Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 291
... flow - density data . If the density is almost zero , then the traffic usually travels at the maximum speed , umax . Even as the density is somewhat increased , the cars ' velocity remains nearly umax . Thus for small densities the flow ...
... flow - density data . If the density is almost zero , then the traffic usually travels at the maximum speed , umax . Even as the density is somewhat increased , the cars ' velocity remains nearly umax . Thus for small densities the flow ...
Page 322
... density wave velocity and car velocity . To do so the characteristic velocity is conveniently expressed in terms of the traffic velocity and density ... density . 71.3 . Suppose that the flow - density relationship was 322 Traffic Flow.
... density wave velocity and car velocity . To do so the characteristic velocity is conveniently expressed in terms of the traffic velocity and density ... density . 71.3 . Suppose that the flow - density relationship was 322 Traffic Flow.
Page 331
... flow occurs where dq / dp 0. Thus the density wave that is stationary ( density wave velocity equals zero ) indicates positions at which the flow of cars is a maximum . In the problem just discussed , as soon as the light changes from ...
... flow occurs where dq / dp 0. Thus the density wave that is stationary ( density wave velocity equals zero ) indicates positions at which the flow of cars is a maximum . In the problem just discussed , as soon as the light changes from ...
Contents
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude of oscillation analyze approximation Assume birth c₁ calculation characteristics Consider constant coefficient corresponding d2x dt2 damping de/dt decreases delay depend derived determine difference equation discussed dx dt dx/dt energy integral equilibrium population equilibrium solution equivalent example exercise exponential Figure formula function growth rate Hint increases initial conditions initial value problem isoclines linearized stability analysis logistic equation mass mathematical model maximum method of characteristics motion moving N₁ Newton's nonlinear pendulum number of cars obtained occur ordinary differential equations oscillation P₁ partial differential equation period phase plane Pmax population growth potential energy r₁ result sharks shock Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solution curves solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow trajectories Umax unstable equilibrium position variables vector x₁ yields zero