Dynamic modelling of entrainment in rapid landslides

2005 ◽  
Vol 42 (5) ◽  
pp. 1437-1448 ◽  
Author(s):  
Scott McDougall ◽  
Oldrich Hungr
Keyword(s):  
Growth Rate ◽  
Simple Model ◽  
Computer Model ◽  
Exponential Growth ◽  
Debris Flows ◽  
Dynamic Modelling ◽  
Back Analysis ◽  
Simple Material ◽  
3D Terrain ◽  
Rapid Landslide

Entrainment of path material is an important feature of many rapid landslides. The associated increases in volume and changes in flow character can significantly influence mobility. A simple material entrainment algorithm, based on the assumption of natural exponential growth with displacement, has been incorporated into a new computer model designed to simulate rapid landslide motion across 3D terrain. The user controls the growth rate and can also implement a change in rheology at the onset of entrainment. A hypothetical example is used to demonstrate the influence of the mass and momentum transfer assumptions. A back-analysis of the 1999 Nomash River landslide is included to show that the simple model is capable of simulating the bulk characteristics of a complex event involving substantial entrainment.Key words: landslides, debris flows, rock avalanches, entrainment, erosion, dynamic modelling.

scholarly journals Interim estimates of increased transmissibility, growth rate, and reproduction number of the Covid-19 B.1.617.2 variant of concern in the United Kingdom

2021 ◽  
Author(s):  
John S Dagpunar
Keyword(s):  
Growth Rate ◽  
Simple Model ◽  
Exponential Growth ◽  
Reproduction Number ◽  
Actual Distribution ◽  
Sanger Institute ◽  
The United Kingdom ◽  
Point Estimates ◽  
Reproduction Numbers ◽  
The Uk

This paper relates to data from the Wellcome Sanger Institute, UK, regarding Covid-19 genomic surveillance. We use a simple model to give point estimates of the effective reproduction numbers of the B.1.617.2 and B.1.1.7 lineages in England, from sequenced data as at 15 May 2021. Comparison with the estimated reproduction number of B.1.1.7 enables an estimate of the increased transmissibility of B.1.617.2. We conclude that it is almost certain that there is increased transmissibility that will rapidly lead to B.1.617.2 becoming the prevailing variant in the UK. The derived estimates of increased transmissibility have uncertainty relating to the actual distribution of the generation interval, but they do point, under present conditions of vaccination coverage and NPIs, to exponential growth of positive cases.

scholarly journals The minimally displaced set of an irreducible automorphism of $$F_N$$ is co-compact

2021 ◽  
Vol 116 (4) ◽  
pp. 369-383
Author(s):  
Stefano Francaviglia ◽  
Armando Martino ◽  
Dionysios Syrigos
Keyword(s):  
Growth Rate ◽  
Free Group ◽  
Exponential Growth ◽  
Single Point ◽  
Irreducible Automorphism

AbstractWe study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth $$\phi $$ ϕ , under the action of the centraliser $$C(\phi )$$ C ( ϕ ) . As a corollary, we get that the same holds for the action of $$ <\phi>$$ < ϕ > on $$Min(\phi )$$ M i n ( ϕ ) . Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.

scholarly journals Optimal Strategies for Prudent Investors

1998 ◽  
Vol 01 (04) ◽  
pp. 473-486 ◽  
Author(s):  
Roberto Baviera ◽  
Michele Pasquini ◽  
Maurizio Serva ◽  
Angelo Vulpiani
Keyword(s):  
Growth Rate ◽  
Random Walk ◽  
Exponential Growth ◽  
Optimal Strategies ◽  
Maximum Amount ◽  
Exponential Growth Rate ◽  
One Dimensional ◽  
Economic Level ◽  
Random Walk With Drift ◽  
Analytical Expressions

We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

LANGUAGES WITH A FINITE ANTIDICTIONARY: SOME GROWTH QUESTIONS

2014 ◽  
Vol 25 (08) ◽  
pp. 937-953
Author(s):  
ARSENY M. SHUR
Keyword(s):  
Growth Rate ◽  
Structural Properties ◽  
Exponential Growth ◽  
Regular Languages ◽  
The Other ◽  
Exponential Growth Rate ◽  
Strong Component ◽  
Order Of Growth ◽  
Finite Sets ◽  
Complex Order

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.

Validation and Analysis of Modeled Predictions of Growth of Bacillus cereus Spores in Boiled Rice

2000 ◽  
Vol 63 (2) ◽  
pp. 268-272 ◽  
Author(s):  
DANA M. McELROY ◽  
LEE-ANN JAYKUS ◽  
PEGGY M. FOEGEDING
Keyword(s):  
Growth Rate ◽  
Bacillus Cereus ◽  
Exponential Growth ◽  
Generation Time ◽  
Time Lag ◽  
Lag Phase ◽  
Exponential Growth Rate ◽  
Phase Duration ◽  
Margin Of Safety ◽  
Fail Safe

The growth of psychrotrophic Bacillus cereus 404 from spores in boiled rice was examined experimentally at 15, 20, and 30°C. Using the Gompertz function, observed growth was modeled, and these kinetic values were compared with kinetic values for the growth of mesophilic vegetative cells as predicted by the U.S. Department of Agriculture's Pathogen Modeling Program, version 5.1. An analysis of variance indicated no statistically significant difference between observed and predicted values. A graphical comparison of kinetic values demonstrated that modeled predictions were “fail safe” for generation time and exponential growth rate at all temperatures. The model also was fail safe for lag-phase duration at 20 and 30°C but not at l5°C. Bias factors of 0.55, 0.82, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, indicated that the model generally was fail safe and hence provided a margin of safety in its growth predictions. Accuracy factors of 1.82, 1.60, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, quantitatively demonstrated the degree of difference between predicted and observed values. Although the Pathogen Modeling Program produced reasonably accurate predictions of the growth of psychrotrophic B. cereus from spores in boiled rice, the margin of safety provided by the model may be more conservative than desired for some applications. It is recommended that if microbial growth modeling is to be applied to any food safety or processing situation, it is best to validate the model before use. Once experimental data are gathered, graphical and quantitative methods of analysis can be useful tools for evaluating specific trends in model prediction and identifying important deviations between predicted and observed data.

TOPOLOGICAL ENTROPY VERSUS GEODESIC ENTROPY

1994 ◽  
Vol 05 (02) ◽  
pp. 213-218 ◽  
Author(s):  
GABRIEL P. PATERNAIN ◽  
MIGUEL PATERNAIN
Keyword(s):  
Growth Rate ◽  
Topological Entropy ◽  
Exponential Growth ◽  
Geodesic Flow ◽  
Compact Riemannian Manifold ◽  
Betti Numbers ◽  
Exponential Growth Rate ◽  
Sphere Bundle ◽  
Space Of Paths ◽  
Simply Connected

Using Yomdin's Theorem [8], we show that for a compact Riemannian manifold M, the geodesic entropy — defined as the exponential growth rate of the average number of geodesic segments between two points — is ≤ the topological entropy of the geodesic flow of M. We also show that if M is simply connected and N ⊂ M is a compact simply connected submanifold, then the exponential growth rate of the sequence given by the Betti numbers of the space of paths starting in N and ending in a fixed point of M, is bounded above by the topological entropy of the geodesic flow on the normal sphere bundle of N.

scholarly journals Debris flow run-out simulation and analysis using a dynamic model

2018 ◽  
Vol 18 (2) ◽  
pp. 555-570 ◽  
Author(s):  
Raquel Melo ◽  
Theo van Asch ◽  
José L. Zêzere
Keyword(s):  
Debris Flow ◽  
Dynamic Model ◽  
Debris Flows ◽  
Back Analysis ◽  
Rheological Parameters ◽  
Economic Damage ◽  
Case Scenario ◽  
Worst Case ◽  
Basin Scale ◽  
Central Portugal

Abstract. Only two months after a huge forest fire occurred in the upper part of a valley located in central Portugal, several debris flows were triggered by intense rainfall. The event caused infrastructural and economic damage, although no lives were lost. The present research aims to simulate the run-out of two debris flows that occurred during the event as well as to calculate via back-analysis the rheological parameters and the excess rain involved. Thus, a dynamic model was used, which integrates surface runoff, concentrated erosion along the channels, propagation and deposition of flow material. Afterwards, the model was validated using 32 debris flows triggered during the same event that were not considered for calibration. The rheological and entrainment parameters obtained for the most accurate simulation were then used to perform three scenarios of debris flow run-out on the basin scale. The results were confronted with the existing buildings exposed in the study area and the worst-case scenario showed a potential inundation that may affect 345 buildings. In addition, six streams where debris flow occurred in the past and caused material damage and loss of lives were identified.

A model for the analysis of rapid landslide motion across three-dimensional terrain

2004 ◽  
Vol 41 (6) ◽  
pp. 1084-1097 ◽  
Author(s):  
Scott McDougall ◽  
Oldrich Hungr
Keyword(s):  
Debris Flows ◽  
Three Dimensional ◽  
Dynamic Modelling ◽  
Rock Avalanche ◽  
Stress Distributions ◽  
Flume Experiments ◽  
Mesh Distortion ◽  
Flow Slides ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

A new numerical model for the dynamic analysis of rapid flow slides, debris flows, and avalanches has been developed. The model is an extension of an earlier algorithm and is implemented using a numerical method adapted from smoothed particle hydrodynamics. Its features include (i) the ability to simulate flow across complex three-dimensional terrain; (ii) the ability to allow nonhydrostatic and anisotropic internal stress distributions, coupled with strain changes through frictional relationships; (iii) the ability to simulate material entrainment; (iv) a choice of different rheological kernels, including frictional, plastic, viscous, Bingham, and Voellmy; (v) a meshless solution, which eliminates problems with mesh distortion during long displacements; and (vi) highly efficient and simple operation. The model has been tested by analysing a series of laboratory flume experiments with granular materials, both on straight and curved paths. The model is capable of accurately predicting the margins of various curving flows using a single set of input parameters. A preliminary analysis of a real rock avalanche case history is also included.Key words: landslides, debris flows, rock avalanches, runout analysis, dynamic modelling, numerical methods.

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