G. Roman | Searcharxiv

arXiv2022

On square-free numbers generated from given sets of primes

Let $x$ be a positive real number, and $\mathcal{P} \subset [2,\lambda(x)]$ be a set of primes, where $\lambda(x) \in \Omega(x^\varepsilon)$ is a monotone increasing function with $\varepsilon \in (0,1)$. We examine $Q_{\mathcal{P}}(x)$, where $Q_{\mathcal{P}}(x)$ is the element count of the set containing those positive square-free integers, which are smaller than-, or equal to $x$, and which are only divisible by the elements of $\mathcal{P}$.

math.NT↗

arXiv2015

Adsorption desorption processes on mesoscopic pores conected to microscopic pores of complex geometry using the Ising model

In this work we report studies of nitrogen adsorption and desorption onto solid surfaces using computer simulations of the three dimensional Ising model, for systems with complex porous structures at the mesoscopic and microscopic levels. A hysteresis cycle between the adsorption and desorption processes appears and we find that its characteristics are dependent on the geometry of the pore and on the strength of the surface fluid interaction. We obtained also an average adsorption isotherm, which represents a combination of differently shaped pores, and shows robust jumps at certain values of the chemical potential as a consequence of the structures of the pores. Lastly, we compare our results with experimental data and also report the filling process of microscopic pores connected with mesopores. It is argued that these predictions are useful for researchers working on the enhanced recovery of oil and for the design of new nanomaterials, among others.

cond-mat.soft↗