We describe an Eulerian path approach to the DNA fragment assembly that was originated by Idury and Waterman 1995, and then advanced by Pevzner et al. 2001b. This combinatorial approach bypasses the traditional “overlap-layout-consensus” approach and successfully resolved some of the troublesome repeats in practical assembly projects. The assembly results by the Eulerian path approach are accur...

Dilute liquid sprays can be modeled at the mesoscale using a kinetic equation, namely the Williams-Boltzmann equation, containing terms for spatial transport, evaporation and fluid drag. The most common method for simulating the Williams-Boltzmann equation uses Lagrangian particle tracking wherein a finite ensemble of numerical “parcels” provides a statistical estimate of the joint surface area...

Coarse Particles and Dust Storm Mortality In a paper titled "Episodes of High Coarse Partide Concentrations Are Not Associated with Increased Mortality," Schwartz et al. (1) concluded that "coarse particles from windblown dust are not associated with mortality risk." The authors seem to have overlooked the medical literature on the health effects of the historic U.S. dust storms of the dust bow...

We show that strictly abnormal geodesics arise in graded nilpotent Lie groups. We construct such a group, for which some Carnot geodesics are strictly abnormal and, in fact, not normal in any subgroup. In the 2-step case we also prove that these geodesics are always smooth. Our main technique is based on the equations for the normal and abnormal curves, that we derive (for any Lie group) explic...

We propose an Eulerian description of the bounce-back boundary condition based on the high-order implicit time marching schemes to improve the accuracy of lattice Boltzmann simulation in the vicinity of curved boundary. The Eulerian description requires only one grid spacing between fluid nodes when the second-order accuracy in time and space is desired, although high-order accurate boundary co...

The (q, r)-Eulerian polynomials are the (maj−exc, fix, exc) enumerative polynomials of permutations. Using Shareshian and Wachs’ exponential generating function of these Eulerian polynomials, Chung and Graham proved two symmetrical q-Eulerian identities and asked for bijective proofs. We provide such proofs using Foata and Han’s three-variable statistic (inv−lec, pix, lec). We also prove a new ...

1.1. Eulerian and Lagrangian coordinates. Let us begin with Eulerian and Lagrangian coordinates. The Eulerian coordinate (x, t) is the physical space plus time. The Eulerian description of the flow is to describe the flow using quantities as a function of a spatial location x and time t, e.g. the flow velocity u(x, t). This can be visualized by sitting on the bank of a river and watching the wa...