52 research outputs found
Regularity of the free boundary for a parabolic cooperative system
In this paper we study the following parabolic system Delta u - partial derivative(t)u = vertical bar u vertical bar(q-1) u chi({vertical bar u vertical bar > 0}), = (u(1), ... , u(m)), with free boundary partial derivative{vertical bar u vertical bar > 0). For 0Peer reviewe
Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions
The main result of this paper concerns the behavior of a free boundary
arising from a minimization problem, close to the fixed boundary in two
dimensions
Scaling Limits for Internal Aggregation Models with Multiple Sources
We study the scaling limits of three different aggregation models on Z^d:
internal DLA, in which particles perform random walks until reaching an
unoccupied site; the rotor-router model, in which particles perform
deterministic analogues of random walks; and the divisible sandpile, in which
each site distributes its excess mass equally among its neighbors. As the
lattice spacing tends to zero, all three models are found to have the same
scaling limit, which we describe as the solution to a certain PDE free boundary
problem in R^d. In particular, internal DLA has a deterministic scaling limit.
We find that the scaling limits are quadrature domains, which have arisen
independently in many fields such as potential theory and fluid dynamics. Our
results apply both to the case of multiple point sources and to the
Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in
v2: added "least action principle" (Lemma 3.2); small corrections in section
4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version);
expanded section 6.
Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration
Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is parallel to the boundary of the domain. Here, for the elliptic case, we prove the stability counterpart of that result. In fact, we show that if the solution is almost constant on a surface at a fixed distance from the boundary, then the domain is almost radially symmetric, in the sense that is contained in and contains two concentric balls Bre and Bri, with the difference re 12ri (linearly) controlled by a suitable norm of the deviation of the solution from a constant. The proof relies on and enhances arguments developed in a paper by Aftalion, Busca and Reichel
Improving Power System Stability Using Transfer Function: A Comparative Analysis
In this paper, a small-signal dynamic model of a single-machine infinite-bus (SMIB) power system that includes IEEE type-ST1 excitation system and PSS based on transfer function structure is presented. The changes in the operating condition of a power system on dynamic performance have been examined. The dynamic performance of the closed-loop system is analyzed base on its eigenvalues. The effectiveness of the parameters changes on dynamic stability is verified by simulation results. Three types of PSS have been considered for analysis: (a) the derivative PSS, (b) the lead-lag PSS or conventional PSS, and (c) the proportional-integral-derivative PSS. The objective function is formulated to increase the damping ratio of the electromechanical mode eigenvalues. Simulation results show that the PID-PSS performs better for less overshoot and less settling time compared with the CPSS and DPSS under different load operation and the significant system parameter variation conditions
Impact of PSS and STATCOM Devices to the Dynamic Performance of a Multi-Machine Power System
This paper studies the impact of leveraging both static synchronous compensator (STATCOM) and power system stabilizer (PSS) on multi-machine power systems. Considering a standard IEEE 9-bus test power network, classic and intelligent controllers are applied to achieve the desirable system performance. Simulated tests show the usefulness of STATCOM on network power quality in terms of voltage profile. In addition, it is shown that it can significantly improve the damping oscillations of synchronous generator under normal and abnormal network conditions. As shown, the PSS also contributes to improving the synchronous generator parameters. It is also observed that using intelligent controllers with STATCOM and PSS leads to a better performance relative to the classic controllers
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