Dynamic stability and spatial heterogeneity in the individual-based modelling of a Lotka-Volterra gas

Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of 800 x 800 squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the mathematical description by the Lotka-Volterra equations. The spatial patterns were evaluated using entropy and a cross correlation coefficient for the spatial distribution of both populations. In some simulations the system oscillated with variable amplitude but rather stable period, but the particle distribution departed from the (quasi) homogeneous state and did not return to it. The distribution entropy oscillated in the same rhythm as the population, but its value was smaller than in the initial homogeneous state. The cross correlation coefficient oscillated between positive and negative values. Its average value depended on the space scale applied for its evaluation with the negative values on the small scale (separation of preys from predators) and the positive values on the large scale (aggregation of both populations). The stability of such oscillation patterns was based on a balance of the population parameters and particle mobility. The increased mobility (particle mixing) resulted in unstable oscillations with high amplitude, sustained homogeneity of the particle distribution, and final extinction of one or both populations

Statistical Assessment of the Microstructure of Barite Aggregate from Different Deposits Using X-Ray Microtomography and Optical Microscopy

Two different barite ore (barium sulfate BaSO4) specimens from different localizations were tested and described in this paper. Analysis of the microstructure was performed on polished sections, and on thin sections using X-ray microtomography (micro-CT), and optical microscopy (MO). Microtomography allowed obtaining three-dimensional images of the barite aggregate specimens. In the tomograms, the spatial distribution of the other polluting phases, empty space as well as cracks, pores, and voids – that exceeded ten micrometers of diameter-were possible to visualize. Also, the micro-CT allowed distinguishing between minerals of different density, like SiO2 and BaSO4. Images obtained and analyzed on thin sections with various methods using the optical microscopy in transmitted light delivered additional information on the aggregate microstructure, i.e. allow for estimation of the different kinds of inclusions (like the different density of the minerals) in the investigated specimens. Above methods, which were used in the tests, completed each another in order to supply a set of information on inclusions’ distribution and to present the important differences of the barite aggregate specimens microstructure

Statistical Assessment of the Microstructure of Barite Aggregate from Different Deposits Using X-Ray Microtomography and Optical Microscopy

Two different barite ore (barium sulfate BaSO4) specimens from different localizations were tested and described in this paper. Analysis of the microstructure was performed on polished sections, and on thin sections using X-ray microtomography (micro-CT), and optical microscopy (MO). Microtomography allowed obtaining three-dimensional images of the barite aggregate specimens. In the tomograms, the spatial distribution of the other polluting phases, empty space as well as cracks, pores, and voids – that exceeded ten micrometers of diameter-were possible to visualize. Also, the micro-CT allowed distinguishing between minerals of different density, like SiO2 and BaSO4. Images obtained and analyzed on thin sections with various methods using the optical microscopy in transmitted light delivered additional information on the aggregate microstructure, i.e. allow for estimation of the different kinds of inclusions (like the different density of the minerals) in the investigated specimens. Above methods, which were used in the tests, completed each another in order to supply a set of information on inclusions’ distribution and to present the important differences of the barite aggregate specimens microstructure