The numerical simulation of a Poiseuille flow in a narrow channel using the molecular dynamics simulation (MDS) is performed. Poiseuille flow of liquid Argon in a nanochannel is simulated by embedding the fluid particles in a uniform force field. Density, velocity and Temperature profiles across the channel are investigated. When particles will be inserted into the flow, it is expected that the...

We consider an embedding of planar maps into equilateral triangle $\Delta$ which we call the Cardy embedding. The is a discrete approximation conformal map based on percolation observables that are used in Smirnov's proof Cardy's formula. Under embedding, induces metric and area measure boundary $\partial \Delta$. prove for uniformly sampled triangulations, measures converge jointly scaling lim...

In a random graph with a spatial embedding, the probability of linking to a particular vertex v decreases with distance, but the rate of decrease may depend on the particular vertex v, and on the direction in which the distance increases. In this article, we consider the question when the embedding can be chosen to be uniform, so the probability of a link between two vertices depends only on th...

Chvátal, Rödl, Szemerédi and Trotter [1] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform ‘pseudo-random’ hypergraphs. keywords: hypergraphs; regularity lemm...