Two-dimensional Models of Human Dispersals: Tracking Reaction-Diffusion Fronts on Heterogeneous Surfaces

2015 ◽  
pp. 430-444 ◽  
Keyword(s):  
Reaction Diffusion ◽  
Two Dimensional ◽  
Heterogeneous Surfaces ◽  
Dimensional Models

Simulations of a Fox-Rabies Epidemic on an Island Using Space-Time Finite Elements

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1230-1240 ◽  
Author(s):  
Gwen A. Gardner ◽  
Leslie R. T. Gardner
Keyword(s):  
Numerical Model ◽  
Finite Elements ◽  
Field Data ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Dimensional Models

Abstract The two-dimensional reaction diffusion equations for the spread of rabies in a logistically growing fox population are solved numerically. The method, based upon Galerkin’s approach, uses space-time finite elements. The numerical model is shown, quantitatively, to possess the essential features of earlier one and two-dimensional models and to reproduce the values of field data accurately. A more realistic illustration of the use of the model, a study of the spread of rabies over the Isle of Anglesey, is then discussed.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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
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