The rapid spread of COVID-19 has severely impacted many sectors, including the electricity sector. The reliability of the electricity sector is critical to the economy, health, and welfare of society; therefore, supply and demand need to be balanced in real-time, and the impact of unexpected factors should be analyzed. During the pandemic, behavioral restrictions such as lockdowns, closure of factories, schools, and shopping malls, and changing habits, such as shifted work and leisure hours at home, significantly affected the demand structure. In this research, the restrictions and their corresponding timing are classified and mapped with the Turkish electricity demand data to analyze the estimated impact of the restrictions on total demand and daily demand profile. A modulated Fourier Series Expansion evaluates deviations from normal conditions in the aggregate demand and the daily consumption profile. The aggregate demand shows a significant decrease in the early phase of the pandemic, during the period March–June 2020. The shape of the daily demand curve is analyzed to estimate how much demand shifted from daytime to night-time. A population-based restriction index is proposed to analyze the relationship between the strength and coverage of the restrictions and the total demand. The persistency of the changes in the daily demand curve in the post-contingency period is analyzed. These findings imply that new scheduling approaches for daily and weekly loads are required to avoid supply-demand mismatches in the future. The long-term policy implications for the energy transition and lessons learned from the COVID-19 pandemic experience are also presented.

Einstein’s equations in the Newman–Penrose formalism for vacuum, vacuum with cosmological constant, and electrovacuum fields are expressed as Cartan ideals. Two different prolongations of these ideals are obtained. These two types of prolonged ideals generalize previous prolongations for vacuum fields to vacuum with cosmological constant and electrovacuum fields. Some Bäcklund transformations are obtained for vacuum, vacuum with cosmological constant, and electrovacuum fields. These Bäcklund transformations include the generalized Kerr–Schild (GKS) transformation, and a two-parameter generalization of the GKS transformation. GKS transformations are studied in detail. Expressions for the transformation of Newman–Penrose quantities are given and algebraic properties are discussed. It is shown that the GKS transformation cannot give algebraically general and asymptotically flat vacuum and electrovacuum space-time metrics.

The thermal phase transition temperatures of high (HMP) and low melting point (LMP) agarose gels were investigated by using UV–vis spectroscopy techniques. Transmitted light intensities from the gel samples with different agarose concentrations were monitored during the heating (gel-sol) and cooling (sol–gel) processes. It was observed that the transition temperatures, T_m, defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from the UV–vis technique, slightly increased by increasing the agarose concentration in both the HMP and LMP samples. Here, we express the phase transitions of the agar-water system, as a representative of reversible physical gels, in terms of a modified Susceptible-Infected-Susceptible epidemic model whose solutions are the well-known 5-point sigmoidal curves. The gel point is hard to determine experimentally and various computational techniques are used for its characterization. Based on previous work, we locate the gel point, T₀, of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating), T₀ is greater than T_m, i.e. later in time, and the difference between T₀ and T_m is reduced as the agarose content increases. For the sol-gel transition (cooling), T₀ is again greater than T_m, but it is earlier in time for all agarose contents and moves forward in time and gets closer to T_m as the agarose content increases.