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A combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schr\"odinger equation. The latter is replaced by a system of linear first-order differential equations, which enables one to…
Future power grids will be operating a large number of heterogeneous dynamical actors. Many of these will contribute to the fundamental dynamical stability of the system. By taking a complexity theoretic perspective we derive a normal form…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
Determining the underlying equations of motion and parameter values for vibrating structures is of great concern in science and engineering. This work introduces a new data-driven approach called the energy-based dual-phase dynamics…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
This article presents a simple port-Hamiltonian formulation of the equations for an RLC electric circuit as a differential-algebraic equation system, and a proof that structural analysis always succeeds on it for a well-posed circuit, thus…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a…
Considering increasing distributed energy resources and responsive loads in smart grid, this paper proposes a stochastic simulation approach for stability analysis of a power system having stochastic loads. The proposed approach solves a…
The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…
Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…
The study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…
We address the linear-mode analysis performed near an equilibrium configuration in the fluid rest frame with a dynamical magnetic field perturbed on a constant configuration. We develop a simple and general algorithm for an analytic…
We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In keeping with the literature we study a class of initial…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as…
Transient stability analysis (TSA) plays an important role in power system analysis to investigate the stability of power system. Traditionally, transient stability analysis methods have been developed using time domain simulation by means…
Secure operation of electric power grids fundamentally relies on their dynamical stability properties. For the third order model, a paradigmatic model that captures voltage dynamics, three routes to instability are established in the…