In this paper, we develop what we refer to as economic circuit theory. Our purpose is to exploit the proven effectiveness of electrical circuit theory for the design, modeling, and analysis of complex electrical networks to economic systems; in particular, it permits us to incorporate the dynamics of price into those of the flow of physical commodities, analogous to how this is done for magnetic flux and electrical charge. The theory is agent-based, wherein agents are conceptualized as electrical components and the dynamics are determined by matching the agents' behavioral laws with the constitutive equations of the analogous components. We take a modern graph-theoretic approach, identifying the conditions for stock-flow consistency (Kirchhoff's current law) and price clearing (Kirchhoff's voltage law). With this, we develop the theory to model representative agents (equivalent networks), single-good markets (circuits), and general competitive markets (magnetically coupled circuits). The effectiveness of our theory is demonstrated through a dynamic scenario analysis of the economic circuit model for a two-good market.

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Current oil modeling techniques lack a comprehensive approach, as long-term oil prices are qualitatively modeled based on first principles, while short-term price transients are modeled using econometric methods. In this paper we propose a comprehensive bond-graph modeling approach in which price dynamics follow from first principles. The first principles that we use are derived from the recently developed economic-engineering theory in which price dynamics are modeled using Newtonian mechanics and price drivers are identified as forces. We reformulate a qualitative first-principles model developed by the Energy Information Administration (EIA) as a bond graph by modeling six identified price-driving factors as port-elements. The constitutive laws of these port-elements generate the price drivers, which through the interconnection structure of the bond graph yield the price dynamics. We demonstrate the bond-graph model by identifying its parameters and letting it estimate the oil price given historic oil supply data. Compared to a benchmark black-box model, we find that the bond graph has two advantages: (i) it achieves a better performance, and (ii) we know what its parameters and variables represent. The latter advantage allows us to validate the bond-graph model by reconstructing the oil inventory stocks and to manually adjust parameters by expert input.

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The dissipation obstacle refers to the problem that there is no general solution to shape the energy of dissipative port-Hamiltonian (pH) systems with the method of Casimir functions. This paper argues that it is caused by lack of a strictly symplectic structure of a dissipative port-Hamiltonian system. We develop a method of bicomplex pH systems that is strictly symplectic and we show how it overcomes the obstacle and allows one to systematically use Casimir functions to shape the energy.@en

We propose a new definition of collision risk that we call projective risk that is based on human perception.We showhowvarious collision scenarios can be modelled in a unified manner on the Riemann Sphere using projective and hyperbolic geometry. From this we show how a practical gauge for risk can be developed that we call the Risk Watch. Lastly, we show how the general problem of ship collision risk can be modelled using projective geometry and the cross ratio. @en

Ships collision assessment and conflict resolution are two main research problems in the maritime domain. In this paper, a methodology of collision risk assessment is introduced which is based on Velocity Obstacle (VO). In this paper, VO is employed to distinguish the dangerous velocities and judge the collision probability. The ship maneuverability is also considered to find the reachable velocities (RV) in a given time window. The percentage of dangerous velocities in all RV is defined as collision risk. By this approach, the proposed assessment model not only can identify the collision dangers, but also measure the probability of surviving in the encounter situation, regarding to its maneuverability. Several simulated encounter situations are presented to demonstrate this model. @en