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A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…
With increasing availability of communication and control infrastructure at the distribution systems, it is expected that the distributed energy resources (DERs) will take an active part in future power systems operations. One of the main…
In this article we consider the multi-layer shallow water system for the propagation of gravity waves in density-stratified flows, with additional terms introduced by the oceanographers Gent and McWilliams in order to take into account…
Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a…
Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…
To figure out the stability issues brought by renewable energy sources (RES) with non-Gaussian uncertainties in isolated microgrids, this paper proposes a chance constrained stability constrained optimal power flow (CC-SC-OPF) model.…
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear…
Power systems are currently undergoing a rapid paradigm change in their operation. Centralised energy production is being replaced by a number of Distributed Generation (DG) units that are placed at different locations and voltage levels in…
Deep learning (DL) algorithms have been widely applied to short-term voltage stability (STVS) assessment in power systems. However, transferring the knowledge learned in one power grid to other power grids with topology changes is still a…
In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous…
Power flow (PF) calculations are the backbone of real-time grid operations, across workflows such as contingency analysis (where repeated PF evaluations assess grid security under outages) and topology optimization (which involves PF-based…
Efficient control of power systems is becoming increasingly difficult as they gain in complexity and size. We propose an automatic control strategy that regulates the mechanical power output of the generators in a power grid based on…
In the linear theory of hydrodynamic stability up to now there exist examples of flows for which there is full quantitative distinction, as for cylindrical Hagen-Poiseuille (HP) flow in a pipe with round section, between theory conclusions…
Geometric Representation Learning (GRL) aims to approximate the non-Euclidean topology of high-dimensional data through discrete graph structures, grounded in the manifold hypothesis. However, traditional static graph construction methods…
Modeling microstructural evolution at large strains requires mechanical formulations that remain thermodynamically consistent while capturing significant lattice rotations and transformation-induced stresses. However, most existing…
We report an instability exhibited by a fluid system when coupling two distinct types of waves, both linearly damped. While none of them is unstable on its own, they amplify one another, resulting in a previously unreported convective…
Load models have a great impact on voltage behaviors as well as power system transient dynamics. Extensive work has been done on this topic, proposing appropriate load models and capturing better load behaviors during transient. This paper…
We present Riemannian Gaussian Variational Flow Matching (RG-VFM), a geometric extension of Variational Flow Matching (VFM) for generative modeling on manifolds. Motivated by the benefits of VFM, we derive a variational flow matching…
The increasing penetration of renewable energy along with the variations of the loads bring large uncertainties in the power system states that are threatening the security of power system planning and operation. Facing these challenges,…
For many nonlinear control systems, the chosen equilibrium determines both the steady-state efficiency and the dynamic performance. This paper addresses the issue of obtaining an optimal equilibrium in terms of some steady-state operation…