For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods Tγ lying in exponentially shrinking intervals (x−e−δx, x+ e), δ > 0, x → +∞. A general result is established which concerns hyperbolic flows admitting symbolic models whose corresponding Ruelle transfer operators satisfy some spectral estimates. This result applies to a variety of hy...

In this article we introduce the flow polynomial of a digraph and use it to study nowherezero flows from a commutative algebraic perspective. Using Hilbert’s Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals. It also yields an appealing proof that every bridgeless...

We study different renormalisation group flows for scale dependent effective actions, including exact and proper-time renormalisation group flows. These flows have a simple one loop structure. They differ in their dependence on the full field-dependent propagator, which is linear for exact flows. We investigate the inherent approximations of flows with a non-linear dependence on the propagator....

We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kote...

The discrete particle method (DPM) is used to model granular flows down an inclined chute with varying basal roughness, thickness and inclination. We observe three major regimes: arresting flows, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed: for small inclinations the flow can be highly energetic and strongly layered in dep...

In this paper we study algorithms for pricing of financial contracts using a lattice process of interest rates. If the cash-flows generated by the contract depend on the history of the interest rates (path dependent contracts), then the pricing algorithms are typically of exponential complexity. We demonstrate that for some models, there exist polynomial algorithms for path dependent contracts....

BACKGROUND Severe acute respiratory syndrome (SARS) originated in China in 2002, and it spread to 26 provinces in mainland China and 32 countries across five continents in a matter of months. This outbreak resulted in 774 deaths. However, the spatial features and potential determinants of SARS input-output flows remain unclear. METHODS We used an adjusted spatial interaction model to examine ...

We study generation of magnetic fields involving large spatial scales by time-and space-periodic small-scale parity-invariant flows. The anisotropic magnetic eddy diffusivity tensor is calculated by the standard procedure involving expansion of magnetic modes and their growth rates in power series in the scale ratio. Our simulations, conducted for flows with random harmonic composition and expo...

We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...

An explosive growth in business applications using the Internet have resulted in a strong demand for some notion of reliability or quality of service. During periods of congestion or failure, the quality of service of all flows is degraded. As a result, a strong need for service differentiation in the flows to provide service guarantees. Today the internet carries different types of traffic wit...