How Computers Pave the Way for Science Daniel O’Hara Modeling in Science

Overview Definition of Model The Main Types of Models Explanation of Analog Model Example of Analog Model Explanation of Numerical Model Explanation and Example of Domained Model Explanation and Example of Non–Domained Model Summary

Definition of a Model Definition: A schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics [1]. In Summary: A simplified representation of a system. Used To: Observe the Natural Occurrence of Events Create Equations for Processes Test Hypotheses and Theories Predict the Outcome of Occurrences

Main Types of Models Analog Model Numerical Model [2] [3]

Analog Models Definition: An analog model is a scaled representation of a system using physical materials. Used to: Observe the Natural Occurrences of Events Create Equations for Processes Major Constraint: Finding similarties between the actual environment and scaled materials (i.e. Size, Density, etc.)

Analog Models - Example [4]

Numerical Models Definition: A Numerical Model is a computer generated representation of the system which applies known equations to calculate the results of processes. Used to: Test Hypotheses and Theories Predict the Outcome of Occurrences Differences in Numeric Models: Domained vs. Non–Domained

Numeric Models (cont’d) Environment is made of multi-dimensional grids/matrices with each cell holding multiple variables for the model [5] [6]

Domained Model Area of study has set boundaries that determine input/output interaction with the surrounding environment. Boundaries must be well controlled as to not alter the law of the conservation of mass. If model focuses on processes over time, loops are used to perform each calculation in every cell per step in time, that represents the overall activity of the environment.

Case Study – Shelf Processes Sediment Salinity Temperature Long-shore Current Cross-shore Current Solar Radiation Wind Boundary Cases: No Boundary Impermeable Boundary Permeable Boundary [7]

Model Results – Shelf Processes [7]

Non–Domained Model Data is not constrained to a set scale, so that the data set analyzed can represent an infinitesimally small or large area. Used mainly for prediction Drawbacks: Variable values are assumed based on presumptions of the study area. Result has high uncertainty, and in some cases cannot be tested for accuracy.

Case Study – Earthquakes [8]

Case Study – Earthquakes [9]

Summary Two Main Types of Models Analog Models use Physical Material Used for Observance and Creation of Equations Numerical Models use Computers for Calculations Used to Test Hypotheses and Theories, and to Predict Events.

References [1] Houghton Mifflin Company (2009). “Model”. The American Heritage Dictionary of the English Language. Received Feb. 20, [2] Weller, R. (2009). “Sandbox Experiment – Overall”. Cochise College Structural Geology Illustrations. Received Feb. 20, [3] Ghiasi, V., Omar, H., Huat, B.B.K., Muniandi, R., Yusof, Z.B.M. (2011) "Risk management overview of tunnels using numerical modeling", Journal of Engineering, Design and Technology, Vol. 9 Iss: 1, pp.110 – 124 [4] HVBStructGeol (2010). “Sandbox Model”. YouTube. Received Feb. 20, [5] MathWorks (2012). “Curve Fitting Toolbox”. The MathWorks, Inc html. Received Feb. 20, html [6] vBulletin (2012). “Space time distortion grid representations”. Physics Forums. Received Feb. 20, [7] O’Hara, D., Harris, C., Kniskern, T., Moriarty, J. (2011). “Gravity Driven Sediment Transport on Different Continental Shelves: Analysis from Numerical Modeling”. Virginia Institute of Marine Sciences. Gloucester Point, VA. [8] Dutch, S. (2010). “Faults and Earthquakes”. University of Wisconsin – Green Bay. Received Feb. 21, [9] Zalohar, J. and Vrabec, M. (2010). “Kinematics and Dynamics of Fault Reactivation: The Cosserat Approach”. Journal of Structural Geology, v. 32, p. 15 – 27. [10] O’Hara, D., Lewis, J., Rau, R. – J. (2011). “Slip Partitioning Offshore Southeast Taiwan and Southward Propagation of the Longitudinal Valley Fault: Evidence from Preferred Nodal Plane Slip Vectors”. American Geophysical Union Fall Conference San Francisco, CA.

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