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  • Fault-tolerance  (1)
  • numerical model
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Distributed computing 5 (1992), S. 175-186 
    ISSN: 1432-0452
    Keywords: Fault-tolerance ; Agreement ; Distributed system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Summary The binary Byzantine Agreement problem requiresn−1 receivers to agree on the binary value broadcast by a sender even when some of thesen processes may be faulty. We investigate the message complexity of protocols that solve this problem in the case of crash failures. In particular, we derive matching upper and lower bounds on the total, worst and average case number of meassages needed in the failure-free executions of such protocols. More specifically, we prove that any protocol that tolerates up tot faulty processes requires a total of at leastn+t−1 messages in its failure-free executions —and, therefore, at least [(n+t−1)/2] messages in the worst case and min (P 0,P 1)·(n+t−1) meassages in the average case, whereP v is the probability that the value of the bit that the sender wants to broadcast isv. We also give protocols that solve the problem using only the minimum number of meassages for these three complexity measures. These protocols can be implemented by using 1-bit messages. Since a lower bound on the number of messages is also a lower bound on the number of meassage bits, this means that the above tight bounds on the number of messages are also tight bounds on the number of meassage bits.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2021-07-21
    Description: Lahars are among the most hazardous mass flow processes on earth and have caused up to 23 000 casualties in single events in the recent past. The Cotopaxi volcano, 60 km southeast of Quito, has a well‐documented history of massively destructive lahars and is a hotspot for future lahars due to (i) its ~10 km2 glacier cap, (ii) its 117–147‐year return period of (Sub)‐Plinian eruptions, and (iii) the densely populated potential inundation zones (300 000 inhabitants). Previous mechanical lahar models often do not (i) capture the steep initial lahar trajectory, (ii) reproduce multiple flow paths including bifurcation and confluence, and (iii) generate appropriate key parameters like flow speed and pressure at the base as a measure of erosion capacity. Here, we back‐calculate the well‐documented 1877 lahar using the RAMMS debris flow model with an implemented entrainment algorithm, covering the entire lahar path from the volcano edifice to an extent of ~70 km from the source. To evaluate the sensitivity and to constrain the model input range, we systematically explore input parameter values, especially the Voellmy–Salm friction coefficients μ and ξ. Objective selection of the most likely parameter combinations enables a realistic and robust lahar hazard representation. Detailed historic records for flow height, flow velocity, peak discharge, travel time and inundation limits match best with a very low Coulomb‐type friction μ (0.0025–0.005) and a high turbulent friction ξ (1000–1400 m/s2). Finally, we apply the calibrated model to future eruption scenarios (Volcanic Explosivity Index = 2–3, 3–4, 〉4) at Cotopaxi and accordingly scaled lahars. For the first time, we anticipate a potential volume growth of 50–400% due to lahar erosivity on steep volcano flanks. Here we develop a generic Voellmy–Salm approach across different scales of high‐magnitude lahars and show how it can be used to anticipate future syneruptive lahars.
    Description: A generic model approach is developed to simulate massive syneruptive lahars at Cotopaxi from initiation on the steep volcano flanks to distal reaches. Evaluation of 14 calibration constraints shows that the Voellmy–Salm model reliably reproduces bulk behaviour of syneruptive lahars. Estimations of lahar erosivity on the volcano flanks anticipate an erosion‐related volume increase for future Cotopaxi lahars between 50 and 400%.
    Description: Bundesministerium für Bildung und Forschung http://dx.doi.org/10.13039/501100002347
    Keywords: 551 ; debris flow erosion ; lahar ; model calibration ; numerical model ; predictive modelling
    Type: article
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