Search results for "OPF"
showing 10 items of 89 documents
Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model
2005
A homogeneously broadened unidirectonal ring laser can emit in several longitudinal modes for large enough pump and cavity length because of Rabi splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken (RNGH) instability. We investigate numerically the properties of the multi-mode solution. We show that this solution can coexist with the single-mode one, and its stability domain can extend to pump values smaller than the critical pump of the RNGH instability. Morevoer, we show that the multi-mode solution for large pump values is affected by two different instabilities: a pitchfork bifurcation, which preserves phase-locking, and a Hopf bifurcation, which destroys it.
A Seven Mode Truncation of the Kolmogorov Flow with Drag: Analysis and Control
2009
The transition from laminar to chaotic motions in a viscous °uid °ow is in- vestigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov °ow with drag friction. An- alytical expressions of the Hopf bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynolds num- ber is increased for ¯xed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is ob- tained through a model reference approach which makes the control global. Finally, the e®ectiveness of this control strategy is numerically illustra…
Remarks on the economic interpretation of Hopf bifurcations
1999
Abstract The Hopf bifurcation theorem has become a frequently used tool in the study of nonlinear dynamical economic systems. In this paper, it is shown that phenomena like multiple limit cycles, hysteresis loops and catastrophic transitions may possibly accompany a Hopf bifurcation. The theoretical argument is illustrated in Foley's liquidity cost–business cycle model.
Progress in Modelling Coherently Pumped Far-Infrared Laser Dynamics
1990
Coherently pumped lasers (CPL) operating in the far-infrared spectral region shown a wealth of instabilities1, including a behavior remarkably similar2,3 with the predictions of the paradigmatic Lorenz-Haken model of a single-mode homogeneously broadened laser4,5. The qualitative agreement; between theory and experiments2,3 was rather surprising, for the model4,5 refers to a two-level system whereas the CPL operate on a three-level scheme, where the pumping and lasing transitions share a common upper level. Dupertuis et al.6 have identified conditions for the mathematical reduction of the CPL equations to the Lorenz-Haken equations4, but these conditions were not all fulfilled in the experi…
A distributed minimum losses optimal power flow for islanded microgrids
2017
Abstract In this work, the minimum losses optimal power dispatch problem for islanded microgrids with distributed energy resources (DER) is solved by means of a distributed heuristic approach. Optimal power management is performed almost in real time, with a predefined schedule, i.e. every 5 min, and the solution is applied to generators when the current operating solution violates voltage or current constraints or when the current configuration produces too large power losses. The operating point of both inverter-interfaced generation units as well as rotating production systems can be modified simply using local information. The latter are voltage measurements and power injections or load…
Generalization of the Lorenz-Haken model to atomic systems with different relaxation rates for the two laser levels
1995
Abstract The fundamental Lorenz-Haken laser model is generalized to the case of a two-level amplifying medium with different external relaxation rates for the two levels and with internal relaxation. This represents one further degree of freedom, and important quantitative differences in the laser dynamics. i.e., in the stationary solutions, linear stability analysis, and timedependent solutions, are found. No significant qualitative differences, however, are observed.
Modified post-bifurcation dynamics and routes to chaos from double-Hopf bifurcations in a hyperchaotic system
2012
In order to understand the onset of hyperchaotic behavior recently observed in many systems, we study bifurcations in the modified Chen system leading from simple dynamics into chaotic regimes. In particular, we demonstrate that the existence of only one fixed point of the system in all regions of parameter space implies that this simple point attractor may only be destabilized via a Hopf or double Hopf bifurcation as system parameters are varied. Saddle-node, transcritical and pitchfork bifurcations are precluded. The normal form immediately following double Hopf bifurcations is constructed analytically by the method of multiple scales. Analysis of this generalized double Hopf normal form …
Savstarpējo aizdevumu platformu tiesiskā regulējuma problēmas Latvijā un Eiropas Savienībā.
2020
Kopfinansējums ir viens no relatīvi jaunajiem alternatīvajiem finansējuma piesaistes veidiem, kas vienlaicīgi ļauj personām, kas vēlas īstenot kādu biznesa ideju, uzsākt saimniecisko darbību vai īstenot kādu projektu, viegli piesaistīt lielu daudzumu investoru, savukārt investoriem ir iespēja ieguldīt savus personīgos līdzekļus, tādā veidā palielinot savu kapitālu vai saņemto pretī kādu labumu (piemēram, produktu vai pakalpojumu). Savstarpējo aizdevumu modelis, kas ir viens no kopfinansējuma veidiem, dod iespēju projektu izstrādātājiem saņemt aizdevumu no citām fiziskām vai juridiskām personām, izmantojot savstarpējo aizdevumu platformu, un ļauj investoriem aktīvi izvēlēties kā to līdzekļi …
Observation of Poincaré-Andronov-Hopf Bifurcation in Cyclotron Maser Emission from a Magnetic Plasma Trap
2018
We report the first experimental evidence of a controlled transition from the generation of periodic bursts of electromagnetic radiation into the continuous-wave regime of a cyclotron maser formed in magnetically confined nonequilibrium plasma. The kinetic cyclotron instability of the extraordinary wave of weakly inhomogeneous magnetized plasma is driven by the anisotropic electron population resulting from electron cyclotron plasma heating in a MHD-stable minimum-B open magnetic trap. peerReviewed
FLUCTUATION-INDUCED LOCAL OSCILLATIONS AND FRACTAL PATTERNS IN THE LATTICE LIMIT CYCLE MODEL
2003
The fractal properties of the Lattice Limit Cycle model are explored when the process is realized on a 2-dimensional square lattice support via Monte Carlo Simulations. It is shown that the structure of the steady state presents inhomogeneous fluctuations in the form of domains of identical particles. The various domains compete with one another via their borders which have self-similar, fractal structure. The fractality is more prominent, (fractal dimensions df < 2), when the parameter values are near the critical point where the Hopf bifurcation occurs. As the distance from the Hopf bifurcation increases in the parameter space the system becomes more homogeneous and the fractal dimens…