A study involving the completion of quasi 2-normed space

The fundamental aim of this paper is to introduce and investigate a new property of quasi 2-normed space based on a question given by C. Park (2006) [2] for the completion quasi 2-normed space. Finally, we also find an answer for a question Park's.Comment: 7 page

Numerical simulation of single droplet dynamics in three-phase flows using ISPH

In this study, a new surface tension formulation for modeling incompressible, immiscible three-phase fluid flows in the context of incompressible smoothed particle hydrodynamics (ISPH) in two dimensions has been proposed. A continuum surface force model is employed to transform local surface tension force to a volumetric force while physical surface tension coefficients are expressed as the sum of phase specific surface tension coefficients, facilitating the implementation of the proposed method at triple junctions where all three phases are present. Smoothed color functions at fluid interfaces along with artificial particle displacement throughout the computational domain are combined to increase accuracy and robustness of the model. In order to illustrate the effectiveness of the proposed method, several numerical simulations have been carried out and results are compared to analytical data available in literature. Results obtained by simulations are compatible with analytical data, demonstrating that the ISPH scheme proposed here is capable of handling three-phase flows accurately

Numerical investigation of three-phase flows using incompressible smoothed particle hydrodynamics

An ISPH method for the simulation of three-phase °ows is presented in this article. The proposed method is investigated through the simulation of a droplet located at the interface of two immiscible °uids as well as diamond droplet deformation. The extendibility of the proposed surface tension formulations for three-phase fows to two-phase fows is also investigated. It is observed that the results obtained from the numerical simulations are in good agreement with the analytical ones

Process simulation for 5-axis machining using generalized milling tool geometries

Multi-axis machining (especially 5-axis machining) is widely used in precision machining for automotive, aerospace and die-mold manufacturing. The goal in precision machining is to increase production while meeting high part quality needs which can be achieved through decision of appropriate process parameters considering machine tool constraints (such as power and torque), chatter-free operations and part quality. In order to predict and decide on optimal process parameters, simulation models are used. In the literature, individual tool geometries for multi-axis machining are examined in detailed with different modeling approaches to simulate cutting forces. In this study, a general numerical model for 5-axis machining is proposed covering all possible tool geometries. Tool envelope is extracted from CAD data, and helical flutes points are represented in cylindrical coordinates. Equal parallel slicing method is utilized to find cutter engagement boundaries (CEB) determining cutting region of the tool surface. for each axial level in the tool axis direction. For each level uncut chip thickness value is found and total forces are calculated by summing force values for each point along the cutting flutes. For arbitrary cases forces are simulated and obtained results are experimentally verified

Probabilistic mathematical formula recognition using a 2D context-free graph grammar

We present a probabilistic framework for the mathematical expression recognition problem. The developed system is flexible in that its grammar can be extended easily thanks to its graph grammar which eliminates the need for specifying rule precedence. It is also optimal in the sense that all possible interpretations of the expressions are expanded without making early commitments or hard decisions. In this paper, we give an overview of the whole system and describe in detail the graph grammar and the parsing process used in the system, along with some preliminary results on character, structure and expression recognition performances