An Advanced Coupled Genetic Algorithm for Identifying Unknown Moving Loads on Bridge Decks

This study deals with an inverse method to identify moving loads on bridge decks using the finite element method (FEM) and a coupled genetic algorithm (c-GA). We developed the inverse technique using a coupled genetic algorithm that can make global solution searches possible as opposed to classical gradient-based optimization techniques. The technique described in this paper allows us to not only detect the weight of moving vehicles but also find their moving velocities. To demonstrate the feasibility of the method, the algorithm is applied to a bridge deck model with beam elements. In addition, 1D and 3D finite element models are simulated to study the influence of measurement errors and model uncertainty between numerical and real structures. The results demonstrate the excellence of the method from the standpoints of computation efficiency and avoidance of premature convergence

A formula for the braid index of links

AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a link L in S3 in terms of the v-span of the Homfly-pt polynomial PL(v,z) of L: 12spanvPL(v,z)+1⩽b(L). Up to now, many classes of knots and links satisfying the equality of this Morton–Franks–Williams's inequality have been founded. In this paper, we give a new such a class K of knots and links and make an explicit formula for determining the braid index of knots and links that belong to the class K. This gives simultaneously a new class of knots and links satisfying the Jones conjecture which says that the algebraic crossing number in a minimal braid representation is a link invariant. We also give an algorithm to find a minimal braid representative for a given knot or link in K

The canonical genus for Whitehead doubles of a family of alternating knots

For any given integer $r \geq 1$ and a quasitoric braid $\beta_r=(\sigma_r^{-\epsilon} \sigma_{r-1}^{\epsilon}...$ $\sigma_{1}^{(-1)^{r}\epsilon})^3$ with $\epsilon=\pm 1$, we prove that the maximum degree in $z$ of the HOMFLYPT polynomial $P_{W_2(\hat\beta_r)}(v,z)$ of the doubled link $W_2(\hat\beta_r)$ of the closure $\hat\beta_r$ is equal to $6r-1$. As an application, we give a family $\mathcal K^3$ of alternating knots, including $(2,n)$ torus knots, 2-bridge knots and alternating pretzel knots as its subfamilies, such that the minimal crossing number of any alternating knot in $\mathcal K^3$ coincides with the canonical genus of its Whitehead double. Consequently, we give a new family $\mathcal K^3$ of alternating knots for which Tripp's conjecture holds.Comment: 33 pages, 27 figure