A Matrix Representation of Polymer Chain Size Distributions, 1. Linear Polymerization Mechanisms at Steady-State Conditions

2001 ◽  
Vol 10 (2) ◽  
pp. 79-99 ◽  
Author(s):  
José Carlos Pinto
Keyword(s):  
Steady State ◽  
Polymer Chain ◽  
Matrix Representation ◽  
Size Distributions

Matrix Representation of Polymer Chain Size Distributions, 2

2007 ◽  
Vol 16 (2) ◽  
pp. 178-193 ◽  
Author(s):  
Heloísa L. Sanches ◽  
Príamo A. Melo ◽  
José Carlos Pinto
Keyword(s):  
Polymer Chain ◽  
Matrix Representation ◽  
Size Distributions

scholarly journals Steady-State Size Distributions in Probabilistic Models of the Cell Division Cycle

1985 ◽  
Vol 45 (4) ◽  
pp. 523-540 ◽  
Author(s):  
Kenneth B. Hannsgen ◽  
John J. Tyson ◽  
Layne T. Watson
Keyword(s):  
Steady State ◽  
Cell Division ◽  
Probabilistic Models ◽  
Cell Division Cycle ◽  
Size Distributions ◽  
State Size

scholarly journals Steady-state size distributions for collisional populations:

Icarus ◽  
2003 ◽  
Vol 164 (2) ◽  
pp. 334-345 ◽  
Author(s):  
David P. O'Brien ◽  
Richard Greenberg
Keyword(s):  
Steady State ◽  
Size Distributions ◽  
State Size

scholarly journals Steady-state aerosol distributions in the extra-tropical, lower stratosphere and the processes that maintain them

2008 ◽  
Vol 8 (1) ◽  
pp. 3665-3692 ◽  
Author(s):  
J. C. Wilson ◽  
S.-H. Lee ◽  
J. M. Reeves ◽  
C. A. Brock ◽  
H. H. Jonsson ◽  
...  
Keyword(s):  
Steady State ◽  
Atmospheric Circulation ◽  
Northern Hemisphere ◽  
Lower Stratosphere ◽  
Size Distributions ◽  
Aerosol Properties ◽  
Made In

Abstract. Measurements of aerosol, N2O and OCS made in the Northern Hemisphere below 21 km altitude following the eruption of Pinatubo are presented and analyzed. After September 1999, the oxidation of OCS and the sedimentation of particles in the extra-tropical overworld maintain the aerosol in a steady state. This analysis empirically links precursor gas to aerosol abundance throughout this region. These processes are tracked with age-of-air which offers advantages over tracking as a function of latitude and altitude. In the extra-tropical, lowermost stratosphere, normalized volume distributions appear constant in time after the fall of 1999. Exchange with the troposphere is important in understanding aerosol evolution there. Size distributions of volcanically perturbed aerosol are included to distinguish between volcanic and non-volcanic conditions. This analysis suggests that model failures to correctly predict OCS and aerosol properties below 20 km in the Northern Hemisphere extra tropics result from inadequate descriptions of atmospheric circulation.

scholarly journals THE STEADY STATE CONFIGURATIONAL DISTRIBUTION DIFFUSION EQUATION OF THE STANDARD FENE DUMBBELL POLYMER MODEL: EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR ARBITRARY VELOCITY GRADIENTS

2009 ◽  
Vol 19 (11) ◽  
pp. 2039-2064 ◽  
Author(s):  
IONEL SORIN CIUPERCA ◽  
LIVIU IULIAN PALADE
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Polymer Chain ◽  
Viscoelastic Flows ◽  
Uniqueness Of Solutions ◽  
Outer Flow ◽  
Function Solution ◽  
Velocity Gradients ◽  
Nonlinear Elastic ◽  
Arbitrary Velocity

The configurational distribution function, solution of an evolution (diffusion) equation of the Fokker–Planck–Smoluchowski type, is (at least part of) the corner stone of polymer dynamics: it is the key to calculating the stress tensor components. This can be reckoned from Ref. 1, where a wealth of calculation details is presented regarding various polymer chain models and their ability to accurately predict viscoelastic flows. One of the simplest polymer chain idealization is the Bird and Warner's model of finitely extensible nonlinear elastic (FENE) chains. In this work we offer a proof that the steady state configurational distribution equation has unique solutions irrespective of the (outer) flow velocity gradients (i.e. for both slow and fast flows).

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