Hierarchical Modeling of Liquid-Liquid Dispersions: From Simple Lumped Models to Multidimensional Population Balances

2015 ◽  
Vol 87 (8) ◽  
pp. 1035-1035
Author(s):  
D. L. Marchisio
Keyword(s):  
Hierarchical Modeling ◽  
Lumped Models ◽  
Population Balances

ANALYSIS OF IMPROVED-LUMPED MODELS FOR PROPERTY ESTIMATION FROM TEMPERATURE FIELD DATA USING A FIN MODEL

2015 ◽  
Vol 18 (10) ◽  
pp. 985-996 ◽  
Author(s):  
D. C. Moreira ◽  
M.C. de O. Telles ◽  
L. C. S. Nunes ◽  
Leandro A. Sphaier
Keyword(s):  
Temperature Field ◽  
Field Data ◽  
Property Estimation ◽  
Lumped Models

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Diffusional Change of Solid Particle Size

1996 ◽  
Vol 61 (4) ◽  
pp. 536-563
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal
Keyword(s):  
Particle Size ◽  
Solid Particle ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Granular Systems ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Diffusion Term ◽  
Population Balances ◽  
And Diffusion

To the description of changes of solid particle size in population, the application was proposed of stochastic differential equations and diffusion equations adequate to them making it possible to express the development of these populations in time. Particular relations were derived for some particle size distributions in flow and batch equipments. It was shown that it is expedient to complement the population balances often used for the description of granular systems by a "diffusion" term making it possible to express the effects of random influences in the growth process and/or particle diminution.

scholarly journals Assessing the Response of Snow Avalanche Runout Altitudes to Climate Fluctuations Using Hierarchical Modeling: Application to 61 Winters of Data in France

2010 ◽  
Vol 23 (12) ◽  
pp. 3157-3180 ◽  
Author(s):  
N. Eckert ◽  
H. Baya ◽  
M. Deschatres
Keyword(s):  
Climate Change ◽  
Large Scale ◽  
Hierarchical Modeling ◽  
Control Measures ◽  
Level Shift ◽  
Snow Avalanches ◽  
Winter Climate ◽  
Climate Fluctuations ◽  
High Magnitude ◽  
Proposed Model

Abstract Snow avalanches are natural hazards strongly controlled by the mountain winter climate, but their recent response to climate change has thus far been poorly documented. In this paper, hierarchical modeling is used to obtain robust indexes of the annual fluctuations of runout altitudes. The proposed model includes a possible level shift, and distinguishes common large-scale signals in both mean- and high-magnitude events from the interannual variability. Application to the data available in France over the last 61 winters shows that the mean runout altitude is not different now than it was 60 yr ago, but that snow avalanches have been retreating since 1977. This trend is of particular note for high-magnitude events, which have seen their probability rates halved, a crucial result in terms of hazard assessment. Avalanche control measures, observation errors, and model limitations are insufficient explanations for these trends. On the other hand, strong similarities in the pattern of behavior of the proposed runout indexes and several climate datasets are shown, as well as a consistent evolution of the preferred flow regime. The proposed runout indexes may therefore be usable as indicators of climate change at high altitudes.

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