Let H be a hypergraph. For a k-edge coloring c : E(H) → {1, . . . , k} let f(H, c) be the number of components in the subhypergraph induced by the color class with the least number of components. Let fk(H) be the maximum possible value of f(H, c) ranging over all k-edge colorings of H . If H is the complete graph Kn then, trivially, f1(Kn) = f2(Kn) = 1. In this paper we prove that for n ≥ 6, f3...

This paper presents a simulation model for a silicon micromachined Knudsen pump that combines analytical and numerical methods. It involves numerical modeling of the thermal response, followed by an analytical estimate of the pumping using Kennard’s model. The loss of performance resulting from gas diffusion though walls of the pump is specifically addressed. The results are subsequently valida...

Molecular dynamics simulations are used to model the evaporation of a Lennard–Jones argon nanodroplet into its own vapor for a wide range of ambient temperatures and ambient pressures. The transitions from i high to low Knudsen number evaporation and ii subcritical to supercritical evaporation are observed. At a low ambient pressure of 0.4 MPa, the initial droplet Knudsen number is 1 and the dr...

Different nonkinetic approaches are adopted in this paper towards theoretically predicting the experimentally observed phenomenon of enhanced mass flow rates accompanying pressure-driven rarefied gas flows through microchannels. Our analysis utilizes a full set of mechanically consistent volume-diffusion hydrodynamic equations, allowing complete, closed-form, analytical solutions to this class ...

At the microscale, even moderate temperature differences can result in significant Knudsen forces generated by the energy exchange between gas molecules and solids immersed in a gas. Creating, controlling and measuring Knudsen forces in microsystems can be an arduous task since only limited theory exists at present. This present study investigates the mechanism of Knudsen forces in detail based...

As a natural generalization of graph coloring, Vince introduced the star chromatic number of a graph G and denoted it by χ∗(G). Later, Zhu called it circular chromatic number and denoted it by χc(G). Let χ(G) be the chromatic number of G. In this paper, it is shown that if the complement of G is non-hamiltonian, then χc(G)=χ(G). Denote by M(G) the Mycielski graph of G. Recursively define Mm(G)=...