This paper is concerned with the modeling and simulation of extremely large networks. We derive a timedependent diffusion–convection partial differential equation, the solution of which captures the global characteristics of a stochastic network model. Continuum modeling provides a powerful way to deal with the number of components in large networks and opens up the use of highly sophisticated ...

We show there is no categorical metric continuum. This means that for every metric continuum X there is another metric continuum Y such that X and Y have (countable) elementarily equivalent bases but X and Y are not homeomorphic. As an application we show that the chainability of the pseudoarc is not a first-order property of its lattice of closed sets.

The continuum field theoretic method has become the method of choice for multiscale structure-formation modeling of very different phase transformations in the past decade. One of the challenges in application of the method to transformations in real materials is to obtain the mesoscopic parameters, which characterize the thermodynamic system of interest. Significant progress has been made in t...

We present the results of our research that is positioned in the domain of system modeling. In particular, we present an object-oriented paradigm that provides a logically rigorous and complete theoretical base for various existing object-oriented frameworks. The strong points of the paradigm are presented by demonstrating how the paradigm can resolve a number of existing problems of the Unifie...

The existence of vugs or cavities in naturally fractured reservoirs has long been observed. Even though these vugs can be largely attributed to reserves of oil, natural gas, and groundwater, few investigations of vuggy fractured reservoirs have been conducted. In this paper, a new multiple-continuum conceptual model is developed, based on geological data and observations of core samples from ca...