scholarly journals MATHEMATICAL MODELLING OF MACROSEGREGATION IN INGOT CASTING

2018 ◽  
Vol 17 (2) ◽  
pp. 74
Author(s):  
M. O. Assunção Jr ◽  
M. Vynnycky
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Chemical Species ◽  
Ternary Alloys ◽  
Ingot Casting ◽  
Two Dimensional ◽  
Computational Simulations ◽  
Macroscopic Scale ◽  
Three Dimensional Models

The occurrence of macrosegregation in alloys produced by ingot casting can adversely affect the quality of the final product. Macrosegregation can be described as a severe variation on the macroscopic scale of the chemical species that compose the alloy, and the ability of computational simulations to predict such defects remains far from perfect. Therefore, this research focuses on the development of a two-dimensional mathematical model that - through computational simulations - could be applied to study and predict the formation of macrosegregation in the ingot casting of binary alloys. Once accomplished, this work can establish the framework to new studies that will tackle more advanced problems, e.g., for actual ingot geometries, three-dimensional models and industrially-important ternary alloys.

scholarly journals Short and Medium-Range Order in Liquid Ternary Al80Co10Ni10, Al72.5Co14.5Ni13, and Al65Co17.5Ni17.5 Alloys

2010 ◽  
Vol 65 (1-2) ◽  
pp. 123-131 ◽  
Author(s):  
Oleksandr S. Roik ◽  
Oleksiy Samsonnikov ◽  
Volodymyr Kazimirov ◽  
Volodymyr Sokolskii
Keyword(s):  
Three Dimensional ◽  
Range Order ◽  
Ternary Alloys ◽  
X Ray Diffraction ◽  
Medium Range Order ◽  
Intermediate Range Order ◽  
Transition Metal Atoms ◽  
Medium Range ◽  
Three Dimensional Models ◽  
Co Alloys

AbstractA local short-to-intermediate range order of liquid Al80Co10Ni10, Al72.5Co14.5Ni13, and Al65Co17.5Ni17.5 alloys was examined by X-ray diffraction and the reverse Monte Carlo modelling. The comprehensive analysis of three-dimensional models of the liquid ternary alloys was performed by means of the Voronoi-Delaunay method. The existence of a prepeak on the S(Q) function of the liquid alloys is caused by medium range ordering of 3d-transition metal atoms in dense-packed polytetrahedral clusters at temperatures close to the liquidus. The non-crystalline clusters, represented by aggregates of pentagons that consist of good tetrahedra, and chemical short-range order lead to the formation of the medium range order in the liquid binary Al-Ni, Al-Co and ternary Al-Ni-Co alloys.

Sight distance red zones on combined horizontal and sag vertical curves

1998 ◽  
Vol 25 (4) ◽  
pp. 621-630 ◽  
Author(s):  
Yasser Hassan ◽  
Said M Easa
Keyword(s):  
Quantitative Analysis ◽  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Horizontal Curve ◽  
Sight Distance ◽  
Stopping Sight Distance ◽  
Three Dimensional Models ◽  
Highway Alignment ◽  
Current Standards

Coordination of highway horizontal and vertical alignments is based on subjective guidelines in current standards. This paper presents a quantitative analysis of coordinating horizontal and sag vertical curves that are designed using two-dimensional standards. The locations where a horizontal curve should not be positioned relative to a sag vertical curve (called red zones) are identified. In the red zone, the available sight distance (computed using three-dimensional models) is less than the required sight distance. Two types of red zones, based on stopping sight distance (SSD) and preview sight distance (PVSD), are examined. The SSD red zone corresponds to the locations where an overlap between a horizontal curve and a sag vertical curve should be avoided because the three-dimensional sight distance will be less than the required SSD. The PVSD red zone corresponds to the locations where a horizontal curve should not start because drivers will not be able to perceive it and safely react to it. The SSD red zones exist for practical highway alignment parameters, and therefore designers should check the alignments for potential SSD red zones. The range of SSD red zones was found to depend on the different alignment parameters, especially the superelevation rate. On the other hand, the results showed that the PVSD red zones exist only for large values of the required PVSD, and therefore this type of red zones is not critical. This paper should be of particular interest to the highway designers and professionals concerned with highway safety.Key words: sight distance, red zone, combined alignment.

scholarly journals TSUNAMI GENERATION AND PROPAGATION

1972 ◽  
Vol 1 (13) ◽  
pp. 146
Author(s):  
Joseph L. Hammack ◽  
Frederic Raichlen
Keyword(s):  
Linear Theory ◽  
Source Region ◽  
Three Dimensional ◽  
Frequency Dispersion ◽  
Nonlinear Effects ◽  
Its Region ◽  
Experimental Results ◽  
Specific Class ◽  
Two Dimensional ◽  
Three Dimensional Models

A linear theory is presented for waves generated by an arbitrary bed deformation {in space and time) for a two-dimensional and a three -dimensional fluid domain of uniform depth. The resulting wave profile near the source is computed for both the two and three-dimensional models for a specific class of bed deformations; experimental results are presented for the two-dimensional model. The growth of nonlinear effects during wave propagation in an ocean of uniform depth and the corresponding limitations of the linear theory are investigated. A strategy is presented for determining wave behavior at large distances from the source where linear and nonlinear effects are of equal magnitude. The strategy is based on a matching technique which employs the linear theory in its region of applicability and an equation similar to that of Korteweg and deVries (KdV) in the region where nonlinearities are equal in magnitude to frequency dispersion. Comparison of the theoretical computations with the experimental results indicates that an equation of the KdV type is the proper model of wave behavior at large distances from the source region.

Mathematical modeling of a generic multi-profile form milling cutter

2012 ◽  
Vol 227 (5) ◽  
pp. 1036-1046 ◽  
Author(s):  
Mohammed Rajik Khan ◽  
Puneet Tandon
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Sculptured Surfaces ◽  
Three Dimensional Model ◽  
Machining Time ◽  
Milling Cutter ◽  
Machined Parts ◽  
Rotary Cutting ◽  
Three Dimensional Models ◽  
The Mathematical Model

In order to machine multiple sculptured surfaces with reduced machining time and high accuracy of the machined parts, shape design of a customised multi-point rotary cutting tool needs to be evolved. In the present work, a novel design of a generic multi-profile form milling cutter is developed for machining various multiple sculptured surfaces. This article describes in detail the mathematical model to design an accurate three-dimensional geometry of a generic multi-profile form milling cutter. Use of non-uniform rational B-spline curve(s) and sweep surfaces enables to control the shape of cutting flutes of the generic multi-profile form milling cutter. The article also discusses the methodology to develop a variety of cutters lying in the same conceptual family of multi-profile form milling cutter. To physically visualise the cutter and to show one of the downstream applications once a three-dimensional model of the cutter is available, one of the multi-profile form milling cutters is fabricated. The proposed methodology offers an intuitive high-quality mathematical model for a generic family of multi-profile form milling cutters, which is different from the traditional three-dimensional models.

Three-Dimensional Mesh Model Watermarking Algorithm

2012 ◽  
Vol 198-199 ◽  
pp. 1481-1486
Author(s):  
Xin Li ◽  
Yi Ping Tian
Keyword(s):  
Wavelet Transform ◽  
Copyright Protection ◽  
Control Point ◽  
Three Dimensional ◽  
Digital Watermark ◽  
Two Dimensional ◽  
Mesh Model ◽  
Watermark Embedding ◽  
Three Dimensional Models ◽  
Watermark Algorithm

Watermark information is embedded in three-dimensional mesh model through three-dimensional watermarking algorithm for effective copyright protection. The widely use of three-dimensional grid model attracts more attention on the copyright protection. The digital watermark algorithm with the NURBS model based on the wavelet transform aims to get the virtual grayscale images using the control point coordinate. Then we can embed the watermark into the virtual gray image watermark. It can change the three-dimensional models into two-dimensional images. And this algorithm can enhance the operability and simplicity of the watermark embedding. Experiments show that the proposed algorithm is easy to implement, simple in principle, and the extracted watermark is clearly visible, moreover, the model does not need to be directly modified, so it has good robustness. Watermarked model does not change in the visual, it has good invisibility.

The Representation of Experience in Architectural Design

1995 ◽  
Vol 4 (3) ◽  
pp. 254-266 ◽  
Author(s):  
Richard W. Zobel
Keyword(s):  
Architectural Design ◽  
New Technology ◽  
Three Dimensional ◽  
Electronic Media ◽  
Physical Models ◽  
Two Dimensional ◽  
Immersive Environments ◽  
Architectural Space ◽  
Experiential Quality

Architecture, which is by its very nature a three-dimensional art, has in the last 500 years evolved to a stage where nearly all of the design exploration and visualization occur in any of a number of two-dimensional media. These media do not effectively portray the experiential quality of approaching, entering, and moving through an architectural space, an aspect which is primary to any design. In discussing this, James J. Gibson's concept of affordance will be used as a basis for the examination of a variety of media that are commonly used to describe the experiential quality of architecture, and how each of these media speaks to this frequently neglected characteristic. Particular attention will be given to the new technology of computer-generated immersive environments, which as a design medium promises to bring the issue of experiential quality in architecture to the forefront of design. Examples of each of the most common media, physical models, perspectives, noninteractive screen-based architectural walk throughs, interactive screen-based architectural walk throughs, and computer-generated immersive environments, will be examined as to their utility in experiential description. A discussion of the specific characteristics of each of the electronic media and the applications benefits and drawbacks will be included.

Two-Dimensional R-Matrices — Descendants of Three-Dimensional R-Matrices

1997 ◽  
Vol 12 (19) ◽  
pp. 1393-1410 ◽  
Author(s):  
S. M. Sergeev
Keyword(s):  
Three Dimensional ◽  
Baxter Equation ◽  
Two Dimensional ◽  
Affine Algebra ◽  
Tetrahedron Equation ◽  
Drinfeld Double ◽  
R Matrix ◽  
Operator Solution ◽  
Dimensional Models ◽  
Three Dimensional Models

Finite layers of three-dimensional models can be regarded as two-dimensional with complicated multi-stated weights. The tetrahedron equation in 3D provides the Yang–Baxter equation for this composite weights in 2D. Such solutions of the Yang–Baxter equation are constructed for the simplest operator solution of the tetrahedron equation. These R-matrices can be regarded as a special projection of universal R-matrix for some Drinfeld double [Formula: see text], associated with the affine algebra [Formula: see text]. Usual R-matrix for [Formula: see text] is another projection of [Formula: see text].

A Study of Wear Rate Estimation of Coatings by a Numerical Method

2011 ◽  
Vol 675-677 ◽  
pp. 675-680 ◽  
Author(s):  
Yu Sen Yang ◽  
Wesley Huang
Keyword(s):  
Mathematical Model ◽  
Mathematical Method ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Numerical Data ◽  
Wear Volume ◽  
Two Dimensional ◽  
Considerable Time ◽  
Volume Measurements ◽  
Ball On Disc

The paper reported using a mathematical model that simulated the wear volume in comparison to measurement by a ball-on-disc for deposited CrN films on tool steel (JIS SKD11). Three dimensional profile instruments were used to measure the wear scar trace for variations of numerical data of two dimensional profiles. By using numerical algorithms, the wear volume measurements of wear profiles are to save considerable time and economical. A new mathematical method is issued for determining wear volumes in this study. The estimated results were precisely fitted as compared with other calculations for three dimensional estimations of wear volumes.

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