STOCHASTICALLY SCALABLE FLOW CONTROL

2009 ◽  
Vol 23 (4) ◽  
pp. 675-698 ◽  
Author(s):  
Thomas Voice

Recent advances in the mathematical analysis of flow control have prompted the creation of the Scalable TCP (STCP) and Exponential RED (E-RED) algorithms. These are designed to be scalable under the popular deterministic delay stability modeling framework. In this article, we analyze stochastic models of STCP and STCP combined with E-RED link behavior. We find that under certain plausible network conditions, these probabilistic models also exhibit scalable behavior. In particular, we derive parameter choice schemes for which the equilibrium coefficients of variation of flow rates are bounded, however large, fast, or complex the network. Our model is shown to exhibit behavior similar to the mean field convergence that has recently been observed in TCP.

Author(s):  
Klaus Morawetz

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.


2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit

2019 ◽  
Vol 46 (3) ◽  
pp. 54-55
Author(s):  
Thirupathaiah Vasantam ◽  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Hui Huang ◽  
Jinniao Qiu

AbstractIn this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.


2021 ◽  
Vol 9 ◽  
Author(s):  
Lea Boßmann ◽  
Sören Petrat ◽  
Robert Seiringer

Abstract We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in $1/N$ .


2006 ◽  
Vol 69 (1) ◽  
pp. 145-153 ◽  
Author(s):  
M. L. HUTCHISON ◽  
L. D. WALTERS ◽  
G. C. MEAD ◽  
M. HOWELL ◽  
V. M. ALLEN

Studies to determine the appropriateness of the use of populations of indicator bacteria on poultry carcasses for process verification were undertaken in commercial slaughterhouses. Samples were collected from neck skin by excision or from whole carcass rinses and were examined for a range of presumptive process hygiene indicator bacteria. Coefficients of variation were calculated for each bacterial indicator and were significantly lower in excised samples, indicating more reproducible bacterial recovery by this sampling method. Total viable counts of aerobic bacteria, Enterobacteriaceae, and Pseudomonas in samples collected by excision had the lowest coefficients of variation when compared with other indicators and were therefore used for further study. The uncertainties associated with the quantification of each bacterial indicator were calculated and were lowest overall for total viable counts of aerobic bacteria. In general, uncertainty was higher for lower bacterial numbers. Results of microbiological testing on pooled excised neck skin samples were not significantly different from the mean of individually analyzed samples. Bacterial numbers increased by 1 log unit when cultures were stored under chilled conditions typical of those used for transporting samples to external laboratories, but the increases were not significant for Pseudomonas and aerobic bacteria when storage time was less than 17 h. Weak relationships were identified between bacterial indicator numbers and duration of processing, although cleanliness of the processing environment diminished visibly during this time. In the plants visited for this study, there was a poor relationship between presumptive bacterial indicator numbers and process hygiene. Consequently, bacterial analyses for process verification purposes may be of limited value.


Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.


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