Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 154
... zero is an equilibrium popula- tion in the sense that if the population was initially at that value it would stay there . That is , the number of births would exactly offset the number of deaths . Using the logistic model , equation ...
... zero is an equilibrium popula- tion in the sense that if the population was initially at that value it would stay there . That is , the number of births would exactly offset the number of deaths . Using the logistic model , equation ...
Page 325
... zero density is always umax , the car velocity for zero density . The characteristic curves which intersect the x - axis for x > 0 are all straight lines with velocity umax . Hence the characteristic which emanates from x = x 。( xo > 0 ...
... zero density is always umax , the car velocity for zero density . The characteristic curves which intersect the x - axis for x > 0 are all straight lines with velocity umax . Hence the characteristic which emanates from x = x 。( xo > 0 ...
Page 372
... zero traffic . It is as though the light separates traffic of zero density from traffic of density Pmax , as illustrated in Fig . 82-2 . In this configuration the lighter traffic ( p = 0 ) is behind heavier traffic ( p = po ) and hence ...
... zero traffic . It is as though the light separates traffic of zero density from traffic of density Pmax , as illustrated in Fig . 82-2 . In this configuration the lighter traffic ( p = 0 ) is behind heavier traffic ( p = po ) and hence ...
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