In this paper we calculate the Casimir energy for a massive fermionic field confined between two points in one spatial dimension, with the MIT Bag Model boundary condition. We compute the Casimir energy directly by summing over the allowed modes. The method that we use is based on the Boyer's method, and there will be no need to resort to any analytic continuation techniques. We explicitly show the graph of the Casimir energy as a function of the distance between the points and the mass of the fermionic field. We also present a rigorous derivation of the MIT Bag Model boundary condition.
This paper is devoted to the presentation of the lateral Casimir force between two sinusoidally corrugated eccentric cylinders. Despite that applying scattering matrix method explains the problem exactly, procedure of applying this method is somehow complicated specially at nonzero temperature. Using the proximity force approximation (PFA) helps to achieve the lateral Casimir force in a truly explicit manner. We assume the cylinders to be slightly eccentric with similar radiuses and separations much smaller than corrugations' wave length for the validity of PFA. For such short distances the effect of finite conductivity would be non negligible. In addition to the effect of finite conductivity, we investigate thermal corrections of the lateral Casimir force to reduce the inaccuracy of the result obtained by PFA. Assuming the Casimir force density between two parallel plates, the normal Casimir force between two cylinders is obtained. With the aid of additive summation of the Casimir energy between cylinders without corrugation, we obtain the lateral Casimir force between corrugated cylinders.
Photovoltaic (PV) systems are the leading solutions for reducing carbon dioxide (CO2) emissions in Iran’s energy system. However, there are some challenges to investing in PV systems in Iran, such as the low energy market price and the high investment cost of PV systems. Although the flat feed-in tariff (FiT) is defined to help purchase energy from the PV systems, it is not attractive to investors. In this paper, a mathematical formulation is developed for the planning problem of the PV systems with battery energy storages (BESs) considering two incentive policies: (1) Designing time-of-use FiT to encourage the PV systems to sell energy to the grid at peak hours (2) Participating in the carbon trading energy market. The insolation in Iran is calculated regarding mathematical formulations which divide Iran into eight zones. The results of the base case show high payback periods for all zones. In the presence of the incentive policies, the payback period decreases considerably from 5.46 yrs. to 3.75 yrs. for the best zone. Also, the net present value increases more than 170 percent in some zones compared to the base case.
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