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Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
The paper is now published in PRX Enegry. Please refer to the PRX version from now on. Anna B\"uttner and Frank Hellmann. "Complex Couplings-A Universal, Adaptive, and Bilinear Formulation of Power Grid Dynamics." The energy transition…
The activated rate process for non-equilibrium open systems is studied taking into account both internal and external noise fluctuations in a unified way. The probability of a particle diffusing passing over the saddle point and the rate…
Power systems are subject to fundamental changes due to the increasing infeed of decentralised renewable energy sources and storage. The decentralised nature of the new actors in the system requires new concepts for structuring the power…
The main topic of this work concerns the formulation of the equations of motion and the consequent energy balance that they imply for this type of systems, In particular, the analytical development that we will carry out on the equations of…
Mesoscopic quantum systems exhibit complex many-body quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, non-interacting theories display a rich landscape of…
Different from the quasi-static network in the traditional power system, the dynamic network in the power-electronic-dominated power system should be considered due to rapid response of converters' controls. In this paper, a nonlinear…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with…
We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a…
We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their…
For a 2-dimensional freely jointed chain with 3 particles and a related model, the average and variance of the kinetic energies of each particle in thermal equilibrium are exactly obtained. The same is done for a related model. The excess…
When a long-term energy constraint is imposed to a transmitter, the average energy-efficiency of a transmitter is, in general, not maximized by always transmitting. In a cognitive radio context, this means that a secondary link can…
A theoretical framework is proposed for an energy decomposition scheme along the reaction coordinate, in which the ensemble average of the potential energy weighted with reactive flux intensity is decomposed into energy components at the…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
Minimizing both power fluctuations and energy waste in an electrical grid is a central challenge to energy policy. Any discrepancy between power production and loads may lead to inefficiencies and instability in the system. Right now, the…
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric…
For systems with only short-range forces and shallow 2-body bound states, the typical strength of any 3-body force in all partial-waves, including external currents, is systematically estimated by renormalisation-group arguments in the…