Physical Mathematics

The study of heat, work, and temperature, as well as their relationships, in large systems typically restricted to equilibrium or near equilibrium states is an essential subfield of physics known as classical thermodynamics. On the other hand, the majority of natural systems are not in thermodynamic equilibrium, or states that are not in equilibrium. Although nonequilibrium thermodynamics was developed more than a century ago to comprehend nonequilibrium phenomena like the measure of irreversibility, it is still a work in progress rather than a well-established field.

An electric load, production, or storages' flexibility on the electricity demand side can be advantageous. When power generation fluctuates with daily varying wind and solar power outputs or to enhance power supply security flexibility can be a solution to balance the electric power system. As a result, numerous projects on flexibility architecture, market models, economic viability, and the history of flexibility-enabling technology investigate the current topic of flexibility. Overall, the goal of flexibility is to provide tools to reduce costs like energy costs, power system investment costs, and operational costs. New strategies to reduce electricity costs are encouraged by rising costs. Since autumn 2021, prices in the European electricity markets have fluctuated more frequently. For instance, the monthly mean prices on the Nordic power market Nord Pool have increased to 140 €/MWh from 60 €/MWh.

Pavement made of Portland cement concrete (PCC) is subjected to a variety of environmental factors, including temperature fluctuations and chloride salt erosion, in addition to fatigue loading. As a result, PCC's durability and mechanical properties gradually decline. Crack initiation and propagation are caused by repeated wheel loading; It is thought to be the primary factor in PCC damage. PCCs' inner structure, durability, and mechanical properties under fatigue loading have all been the subject of research. Yang and others discovered that numerous cracks developed within PCC after it was loaded; The cracks got bigger until the concrete split. Yang and co. separated this procedure into three phases: initial compaction, stable and unstable crack expansion, respectively. Likewise, Zhao et al. investigated the PCC failure following a load and divided the process into three stages: dispersion of microcracks, selection of macrocracks, and expansion of the main crack.

Asphalt is a common building material for roads because it is a crucial adhesive. Asphalt ages through a series of aging processes, including volatilization, oxidation, and polymerization, which cause it to become hard and brittle under the influence of high temperature, oxygen, water, ultraviolet rays, and other factors. Pavement damage such as thermal crack, fatigue crack, and cohesion failure accelerate with asphalt aging, significantly shortening the pavement's service life. During the asphalt aging process, the most important reaction is oxidation. To improve asphalt's resistance to aging, it is essential to comprehend the oxidation reaction mechanism.