Smoluchowski equation with a sink term: Analytical solutions for the rate constant and their numerical test

1998 ◽  
Vol 109 (11) ◽  
pp. 4182-4189 ◽  
Author(s):  
A. M. Berezhkovskii ◽  
Yu. A. D’yakov ◽  
V. Yu. Zitserman
Keyword(s):  
Rate Constant ◽  
Analytical Solutions ◽  
Numerical Test ◽  
Smoluchowski Equation ◽  
Sink Term

A new numerical method to approximate root water uptake fluxes in a mixed-dimensional 1D-3D setting

2021 ◽  
Author(s):  
Timo Koch ◽  
Hanchuan Wu ◽  
Kent-André Mardal ◽  
Rainer Helmig ◽  
Martin Schneider
Keyword(s):  
Analytical Solutions ◽  
Water Pressure ◽  
Numerical Test ◽  
Three Dimensional ◽  
Root Water Uptake ◽  
Richards Equation ◽  
Soil Pressure ◽  
Approximation Accuracy ◽  
Flux Approximation ◽  
Local Water

<p>1D-3D methods are used to describe root water and nutrient uptake in complex root networks. Root systems are described as networks of line segments embedded in a three-dimensional soil domain. Particularly for dry soils, local water pressure and nutrient concentration gradients can be become very large in the vicinity of roots. Commonly used discretization lengths (for example 1cm) in root-soil interaction models do not allow to capture these gradients accurately. We present a new numerical scheme for approximating root-soil interface fluxes. The scheme is formulated in the continuous PDE setting so that is it formally independent of the spatial discretization scheme (e.g. FVM, FD, FEM). The interface flux approximation is based on a reconstruction of interface quantities using local analytical solutions of the steady-rate Richards equation. The local mass exchange is numerically distributed in the vicinity of the root. The distribution results in a regularization of the soil pressure solution which is easier to approximate numerically. This technique allows for coarser grid resolutions while maintaining approximation accuracy. The new scheme is verified numerically against analytical solutions for simplified cases. We also explore limitations and possible errors in the flux approximation with numerical test cases. Finally, we present the results of a recently published benchmark case using this new method.</p>

scholarly journals Finite Element Solution of the Steady-State Smoluchowski Equation for Rate Constant Calculations

2004 ◽  
Vol 86 (4) ◽  
pp. 2017-2029 ◽  
Author(s):  
Yuhua Song ◽  
Yongjie Zhang ◽  
Tongye Shen ◽  
Chandrajit L. Bajaj ◽  
J. Andrew McCammon ◽  
...  
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Rate Constant ◽  
Smoluchowski Equation ◽  
Finite Element Solution ◽  
Element Solution

Functional Properties of p-Anisoylated Plasmin-Staphylokinase Complex

1993 ◽  
Vol 70 (02) ◽  
pp. 326-331 ◽  
Author(s):  
H R Lijnen ◽  
B Van Hoef ◽  
R A G Smith ◽  
D Collen
Keyword(s):  
Human Plasma ◽  
Rate Constant ◽  
Time Course ◽  
Bolus Injection ◽  
Similar Rate ◽  
Clot Lysis ◽  
Lag Phase ◽  
Plasma Clot ◽  
Rapid Clearance ◽  
Stoichiometric Complex

SummaryThe kinetic and fibrinolytic properties of a reversibly acylated stoichiometric complex between human plasmin and recombinant staphylokinase (plasmin-STAR complex) were evaluated. The acylation rate constant of plasmin-STAR by p-amidinophenyl-p’-anisate-HCI was 52 M-1 s-1 and its deacylation rate constant 1.2 × 10-4 s-1 (t½ of 95 min) which are respectively 50-fold and around 3-fold lower than for the plasmin-streptokinase complex. The acylated complex was stable as evidenced by binding to lysine-Sepharose. However, following an initial short lag phase, the acylated plasmin-STAR complex activated plasminogen at a similar rate as the unblocked complex, whereas the acylated plasmin-streptokinase complex did not activate plasminogen. These findings indicate that STAR, unlike streptokinase, dissociates from its acylated complex with plasmin in the presence of excess plasminogen. In agreement with this hypothesis, the time course of the lysis of a 125I-fibrin labeled plasma clot submerged in citrated human plasma, is similar for acylated plasmin-STAR, unblocked plasmin-STAR and free STAR (50% clot lysis in 2 h requires 12 nM of each agent). The plasma clearances of STAR-related antigen following bolus injection in hamsters were 1.0 to 1.5 ml/min for acylated plasmin-STAR, unblocked plasmin-STAR and free STAR, as a result of short initial half-lives of 2.0 to 2.5 min.The dissociation of the anisoylated plasmin-STAR complex and its consequent rapid clearance suggest that it has no apparent advantages as compared to free STAR for clinical thrombolysis.

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