The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the Euclidean plane. The k-planar crossing number crk(G) of G is min{cr(G1) + cr(G2) + . . .+ cr(Gk)}, where the minimum is taken over all possible decompositions of G into k subgraphs G1, G2, . . . , Gk. The problem of computing the crossing number of complete graphs, cr(Kn), exactly for sm...

Abstract. Pumping performance of a disk-type drag pump is studied numerically and experimentally. Molecular transition and slip flows that arise in a spiral channel on the rotating disk are simulated by using particle and continuum methods. The particle approach employs the direct simulation Monte Carlo (DSMC) method, and the continuum approach solves the Navier-Stokes (N-S) equations. A new DS...

In this paper, we investigate rarefied jet gas flows out of a two-dimensional slit and impinges on a flat plate which is set vertically to the plume flow direction. With a relation between velocity-directions and geometry-positions, we obtain several analytical collisionless flow property distributions in front of the plate. This study further provides near-plate collisionless flow properties i...

A non-destructive, fast 2D profile monitor for an ion beam accelerator can be achieved by creating a high-density gas-sheet target in vacuum. It is known that gas flow through long rectangular channel with very small gap-to-width ratio effectual forming sheet. To obtain sheet the desired performance, spatial distribution of emitted molecules candidate should examined more detail. As part develo...

Kinetic theory of gases, as described by the Boltzmann or model kinetic equations, provides a solid theoretical approach for solving microscale transport phenomena in gases. Due to significant advancement in computational kinetic theory and due to the availability of high speed parallel computers, kinetic equations may be solved numerically with modest computational effort. In this framework, r...

Bounds are determined for the smallest m = Dr(Kn) such that every drawing of Km in the plane (two edges have at most one point in common) contains at least one drawing of Kn with the maximum number (:) of crossings. For n = 5 these bounds are improved to 11 :::; Dr(K5) 113. A drawing D( G) of a graph G is a special realization of G in the plane. The vertices are mapped into different points of ...

Coagulation coefficient of aerosol particles due to Brownian motion is an important issue describe change in particle size distribution. Motion diffusive continuous region (small Knudsen number; Kn ), or like free molecular gaseous (large ). Fuchs (1964) presented expression coagulation transition regime by a so-called “Flux Matching” method. In his method, transportation inside the “limiting s...

H2O transport through a packed bed of Johnson Space Center number 1A (JSC-1A) lunar regolith simulant was examined at relevant temperatures and pressures for in-situ resource utilization (ISRU) on the Moon. Experimentation conducted over range from 50 to 2065 Pa ∼350 K, corresponding Knudsen numbers 0.3 < Kn 11. Pressure temperature conditions were toward ISRU technologies. A piecewise f...