Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 314
... traffic , we know that increased traffic density does not appre- ciably reduce a car's velocity . In this case , what is the velocity of a density wave ? 69. An Interpretation of Traffic Waves In this section , we obtain , in an ...
... traffic , we know that increased traffic density does not appre- ciably reduce a car's velocity . In this case , what is the velocity of a density wave ? 69. An Interpretation of Traffic Waves In this section , we obtain , in an ...
Page 348
... density , the differential conservation law becomes a partial differential equation for the traffic density . One or more of these assumptions must be modified , but only in regions along the highway where the traffic density has been ...
... density , the differential conservation law becomes a partial differential equation for the traffic density . One or more of these assumptions must be modified , but only in regions along the highway where the traffic density has been ...
Page 360
... density at the entrance x = = 0 is p ( 0 , 1 ) = { Ρι 0 < t < T ρο t > t and the initial density is uniform along the highway ( p ( x , 0 ) = Po , x > 0 ) . Assume that p1 is lighter traffic than po and both are light traffic ( i.e. ...
... density at the entrance x = = 0 is p ( 0 , 1 ) = { Ρι 0 < t < T ρο t > t and the initial density is uniform along the highway ( p ( x , 0 ) = Po , x > 0 ) . Assume that p1 is lighter traffic than po and both are light traffic ( i.e. ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero