Applicability of two-dimensional boundary scattering models as a proxy for three-dimensional models

2013 ◽  
Author(s):  
Bryant Tran ◽  
Sumedh Joshi ◽  
Marcia Isakson
Keyword(s):  
Three Dimensional ◽  
Boundary Scattering ◽  
Two Dimensional ◽  
Dimensional Boundary ◽  
Dimensional Models ◽  
Three Dimensional Models

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].

scholarly journals Study on airflow and vibraton in a cutting/collection/discharge lawn care system

2021 ◽  
Author(s):  
Evan D. Davidge
Keyword(s):  
Three Dimensional ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Discharge System ◽  
Rotating Blades ◽  
Lawn Care ◽  
Optimal Shapes ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
Care System

Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system. Vibrations of a cutting blade were studied using the finite element method and experiments. It was found that the blades will experience resonance under normal operating conditions.

Experimental investigation of foam flow in two- and three-dimensional models of porous medium

2007 ◽  
Vol 5 ◽  
pp. 91-95
Author(s):  
S.V. Amel’kin ◽  
A.A. Gubaidullin ◽  
A.V. Shnaider
Keyword(s):  
Experimental Investigation ◽  
Porous Medium ◽  
Rock Sample ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Porous Rock ◽  
Foam Flow ◽  
Glass Model ◽  
Dimensional Models ◽  
Three Dimensional Models

The results of experiments on the formation and flow of foam in a two-dimensional glass model of the porous medium and three-dimensional porous rock sample are compared.

Study on airflow and vibraton in a cutting/collection/discharge lawn care system

2021 ◽  
Author(s):  
Evan D Davidge
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Discharge System ◽  
Rotating Blades ◽  
Lawn Care ◽  
Optimal Shapes ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
Dynamics Models ◽  
Care System

Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system. Airflows in the cutting/collection/discharge system of a professional lawn care system were studied numerically and experimentally in this thesis. Various three-dimensional and two-dimensional computational fluid dynamics models were developed in order to investigate the complex airflow created by a pair of counter-rotating blades. The three-dimensional models were used to study the actual flows; the two-dimensional models were developed to investigate the optimal shapes of the rotating blades using the mass flow rate per unit power consumption as the objective function. Experiments were carried out mainly to validate the computer models developed in this study for airflow velocity and power usage for an actual cutting system.Vibrations of a cutting blade were studied using the finite element method and experiments. It was found that the blades will experience resonance under normal operating conditions.

Parts and Wholes: Reduction Allometry and Modularity in Experimental Folsom Points

2021 ◽  
pp. 1-20
Author(s):  
Michael J. Shott ◽  
Erik Otárola-Castillo
Keyword(s):  
Geometric Morphometrics ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Progressive Reduction ◽  
Experimental Control ◽  
Projectile Points ◽  
The Past ◽  
Dimensional Models ◽  
Three Dimensional Models

Projectile points are a common subject of archaeological study. In the past decade, landmark-based geometric morphometrics (LGM) has increasingly been used to analyze points as whole objects. LGM and other studies document allometric changes in points—change in shape with change in size—as a product of resharpening. Allometry registers in part because different segments or modules of points are subject to different degrees of resharpening, with blades often experiencing more reduction than stems. Different modules retain varying degrees of morphological integrity as points move through their use lives. Most previous LGM studies involved two-dimensional point models, and few tested directly for modularity. We apply LGM methods to three-dimensional models of Folsom point replicas whose degree and pattern of reduction are known, finding evidence for both allometry and modularity, with modest integration. Complementary non-LGM data reveal similar results, indicating a robust pattern and ways to approximate LGM results in other data. Moreover, our dataset's experimental control clearly identifies the results as a function of the progressive reduction in use experienced by points.

Chordwise Variation of Vorticity: A Comparison of Approximations for Use in Panel Methods

1977 ◽  
Vol 28 (4) ◽  
pp. 265-270
Author(s):  
J A H Petrie
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Panel Methods ◽  
Dimensional Models ◽  
Three Dimensional Models

SummaryBased on computing efficiency, a comparison is made of three different ways of representing the chordwise variation of bound vorticity for use in panel methods. Because of expense, the two-dimensional analogues of the three-dimensional models were used and the results assumed to hold in both situations. A constant panel of vorticity is found to have inherent difficulties which make it unattractive to use. A linearly varying vorticity model is found to be best but a model using line vortices is almost as good and, moreover, simpler to use.

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