Phonon transport across constrictions formed by a nanowire or a nanoparticle on a substrate is studied by a numerical solution of the gray Boltzmann transport equation (BTE) resolving the effects of two length scales that govern problems of practical importance. Predictions of total thermal resistance for wire/substrate and particle/substrate combinations are made for the entire range of Knudse...

We present a combined experimental and theoretical study of the drag force acting on a high porosity aerogel immersed in liquid (3)He and its effect on sound propagation. The drag force is characterized by the Knudsen number, which is defined as the ratio of the quasiparticle mean free path to the radius of an aerogel strand. Evidence of the Knudsen-hydrodynamic crossover is clearly demonstrate...

For S a subordinator and Πn an independent Poisson process of intensity ne−x, x > 0, we are interested in the number Kn of gaps in the range of S that are hit by at least one point of Πn. Extending previous studies in [7, 10, 11] we focus on the case when the tail of the Lévy measure of S is slowly varying. We view Kn as the terminal value of a random process Kn, and provide an asymptotic analy...

Given a graph G, let fk be the number of forests of cardinality k in G. Then the sequence (fk) has been conjectured to be unimodal for any graph G. In this paper we confirm this conjecture for Kn and Kn,n by showing that the sequence for Kn is strictly increasing (when n ≥ 4) and the sequence for Kn,n is strictly increasing except for the very last term. As a corollary we also confirm the conje...

In this study, the nonequilibrium effects at the stagnation wall in one-dimensional unsteady micro ow responding to the external sinusoidal oscillation are investigated. The  uctuating behavior of the rareŽ ed medium is simulated by employing the unsteady DSMC method under various conditions with different acoustic Reynolds and Knudsen numbers. As a result, it is found that the nonequilibrium...

We establish an incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation (with a general collision kernel) considered over a bounded domain. Appropriately scaled families of DiPerna-Lions renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number ε goes to zero. Every limit point is a weak solut...

Let cr(Kn) be the minimum number of crossings over all rectilinear drawings of the complete graph on n vertices on the plane. In this paper we prove that cr(Kn) < 0.380473 (

On a land suitability assessment map that is derived from an overlay of n parent maps, each bearing k land capability categories, how many permutations of land suitability scores can there be when the scores are calculated by the commonly used rating and weighting method? In this paper, we estimate that this number is between k n(n−1) 2 and kn+1!/(kn!kn−1! · · · k!)k−1.