interfacial properties such as interfacial stiffness and mobility, the former of which demonstrates a remarkable dependence on the exposed facet of the supracrystal. The facet of lower surface energy is favored, consistent with the Wulff construction rule. Our imaging–analysis framework can be applicable to other phenomena, such as electrodeposition, nucleation, and membrane deformation.

A Single Universal Construction Rule for the Structural Synthesis of Mechanisms

In the field of structural synthesis of mechanisms several synthesis methods have been developed using different approaches. One of the more interesting approaches was that of bottom-up construction via the combination of modular structural groups, known as Assur groups. This approach is combined with new graph representations of mechanisms taken from rigidity theory, capable of representing all the different types of planar and spatial mechanisms. With the strong mathematical base of rigidity theory, a new synthesis method is proposed based on Assur groups, which are reformulated in terms of graph theory and renamed Assur Graphs. Using a single universal construction rule, Assur Graphs of different types and of any number of links are constructed, creating a complete set of building blocks for the synthesis of feasible mechanisms. As its name implies, the single universal construction is applicable for mechanisms of all types of joints and links, for planar or spatial motion.

Construction of Baranov Trusses Using a Single Universal Construction Rule

The kinematic structure of Baranov trusses has been widely studied in the field of mechanism theory. Baranov trusses are seen as the fundamental planar linkages which are a basis for all other planar linkages. As such, they have been used for synthesis of mechanisms as well as their analysis. However, up until now only a limited number Baranov trusses are known and cataloged. In this paper, a method is proposed for generation of Baranov trusses using a new graph representation suitable for linkages of the sort. This method, named the Universal construction rule, is capable of generating a complete set of all feasible Baranov trusses with any number of links. The method has been proven using a mathematical basis from rigidity theory. It is based on the correspondence between Baranov trusses and Assur groups, which are reformulated in terms of graph theory to be known as Assur graphs.

Study on Automatic Safety Monitoring and Management System of Tailings Reservoir

The tailings dam is a very important component part in mine production facilities. Meanwhile, it is a potential major risk source with high potential energy. Through collecting many accidents of the tailings dam, it is showed that accident type of the tailings dam mainly is dam-break, damage of drainage system, leakage of tailings, etc. On the basis of this analysis, the main causes of dam-break are slope instability, breaking construction rule, unusual rainfall, etc. The automatic safety monitoring and management system of the tailings reservoir (ASMMS) is a powerful measure for mine safety production. The basic frame of the ASMMS is proposed. The main contents and key problems of the ASMMS are also analyzed. It can provide a strong theoretical and technical basis for the safety and management of the tailings dam.

Optimizing Route for Hazardous Materials Logistics Based on Hybrid Ant Colony Algorithm

Optimizing Route for Hazardous Materials Logistics (ORHML) belongs to a class of problems referred to as NP-Hard, and a strict constraint of it makes it harder to solve. In order to dealing with ORHML, an improved hybrid ant colony algorithm (HACA) was devised. To achieve the purpose of balancing risk and cost for route based on the principle of ACA that used to solve TSP, the improved HACA was designed. Considering the capacity of road network and the maximum expected risk limits, a route optimization model to minimize the total cost is established based on network flow theory. Improvement on route construction rule and pheromone updating rule was adopted on the basis of the former algorithm. An example was analyzed to demonstrate the correctness of the application. It is proved that improved HACA is efficient and feasible in solving ORHML.

Verbal suffix-repetition construction in Korean: A constraint- and construction-based approach

There are various Verbal Suffix-Repetition (VSR) constructions in Korean, where suffixes such as -kena/tun(ci)/tun(ka) are attached to the repeated verbs. Calling the VSR Choice-denying Repeated Verbs construction, Lee (2011) claims that the following verb of the VSR, which can be replaced with mal-, should contain a negative but the preceding verb should be affirmative in the VSR construction which disallows any NPI within it. Unlike Lee (2011), we claim that the verbs in the VSR can freely occur either in the preceding position or in the following one regardless of their Neg value so long as they share the same verbal suffix forms such as -tun(ka). Furthermore, NPIs may occur within the VSR construction if they occur with a negative predicate within the same clause. To implement the findings above into HPSG, we have proposed the two lexical entries for mal-, the VSR Construction Rule, and the NPI Clause-mate Constraint. These tools enable us to account for the idiosyncratic properties of the VSR constructions under this constraint- and construction-based approach.