Periodic switching strategies for an isoperimetric control problem with application to nonlinear chemical reactions

This paper deals with an isoperimetric optimal control problem for nonlinear control-affine systems with periodic boundary conditions. As it was shown previously, the candidates for optimal controls for this problem can be obtained within the class of bang-bang input functions. We consider a parametrization of these inputs in terms of switching times. The control-affine system under consideration is transformed into a driftless system by assuming that the controls possess properties of a partition of unity. Then the problem of constructing periodic trajectories is studied analytically by applying the Fliess series expansion over a small time horizon. We propose analytical results concerning the relation between the boundary conditions and switching parameters for an arbitrary number of switchings. These analytical results are applied to a mathematical model of non-isothermal chemical reactions. It is shown that the proposed control strategies can be exploited to improve the reaction performance in comparison to the steady-state operation mode.Comment: Submitted to "Applied Mathematical Modelling

Ab-initio calculations of fission product diffusion on graphene

A clear understanding of the diffusive behaviour of a wide variety of impurities is essential for the construction and safe operation of the class of nuclear reactors which employ graphite as a shielding material. As a means of gaining insight into this important problem, the bonding, activation energy and structural properties of a variety of the most common nuclear fission products on graphene have been examined using Density Functional Theory (DFT), illustrating the attendant mechanisms of bonding and ionic transport of the different species, as well as the tendency to form nanoscale clusters in bulk graphite. Simulations have been conducted using a variety of approximations to the exchange-correlation functional, and the relative importance of functional choice is discussed in the context of the adsorption and activation energies. Finally, our calculations are compared to the relevant experimental results, allowing us to draw some conclusions about the likely transport mechanisms at larger length and time scales

Mathematical modelling of a low-temperature hydrogen production process with In Situ CO2 capture

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Bombardment of Graphite and Amorphous Carbon Surfaces Using Molecular Dynamics Simulations: Toward A More Realistic Experimental Model

Molecular dynamics (MD) simulations are a useful computational tool in fields such as fusion research. Small but vital portions of fusion reactors are essential to their correct operation and longevity. Using the reactive bond order (REBO) and adaptive intermolecular REBO potentials, it is possible to model carbon-based systems, such as graphite diverter plates, under simulated bombardment. The degradation of these plates due to random bombardments from plasma can eventually incur costly shut downs. To gain a better understanding of the atomic-level dynamics that occur when a graphite and amorphous carbon surface undergo energetic, serial bombardment by atoms such as hydrogen, deuterium, and tritium, these two systems were evolved with the REBO and AIREBO potentials. It was found that the AIREBO potential gave different results with regards to surface evolution, sputter yield, and steady state formation. Graphite surfaces evolved to a much different steady state when compared to amorphous carbon, which lead to varied surface structure and may also lead to differing sputtering yields. An additional round of simulations was performed on graphite surfaces that were deeper in the direction normal to the surface. Based on the previous results, the AIREBO potential and two different bombardment energies were used, and the additional layers added allowed for greater fluences, defined by the number of impacts per unit area, to be achieved. As an additional improvement of the previous work, thermostats were set by using zones of control rather than employing the thermostat on the entire system, achieving atomic layer control of the thermostatted regions during the simulation. After employing these changes and evolving the simulations for only slightly larger fluences than previous simulations, the formation of voids within the graphite layers, or \u27bubbles\u27, was produced. Particle build-up consisting of gaseous D, D2, and other small molecules near the penetration depth caused the formation of these bubbles. It was found for 20 eV impact energies the penetration depth is well defined, because of the lower energy of insertion. The stopping power of the potential on these low energy insertions leads to a noticable build-up of D atoms near the penetration depth. For the 80 eV simulations, the penetration depth is broadened when compared with the 20 eV simulations. The impacts penetrate more layers with increased impact energy, with bubble formation occurring away from the average penetration depth. A comparison of retention ratios is also discussed, and found that the 80 eV simulations retained more D than the 20 eV simulations. To attempt to avoid the issue of bubble formation, and to expand on the capabilities of the MD code, graphite surfaces were expanded in the directions perpendicular to the insertion direction, and the ability to bombard the surface with multiple atom types was implemented. Another improvement was introduced in the code to allow the variable time step algorithm to be used in conjunction with the thermostat. These systems yielded a closer model to experimental conditions, where the energy of interaction between the layers of graphite is larger than the insertion energy of the incident particles. While only smaller fluences compared to previous work have been achieved for these systems, the systems have shown promise in terms of their surface evolution and behavior

Development in lithium neutron spectrometry for measurements of fast reactor spectra

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A theoretical study of pure and simple competition between two microbial species in configurations of two interconnected chemostat

It is known that two microbial populations competing purely and simply for a common substrate cannot coexist in a steady state in an environment which is spatially homogeneous. Hence they cannot coexist in a chemostat something which implies that a mixed culture of two pure and simple competitors cannot be maintained in a single ideal reactor in a steady state. The present study investigates theoretically pure and simple competition between two populations in two interconnected chemostats. Three reactor configurations are considered and analyzed. It is proved that two pure and simple competitors can coexist in a steady state in both reactors in cases where the conditions are such that they favor the growth of one species in one reactor and the growth of its competitor in the other vessel. It is then concluded that spatial inhomogeneities can lead to steady state coexistence of pure and simple competitors. The results of this study have been derived analytically and numerically. The dynamic behavior of the system at all possible steady states has been studied analytically. A number of conditions sufficient and/or necessary for the existence of each one of the possible steady states have been derived also analytically. The numerical studies have shown that one can always find a range in the operating parameters space where coexistence occurs, that the steady states are mutually exclusive and that no steady state exhibits multiplicity. The results are presented in series of two-dimensional operating diagrams and the effect of all parameters on the behavior of the system is studied and discussed in detail. It has been also proved that it is not necessary for coexistence to externally feed both vessels with nutrient medium and that there is a design configuration which makes the environment always homogeneous in which case coexistence is impossible