相关论文: Power Flow as an Algebraic System
Inflow BC plays a critical role in the study of hyperbolic PDE in a bounded domain. We establish $W^{1,\infty}$ stability for 1D hyperbolic conservation laws with inflow data in a bounded interval, and $W^{2,3+}$ stability of a large class…
We study counting statistics of electric current pumped by pulses of an external field. The fluctuations depend on the pulse shape, and can be minimized by choosing the pulse shape properly. For an optimal pulse shape, the fluctuations are…
We consider a flow-level model of a network operating under an $\alpha$-fair bandwidth sharing policy (with $\alpha>0$) proposed by Roberts and Massouli\'{e} [Telecomunication Systems 15 (2000) 185-201]. This is a probabilistic model that…
An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer \& Trefethen (2000), while providing flexibility to amend the boundary conditions…
In this paper we show that a normal total number-of-particle fluctuation can be obtained consistently from the static thermodynamic relation and dynamic compressibility sum rule. In models using the broken U(1) gauge symmetry, in order to…
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…
An important monitoring task for power systems is accurate estimation of the system operation state. Under the nonlinear AC power flow model, the state estimation (SE) problem is inherently nonconvex giving rise to many local optima. In…
The outflow problem for the viscous full two-phase flow model in a half line is investigated in the present paper. The existence, uniqueness and nonlinear stability of the steady-state are shown respectively corresponding to the supersonic,…
Transient and steady state currents through dc-biased quantum impurity models beyond the linear response regime are of considerable interest, both from an experimental and a theoretical point of view. Here we present a new analytical…
This paper presents stability and accuracy analysis of a high-order explicit time stepping scheme introduced by \cite[Section 2.2]{Buvoli2019}, which exhibits superior stability compared to classical Adams-Bashforth. A conjecture that is…
Some sufficient conditions on the algebraic stability of non-homogeneous regime-switching diffusion processes are established. In this work we focus on determining the decay rate of a stochastic system which switches randomly between…
Sadeghi et al. considered a bottleneck system with periodic inflow rate, and proved that a constant-rate input maximizes the time-averaged output rate among all periodic inflow rates. Here we provide a short and elementary proof of this…
We study computational questions related with the stability of discrete-time linear switching systems with switching sequences constrained by an automaton. We first present a decidable sufficient condition for their boundedness when the…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line…
The stability issue emerges as a growing number of diverse power apparatus connecting to the power system. The stability analysis for such power systems is required to adapt to heterogeneity and scalability. This paper derives a local…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
This work is divided into two parts. First, we analyze the existence of positive bound and ground states for a second order stationary system coming from a coupled system of nonlinear Schr\"odinger--Korteweg-de Vries equations. Second, we…
We investigate the stability of persistent currents in superfluid fermionic gases confined to a ring geometry. Our study, conducted at zero temperature using time-dependent density functional theory, cover interaction regimes from strong…