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linear-formulations
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Linearization error in synchronization of Kuramoto oscillators
, Article Applied Mathematics and Computation ; Volume 411 , December , 2021 ; 00963003 (ISSN) ; Baharifard, F ; Hesaam, B ; Zarei, M ; Sarbazi Azad, H ; Sharif University of Technology
Elsevier Inc
2021
Abstract
Synchronization among a set of networked nodes has attracted much attention in different fields. This paper thoroughly investigates linear formulation of the Kuramoto model, with and without frustration, for an arbitrarily weighted undirected network where all nodes may have different intrinsic frequencies. We develop a mathematical framework to estimate errors of the linear approximation for globally and locally coupled networks. We mathematically prove that the eigenvector corresponding to the largest eigenvalue of the network's Laplacian matrix is enough for examining synchrony alignment and that the functionality of this vector depends on the corresponding eigenvalue. Moreover, we prove...
Linear and nonlinear approaches towards amplitude modulation atomic force microscopy
, Article Current Applied Physics ; Volume 10, Issue 6 , 2010 , Pages 1416-1421 ; 15671739 (ISSN) ; Mahmoodi, S. N ; Jalili, N ; Zohoor, H ; Sharif University of Technology
2010
Abstract
Frequency response behavior of microcantilever is analytically and experimentally investigated in amplitude modulation Atomic Force Microscopy (AFM). AFM microcantilever probe is modeled as a continuous beam, and tip-sample interaction force is considered to include both attractive and repulsive force regimes. The developed model is compared with the linear lumped-parameters model that has been extensively used in the literature so far. Experimental measurements are also provided for the frequency response of a typical microcantilever-sample system to demonstrate the advantages of the developed model over the linear formulation. The results indicate that the nonlinear continuous model is...
Linear formulations for topology-variable-based distribution system reliability assessment considering switching interruptions
, Article IEEE Transactions on Smart Grid ; Volume 11, Issue 5 , May , 2020 , Pages 4032-4043 ; Abbaspour, A ; Fotuhi Firuzabad, M ; Muñoz Delgado, G ; Contreras, J ; Lehtonen, M ; Arroyo, J. M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020
Abstract
Continuity of supply plays a significant role in modern distribution system planning and operational studies. Accordingly, various techniques have been developed for reliability assessment of distribution networks. However, owing to the complexities and restrictions of these methods, many researchers have resorted to several heuristic optimization algorithms for solving reliability-constrained optimization problems. Therefore, solution quality and convergence to global optimality cannot be guaranteed. Aiming to address this issue, two salient mathematical models are introduced in this paper for topology-variable-based reliability evaluation of both radial and radially-operated meshed...
An efficient mixed-integer linear formulation for long-term overhead lines maintenance scheduling in power distribution systems
, Article IEEE Transactions on Power Delivery ; Volume 24, Issue 4 , 2009 , Pages 2043-2053 ; 08858977 (ISSN) ; Fotuhi Firuzabad, M ; Abbasi, E ; Sharif University of Technology
2009
Abstract
This paper presents an efficient mixed-integer linear formulation for long term maintenance schedule of overhead lines. The proposed formulation is based on risk management approach and utilizes the model of decoupled risk factors. The proposed methodology yields a significant computational saving comparing to the previously reported dynamic programming. Risk management approach enables the asset managers to consider the actual condition of electrical equipment and expected consequence of their failures. Furthermore, the decoupled risk strategy in conjunction with the mixed-integer linear programming formulation establishes a precise description of time-dependent deterioration failure rate...