For a two-dimensional fluid in a square domain with no-slip walls, new direct numerical simulations reveal that the transition from steady to chaotic flow occurs through a sequence of various periodic and quasiperiodic flows, similar to the well-known Ruelle-Takens-Newhouse scenario. For all solutions beyond the ground state, the phenomenology is dominated by a domain-filling circulation cell, ...

Analytical results for the velocity distribution, mass flow rate, pressure gradient, wall shear stress, and vorticity in mixed electroosmotic/pressure driven flows are presented for two-dimensional straight channel geometry. We particularly analyze the electric double-layer (EDL) region near the walls and define three new concepts based on the electroosmotic potential distribution. These are th...

Solutions to the route choice problem for assumptions of user-optimality and system-optimality are presented for the road network of the Chicago region. Regionwide results show a 5% decrease in total travel time would be achieved during the morning peak period, if a system-optimal solution based on travel times were implemented. Among the costs of this solution is a 1.5% increase in vehicle-mil...

We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Hölder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modelled by Young towers with moderate tail decay rates. In particular, the position variable of the planar periodic Lorentz gas...

We obtain general results on the stability of mixing and rapid mixing (superpolynomial decay of correlations) for hyperbolic flows. Amongst Cr Axiom A flows, r ≥ 2, we show that there is a C2-open, Cr-dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing. This is the first general result on the stability of rapid mixing (or even mixing) for Axiom A flows that holds i...

Spontaneous spin-up, i.e., the significant increase of the total angular momentum of a flow that initially has no net angular momentum, is very characteristic for decaying two-dimensional turbulence in square domains bounded by rigid no-slip walls. In contrast, spontaneous spin-up is virtually absent for such flows in a circular domain with a no-slip boundary. In order to acquire an understandi...

I. Estabrook-Wahlquist Prolongations and Zero-Curvature Requirements Motivated by a desire to find new solutions of physically-interesting partial differential equations, we think of a k-th order pde as a variety, Y , of a finite jet bundle, J (M, N), with M the independentand N the dependent-variables for the pde. From this geometric approach, we can look for point symmetries, contact symmetri...

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions of subgroups generated by unipotent elements. More precisely: Let G be a Lie group (not necessarily connected) and Γ a closed subgroup of G. Let W be a subgroup of G such that AdG(W ) is contained in the Zariski clos...

Turbulent flows near walls have been the focus of intense study since their first description by Ludwig Prandtl over 100 years ago. They are critical in determining the drag and lift of an aircraft wing for example. Key challenges are to understand the physical mechanisms causing the transition from smooth, laminar flow to turbulent flow and how the turbulence is then maintained. Recent direct ...

A new model for turbulent flows in porous media is developed. The spatialand time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the k and e type equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms...