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

2021 ◽  
pp. 1-20
Author(s):  
Michael J. Shott ◽  
Erik Otárola-Castillo

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.

1997 ◽  
Vol 12 (19) ◽  
pp. 1393-1410 ◽  
Author(s):  
S. M. Sergeev

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].


2021 ◽  
Author(s):  
Evan D. Davidge

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.


2007 ◽  
Vol 5 ◽  
pp. 91-95
Author(s):  
S.V. Amel’kin ◽  
A.A. Gubaidullin ◽  
A.V. Shnaider

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.


2021 ◽  
Author(s):  
Evan D Davidge

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.


1977 ◽  
Vol 28 (4) ◽  
pp. 265-270
Author(s):  
J A H Petrie

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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