Two-dimensional Models of Planar Transformation of Waves in Liquid of Variable Depth

2003 ◽  
Vol 30 (3) ◽  
pp. 347-356
Author(s):  
V. V. Yakovlev
Keyword(s):  
Two Dimensional ◽  
Variable Depth ◽  
Dimensional Models

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

The gauge technique and two dimensional models

1983 ◽  
Vol 131 (4-6) ◽  
pp. 385-389 ◽  
Author(s):  
George Thompson
Keyword(s):  
Two Dimensional ◽  
Dimensional Models

Soluble Two-Dimensional Models of Generally Covariant Field Theories

1973 ◽  
Vol 7 (8) ◽  
pp. 2309-2310
Author(s):  
Joseph Klarfeld ◽  
Alexander L. Harvey
Keyword(s):  
Field Theories ◽  
Two Dimensional ◽  
Dimensional Models ◽  
Generally Covariant ◽  
Covariant Field

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

Towards Real-Time Simulation of Two-Dimensional Models for Electrodeposition/Stripping in Lithium-Metal Batteries

2021 ◽  
Vol MA2021-02 (1) ◽  
pp. 176-176
Author(s):  
Taejin Jang ◽  
Lubhani Mishra ◽  
Krishna Shah ◽  
Akshay Subramaniam ◽  
Maitri Uppaluri ◽  
...  
Keyword(s):  
Real Time ◽  
Two Dimensional ◽  
Lithium Metal ◽  
Real Time Simulation ◽  
Lithium Metal Batteries ◽  
Time Simulation ◽  
Dimensional Models

The large N limit of two-dimensional models

2010 ◽  
pp. 165-174
Author(s):  
Yitzhak Frishman ◽  
Jacob Sonnenschein
Keyword(s):  
Two Dimensional ◽  
Large N ◽  
Dimensional Models
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