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Unformatted text preview: Assignment 1 ( SCI 3510 Mathematical and Statistical Modelling ) (1) Prove the equation of state for variable velocity u ( x, t ) and density ρ ( x, t ). (2) Suppose that the velocity u ( x, t ) is selected as the prime variable. Find the relation between flux q ( x, t ) and velocity u ( x, t ) for Greenshields model. Then prove the identity: U max parenleftbigg ρ- ρ 2 ρ max parenrightbigg = ρ max parenleftbigg u- u 2 U max parenrightbigg , (3) It is officially suggested by the Transportation Department of US to keep three car-length apart from the front car for a safety drive. Show that the maximum flux reaches 3 4 q max for Greenshields model, if the principle of three car-length is obeyed. (4) Suppose the velocity-density relation is modelled as u ( ρ ) = U max parenleftbigg 1- ρ 2 ρ 2 max parenrightbigg , Give a brief discussion with comparison to Greenshields model ( 300 words limited )....
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This note was uploaded on 01/19/2012 for the course ECON 201 taught by Professor Wong during the Spring '11 term at CUHK.
- Spring '11