We consider traffic flow dynamics for a network of signalized intersections, where the outflow from every link is constrained to be equal to a given capacity function if the queue length is positive, and equal to the minimum of cumulative inflow and capacity function otherwise. In spite of the resulting dynamics being discontinuous, recent work has proved existence and uniqueness of the resulti...

We consider traffic dynamics for a network of signalized intersections under fixed time control, where the outflow from every link is constrained to be equal to an autonomous capacity function (and hence fixed-time control) if the queue length is positive and equal to the cumulative inflow otherwise. In spite of the resulting dynamics being nonLipschitz, recent work has shown existence and uniq...

For an n-component link, Milnor’s isotopy invariants are defined for each multi-index I = i1i2...im (ij ∈ {1, ..., n}). Here m is called the length. Let r(I) denote the maximum number of times that any index appears in I. It is known that Milnor invariants with r = 1, i.e., Milnor invariants for all multi-indices I with r(I) = 1, are link-homotopy invariant. N. Habegger and X. S. Lin showed tha...

We construct a pair of isotopic link configurations that are not thick while preserving total length.

Physical knots and links are one-dimensional submanifolds of R with fixed length and thickness. We show that isotopy classes in this category can differ from those of classical knot and link theory. In particular we exhibit a Gordian Split Link, a two component link that is split in the classical theory but cannot be split with a physical isotopy.