Abstract. We study the properties of Braess's paradox in the context of the model of congestion games with flow over time introduced by Koch and Skutella. We compare them to the well known properties of Braess's paradox for Wardrop's model of games with static flows. We show that there are networks which do not admit Braess's paradox in Wardrop's model, but which admit it in the model with flow over time. Moreover, there is a topology that admits a much more severe Braess's ratio for this model. Further, despite its symmetry for games with static flow, we show that Braess's paradox is not symmetric for flows over time. We illustrate that there are network topologies which exhibit Braess's paradox, but for which the transpose does not. Finally, we conjecture a necessary and sufficient condition of existence of Braess's paradox in a network, and prove the condition of existence of the paradox either in the network or in its transpose.
Abstract. We study the properties of Braess's paradox in the context of the model of congestion games with flow over time introduced by Koch and Skutella. We compare them to the well known properties of Braess's paradox for Wardrop's model of games with static flows. We show that there are networks which do not admit Braess's paradox in Wardrop's model, but which admit it in the model with flow over time. Moreover, there is a topology that admits a much more severe Braess's ratio for this model. Further, despite its symmetry for games with static flow, we show that Braess's paradox is not symmetric for flows over time. We illustrate that there are network topologies which exhibit Braess's paradox, but for which the transpose does not. Finally, we conjecture a necessary and sufficient condition of existence of Braess's paradox in a network, and prove the condition of existence of the paradox either in the network or in its transpose.
Continuous wave cavity ring-down spectroscopy using an electronically switched telecom distributed feedback laser module is demonstrated. By adding a compensation waveform current to the step-function switched laser current the laser wavelength stabilisation time is reduced to about 4 ms corresponding to a 200 Hz utmost ring-down transient repetition rate.Introduction: Cavity ring-down spectroscopy (CRDS) [1, 2] is a direct absorption technique based on the measurement of the rate of absorption of laser light injected into a high-finesse optical cavity. The advantage over normal absorption spectroscopy results from the intrinsic insensitivity to light source intensity fluctuations and the extremely long effective path lengths that can be realised in the high-finesse optical cavities.It is particularly convenient to perform CDRS using relatively cheap CW distributed feedback (DFB) telecom lasers operating in the nearinfrared wavelength region. This region covers absorption features of molecules that are interesting in diverse gas-sensing and spectroscopic applications. For example, CW-CRDS measurements with DFB lasers of CO 2 , H 2 O, H 2 S, C 2 H 4 [3], singlet oxygen [4], C 3 H 7 OH and CH 3 OH [5] have been reported.CW-CRDS enables coupling the laser beam to a single TEM 00 mode of the high-finesse optical cavity and achieving high repetition rates. This ensures high sensitivity and wavelength resolution. To produce cavity ring-down transients reliably, it is necessary to interrupt injection after sufficient laser light has been accumulated into the cavity. This is usually realised by an acousto-optic modulator (AOM) that allows high-speed beam interruption ( 100 ns with a 2 ms delay [3]). Other approaches include the use of a semiconductor optical amplifier [6] or a Pockels cell [7]. The advantage of these external optical switches is that they do not interfere with the laser diode operation. However, they introduce undesired transmission losses and are relatively expensive.An alternative strategy is to sweep the cavity rapidly out of resonance with the laser by fast movement of one of the mirrors (possibly aided by sweeping the wavelength of the laser source). However, if laser interruption is not used, a strongly fluctuating decay signal is observed for lasers that have emission linewidth broader than the cavity mode (such as DFB diodes), or smooth frequency-chirped oscillations appear for comparable linewidth lasers. In both cases an exponential decay may be recovered at sufficiently high scanning speed, but for a broad linewidth laser this limit may be hard to attain experimentally and may come at the cost of low cavity injection [8,9].Here, a different approach based on rapidly switching the laser current is proposed. A ring-down transient can be reliably produced by rapidly switching-off the laser current, but step-function current switching induces a significant drift of the laser wavelength at the successive switch-on owing to thermal effects. Consequently, the next ring-down transient would occur at a...
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