Stochastic fluid models for control and optimization of systems with quality of service requirements

2003 ◽  
Author(s):  
C.G. Cassandras ◽  
G. Sun ◽  
C.G. Panayiotou
Keyword(s):  
Quality Of Service ◽  
Fluid Models ◽  
Stochastic Fluid Models ◽  
Stochastic Fluid

scholarly journals Circulation and Energy Theorem Preserving Stochastic Fluids

2019 ◽  
Vol 150 (6) ◽  
pp. 2776-2814 ◽  
Author(s):  
Theodore D. Drivas ◽  
Darryl D. Holm
Keyword(s):  
Variational Principle ◽  
Energy Conservation ◽  
Euler Equations ◽  
Navier Stokes ◽  
Fluid Models ◽  
Smooth Solutions ◽  
Stochastic Fluid Models ◽  
Natural Extensions ◽  
Stochastic Fluid ◽  
Incompressible Euler

AbstractSmooth solutions of the incompressible Euler equations are characterized by the property that circulation around material loops is conserved. This is the Kelvin theorem. Likewise, smooth solutions of Navier–Stokes are characterized by a generalized Kelvin's theorem, introduced by Constantin–Iyer (2008). In this note, we introduce a class of stochastic fluid equations, whose smooth solutions are characterized by natural extensions of the Kelvin theorems of their deterministic counterparts, which hold along certain noisy flows. These equations are called the stochastic Euler–Poincaré and stochastic Navier–Stokes–Poincaré equations respectively. The stochastic Euler–Poincaré equations were previously derived from a stochastic variational principle by Holm (2015), which we briefly review. Solutions of these equations do not obey pathwise energy conservation/dissipation in general. In contrast, we also discuss a class of stochastic fluid models, solutions of which possess energy theorems but do not, in general, preserve circulation theorems.

PERTURBATION ANALYSIS OF MULTICLASS STOCHASTIC FLUID MODELS

2002 ◽  
Vol 35 (1) ◽  
pp. 121-126 ◽  
Author(s):  
Christos G. Cassandras ◽  
Gang Sun ◽  
Christos G. Panayiotou ◽  
Yorai Wardi
Keyword(s):  
Perturbation Analysis ◽  
Fluid Models ◽  
Stochastic Fluid Models ◽  
Stochastic Fluid

A new computational approach for stochastic fluid models of multiplexers with heterogeneous sources

1995 ◽  
Vol 20 (1-2) ◽  
pp. 85-116 ◽  
Author(s):  
Boris Igelnik ◽  
Yaakov Kogan ◽  
Vladimir Kriman ◽  
Debasis Mitra
Keyword(s):  
Computational Approach ◽  
Fluid Models ◽  
Stochastic Fluid Models ◽  
Stochastic Fluid

Second-order stochastic fluid models with fluid-dependent flow rates

2002 ◽  
Vol 49 (1-4) ◽  
pp. 341-358 ◽  
Author(s):  
Dongyan Chen ◽  
Yiguang Hong ◽  
Kishor S. Trivedi
Keyword(s):  
Second Order ◽  
Fluid Models ◽  
Flow Rates ◽  
Stochastic Fluid Models ◽  
Dependent Flow ◽  
Stochastic Fluid
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