Conference Session

Applied Mathematics

Collection

2007 Annual Conference & Exposition

Authors

S.K. Sen, Florida Institute of Technology; Gholam Ali Shaykhian, NASA

Tagged Divisions

Mathematics

kunit length of trail laid by the kth ant on the edge (i, j ) between time t and t - n . The quantity m Fvk ?1 ij k measures the additional trail traffic, whereFv ij ? Q / Lk if kth ant travels the edge (i, j ) in its tour in time [t , t - n], else 0 (6) kwhere Q is a constant and Lk is the tour length of the kth ant so that the shorter the tour is, themore will be the chemical reinforcement. The quantity of trail v ij at time t ? 0 is set to a smallconstant c . A data structure, say, cv list, where cv stands for “city-visited” is maintained. This list is adynamically growing vector that consists of all the cities already visited by an ant up to time t(maintaining the order in which

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

John Quintanilla, University of North Texas; Nandika D'Souza, University of North Texas; Jianguo Liu, University of North Texas; Reza Mirshams, University of North Texas

Tagged Divisions

Mathematics

uniform load of intensity q. The deflection v(x) of the beam satisfies the conditions qx 2 qL2 v' ' ( x ) = − qLx + , 2 2 v' (0) = 0, v ( 0) = 0. Solve this initial-value problem for v(x). Your answer will involve q and L. • A cantilever beam is subjected to a moment M0 acting at the free end. The strain energy is defined to be equal to L M2 U = ∫ 0 dx, Page 12.938.5 0 2 EI 4 where the

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

Günter Bischof, Joanneum University of Applied Sciences, Department of Automotive Engineering,; Emilia Bratschitsch, Joanneum University of Applied Sciences, Department of Automotive; Annette Casey, Joanneum University of Applied Sciences, Department of Automotive Engineering,; Domagoj Rubesa, Joanneum University of Applied Sciences, Department of Automotive Engineering,

Tagged Divisions

Mathematics

least squares procedure by solving it for all j coastdown data sets in conjunction withsimultaneous consideration of appropriate constraining condition q (a1, j ) so that not only r r2( ) A a − b is minimized but r r2 ( ) A a − b + λ q (a1, j ) = min . , (5)where λ is a Lagrangian multiplier. In this way the coefficients a2 of the different vehicleconfigurations and thus their aerodynamic drag coefficients cd can be determined 7.In Figure 3 the velocity-time histories of the coastdowns of a vehicle with three differentaerodynamic configurations is illustrated. The students’ task was the