In this paper, we rst show that there are several equivalent keys for t + 1 chosen plaintexts if the degree of the reduced cipher is t?1. This is against the claim by Jakobsen and Knudsen. We also derive an upper bound on the number of equivalent last round keys for t + 1 chosen plaintexts. We further show an eecient method which nds all the equivalent keys by using Rabin's root nding algorithm...

Abstract. Comparison of particle (DSMC) simulation with the numerical solution of the Navier-Stokes (NS) equations for pressure-driven plane Poiseuille flow is presented and contrasted with that of the acceleration-driven Poiseuille flow. Although for the acceleration-driven case DSMC measurements are qualitatively different from the NS solution at relatively low Knudsen number, the two are in ...

A two dimensional numerical simulation has been performed for incompressible and compressible fluid flow through microchannels in slip flow regime. The Navier-Stokes equations have been solved in conjunction with Maxwell slip conditions for modeling flow field associated with slip flow regime. The wall roughness is simulated with triangular microelements distributed on wall surfaces to study th...

Studies at the University of Southern California have shown that an unconventional solid-state device, the Knudsen Compressor, can be operated as a micro-scale pump or compressor. The critical components of Knudsen Compressors are gas transport membranes, which can be formed from porous materials or densely packed parallel arrays of channels. An applied temperature gradient across a transport m...

This work assesses Lagrangian droplet evaporation models frequently used in spray combustion simulations, with the purpose of identifying influence modeling decisions on single behavior. Besides more simplistic models, evaluated strategies include a simple method to incorporate Stefan flow effects heat transfer (Bird’s correction), consider interaction and mass films (Abramzon–Sirignano model),...

We provide a model for the remarkable stability of surface nanobubbles to bulk dissolution. The key to the solution is that the gas in a nanobubble is of Knudsen type. This leads to the generation of a bulk liquid flow which effectively forces the diffusive gas to remain local. Our model predicts the presence of a vertical water jet immediately above a nanobubble, with an estimated speed of ∼3....

The mysterious stability of nanobubbles on surfaces is a puzzle baffling soft matter and colloid scientists. Bubbles inside a fluid tend to be spherical, but surface bubbles have the appearance of blisters with typical widths of 1000 nanometers (nm) and heights of 20 nm. The existence of surface bubbles was proposed to explain the extremely long range and the magnitude of the strongly attractiv...