412 NOTICES OF THE AMS VOLUME 51, NUMBER 4 Billiards are dynamical systems. In the simplest case, a “billiard table” is a compact domain Q ⊂ Rd with a piecewise smooth boundary. For a large part of the theory the class of smoothness plays no role. The reader is invited to think about components of the boundary ∂Q as subsets of C∞-submanifolds of codimension 1. The phase space M of the billiard ...

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the η-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is ηEinstein manifold if and only if base manifold is the space of constant sectional c...

For these distributions only the leading vehicle in a platoon has its speed measured. The rationale for measuring these is to get an estimate of the desired speed of traffic at the point of measurement. The distributions in Figure 1 are of this type. They are produced by combining the results of a number of surveys at different sites into a representative distribution weighted by the traffic fl...

In this article we give a geometric interpretation of the Hitchin component T (Σ) ⊂ Rep(π1(Σ),PSL4(R)) of a closed oriented surface of genus g ≥ 2. We show that representations in T (Σ) are precisely the holonomy representations of properly convex foliated projective structures on the unit tangent bundle of Σ. From this we also deduce a geometric description of the Hitchin component T (Σ, Sp4(R...

This work presents an electrophysiologically and dynamically consistent musculoskeletal model to predict stiffness in the human ankle and knee joints as derived from the joints constituent biological tissues (i.e., the spanning musculotendon units). The modeling method we propose uses electromyography (EMG) recordings from 13 muscle groups to drive forward dynamic simulations of the human leg i...

The standard eigenfunctions φλ = ei〈λ,x〉 on flat tori Rn/L have L-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that L2normalized eigenfunctions have uniformly bounded L-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with quantum co...

For any ε > 0, we construct an explicit smooth Riemannian metric on the sphere Sn, n ≥ 3, that is within ε of the round metric and has a geodesic for which the corresponding orbit of the geodesic flow is ε-dense in the unit tangent bundle. Moreover, for any ε > 0, we construct a smooth Riemannian metric on S, n ≥ 3, that is within ε of the round metric and has a geodesic for which the complemen...

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. This is the natural generalization of the well known almost Kählerian structure on T (M). W...

Current theories on the role of visuomotor coordination in driving agree that active sampling of the road by the driver informs the arm-motor system in charge of performing actions on the steering wheel. Still under debate, however, is the nature of visual cues and gaze strategies used by drivers. In particular, the tangent point hypothesis, which states that drivers look at a specific point on...

Many applications are based on the use of materials with heterogeneous microstructure. Prominent examples are fiber-reinforced composites, multi-phase steels or soft tissue to name only a few. The modeling of structures composed of such materials is suitably carried out at different scales. At the micro scale, the detailed microstructure is taken into account, whereas the modeling at the macro ...