Metal castingIn metalworking and jewelry making, casting is a process in which a liquid metal is delivered into a mold (usually by a crucible) that contains a negative impression (i.e., a three-dimensional negative image) of the intended shape. The metal is poured into the mold through a hollow channel called a sprue. The metal and mold are then cooled, and the metal part (the casting) is extracted. Casting is most often used for making complex shapes that would be difficult or uneconomical to make by other methods.
K-means clusteringk-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. k-means clustering minimizes within-cluster variances (squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors, whereas only the geometric median minimizes Euclidean distances.
Die castingDie casting is a metal casting process that is characterized by forcing molten metal under high pressure into a mold cavity. The mold cavity is created using two hardened tool steel dies which have been machined into shape and work similarly to an injection mold during the process. Most die castings are made from non-ferrous metals, specifically zinc, copper, aluminium, magnesium, lead, pewter, and tin-based alloys. Depending on the type of metal being cast, a hot- or cold-chamber machine is used.
Sand castingSand casting, also known as sand molded casting, is a metal casting process characterized by using sand known as casting sand as the mold material. The term "sand casting" can also refer to an object produced via the sand casting process. Sand castings are produced in specialized factories called foundries. In 2003, over 60% of all metal castings were produced via sand casting. Molds made of sand are relatively cheap, and sufficiently refractory even for steel foundry use.
Casting defectA casting defect is an undesired irregularity in a metal casting process. Some defects can be tolerated while others can be repaired, otherwise they must be eliminated. They are broken down into five main categories: gas porosity, shrinkage defects, mould material defects, pouring metal defects, and metallurgical defects. The terms "defect" and "" refer to two specific and separate things in castings. Defects are defined as conditions in a casting that must be corrected or removed, or the casting must be rejected.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Cluster analysisCluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, , information retrieval, bioinformatics, data compression, computer graphics and machine learning.
Investment castingInvestment casting is an industrial process based on lost-wax casting, one of the oldest known metal-forming techniques. The term "lost-wax casting" can also refer to modern investment casting processes. Investment casting has been used in various forms for the last 5,000 years. In its earliest forms, beeswax was used to form patterns necessary for the casting process. Today, more advanced waxes, refractory materials and specialist alloys are typically used for making patterns.
Hierarchical clusteringIn data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.
Determining the number of clusters in a data setDetermining the number of clusters in a data set, a quantity often labelled k as in the k-means algorithm, is a frequent problem in data clustering, and is a distinct issue from the process of actually solving the clustering problem. For a certain class of clustering algorithms (in particular k-means, k-medoids and expectation–maximization algorithm), there is a parameter commonly referred to as k that specifies the number of clusters to detect.
