Münch without tears: a steady-state Münch-like model of phloem so simplified that it requires only algebra to predict the speed of translocation

2012 ◽  
Vol 39 (6) ◽  
pp. 531 ◽  
Author(s):  
William F. Pickard
Keyword(s):  
Loading Rate ◽  
Sieve Tube ◽  
Sink Strength ◽  
Square Root ◽  
Algebraic Equations ◽  
Source Regions ◽  
Osmotic Water ◽  
Constant Rate ◽  
Phloem Translocation ◽  
Translocation Speed

The pressure-driven mass-flow hypothesis of phloem translocation associated with Ernst Münch has become hegemonic and has been mathematically modelled in many, many different fashions – but not, apparently, in one chosen so that it gives simple algebraic predictions of (i) the speed of translocation; (ii) the saccharide concentration at the source; and (iii) the pressure offset due to translocation. To overcome this deficit, the problem was drastically simplified by assuming that: (i) radial variations could be neglected; (ii) osmotic water uptake was restricted to sink and source regions of negligible thickness; (iii) there was a constant rate of saccharide loading at the source; and (iv) the sink strength was sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it becomes unimportant. The resulting system of quadratic algebraic equations was then solved for the translocation speed, which was shown to vary as the square-root of the loading rate. Also found were the offset of the intra-tube hydrostatic pressure and the sap saccharide concentration at the source, which, likewise, vary as the square-root of the loading rate.

Time Dependent Deformation During Indentation Testing

1996 ◽  
Vol 436 ◽  
Author(s):  
B. N. Lucas ◽  
W. C. Oliver ◽  
G. M. Pharr ◽  
J-L. Loubet
Keyword(s):  
Loading Rate ◽  
Time History ◽  
Tensile Tests ◽  
Constant Load ◽  
Indentation Creep ◽  
Creep Tests ◽  
Constant Rate ◽  
Indentation Tests ◽  
Constant Loading Rate ◽  
Indentation Strain

AbstractConstant loading rate/load indentation tests (1/P dP/dt) and constant rate of loading followed by constant load (CRL/Hold) indentation creep tests have been conducted on high purity electropolished indium. It is shown that for a material with a constant hardness as a function of depth, a constant (1/P dP/dt) load-time history results in a constant indentation strain rate (1/h dh/dt). The results of the two types of tests are discussed and compared to data in the literature for constant stress tensile tests. The results from the constant (1/P dP/dt) experiments appear to give the best correlation to steady-state uniaxial data.

Interactions between Source, Path and Sink in Determining Phloem Translocation Rate

1978 ◽  
Vol 5 (5) ◽  
pp. 665
Author(s):  
A Lang
Keyword(s):  
Hydrostatic Pressure ◽  
Sap Flow ◽  
Sieve Tube ◽  
Joint Control ◽  
Temperature Changes ◽  
Slightly Compressible ◽  
Steady Rate ◽  
Phloem Translocation ◽  
Sieve Tubes ◽  
The Individual

Treatments involving mild (5-10 Celsius degrees) temperature changes, spanning a range of mean temperatures, were imposed upon the source, path and sink regions of a translocating plant of Nymphoides geminata whilst the translocation rate was monitored. The temperature dependence (Q*10) of the rate of translocation was evaluated for each of these treatments. A new steady rate was achieved in only 3-5 min following a temperature change and was sustained for 2 h or more. Changes in rate were propagated down the sieve tubes at speeds more than ten times greater than those of sap flow, indicating that translocation involves the flow of a slightly compressible sap. The results suggest that translocation rate is normally under the joint control of source, path and sink regions of the plant. An attempt is made to assess their relative contributions to the overall control and this leads to the conclusion that, in this plant situation, the pathway predominates in controlling rate. It would seem that the individual rates of activity of source, path and sink regions are modulated by changes in the sieve tube sap concentration in their vicinity, these changes corresponding to, and being brought about rapidly by, changes in the hydrostatic pressure of this sap.

Modified square root of time relation to predict evaporation trends from bare soil

Soil Research ◽  
1988 ◽  
Vol 26 (2) ◽  
pp. 281 ◽  
Author(s):  
SK Jalota ◽  
SS Prihar ◽  
KS Gill
Keyword(s):  
Evaporation Rate ◽  
Transport Theory ◽  
Sandy Loam ◽  
Empirical Relation ◽  
Bare Soil ◽  
Square Root ◽  
Silt Loam ◽  
Empirical Relations ◽  
Constant Rate ◽  
Time Relation

The existing methods of calculating cumulative evaporation (CE) from water transport theory pose a problem of availability of the governing parameters of the soil and atmospheric evaporativity. An empirical relation between CE, inclusive of the constant rate stage, and its time limit is not available. We investigated relations between CE and time (t) for different evaporativities (4). Estimates of CE by using the empirical relations between CE, t and vt agreed well with the observed values: where tf is the duration of the constant rate stage which can be computed from K and E0 K is the r,egression coefficient of CE on vt and b is the intercept. The results indicated that the duration of the constant rate stage decreased with increasing E0 and increasing redistribution time (T); CE under a lower E0 can exceed that under higher E0. Evaporation rate during the falling rate stage is dependent upon E0. For the same E0, the duration of the constant rate stage was higher in silt loam than in sandy loam.

A simplest steady-state Munch-like model of phloem translocation, with source and pathway and sink

2009 ◽  
Vol 36 (7) ◽  
pp. 629 ◽  
Author(s):  
William F. Pickard ◽  
Barbara Abraham-Shrauner
Keyword(s):  
Steady State ◽  
Flow Model ◽  
Sieve Tube ◽  
Steady State Solution ◽  
Second Order ◽  
Axial Position ◽  
Pressure Drops ◽  
Low Viscosity ◽  
Phloem Translocation ◽  
Source Sink

In the 80 years since its introduction by Münch, the pressure-driven mass-flow model of phloem translocation has become hegemonic, and has been mathematically modelled in many different fashions but not, to our knowledge, by one that incorporated the equations of hydrodynamics with those of osmosis and slice-source and slice-sink boundary conditions to yield a system that admits of an analytical steady-state solution for the sap velocity in a single sieve tube. To overcome this situation, we drastically simplified the problem by: (i) justifying a low Peclet number idealisation in which transverse variations could be neglected; (ii) justifying a low viscosity idealisation in which axial pressure drops could be neglected; and (iii) assuming a sink of strength sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it became unimportant. The resulting ordinary nonlinear second-order differential equation in sap velocity and axial position was of a generalised Liénard form with a single forcing parameter; and this is reason enough for the lack of a known analytic solution. However, since the forcing parameter was very large, it was possible to deduce approximate second-order solutions for behavior in the source, sink and transport regions: the sap velocity is zero at the slice-source, climbs with exponential rapidity to a plateau, maintains this plateau over most of the sieve tube, and then drops with exponential rapidity to zero at the slice-sink.

ON THE ABSORPTION PROBLEM FOR RANDOM DISPERSIONS

1994 ◽  
Vol 04 (06) ◽  
pp. 755-772
Author(s):  
KONSTANTIN Z. MARKOV ◽  
MIKHAIL K. KOLEV
Keyword(s):  
Numerical Procedure ◽  
Sink Strength ◽  
Statistical Solution ◽  
Constant Rate ◽  
The Matrix ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Analytical Formulas ◽  
Random Dispersion ◽  
Steady State Problem

This paper is devoted to the steady-state problem of absorption of a diffusing species (say, irradiation defects) in a random dispersion of spheres. The defects are created at a constant rate throughout the medium and are absorbed afterward, with different sink strengths, by the matrix and by the inclusions. One is to find the random diffusing species field and, in particular, the effective sink strength of the dispersion, having assumed the statistics of the spheres known. The problem is modeled by a Helmhotz equation with a random coefficient (the randomly fluctuating sink strength of the dispersion). The statistical solution of the latter is explicitly constructed, in a simple form, by means of the so-called factorial functional series, recently introduced by one of the authors. In particular, analytical formulas, correct to the order “square of sphere fraction,” are obtained for the effective sink strength of the dispersion and for the two-point correlation function of the diffusing species field. An effective numerical procedure, allowing to specify these quantities, is described and numerical results are finally presented and discussed.

Stress-strain characteristics of thermoplastics at constant rates of loading

1968 ◽  
Vol 3 (3) ◽  
pp. 187-192
Author(s):  
R M Ogorkiewicz ◽  
L E Culver ◽  
M P Bowyer
Keyword(s):  
Tensile Test ◽  
Loading Rate ◽  
Constant Stress ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Stress Strain ◽  
Constant Loading ◽  
Constant Rate ◽  
Constant Loading Rate

The paper describes the development of a uniaxial tensile test, at constant loading rate, for thermoplastics and compares the results obtained with those from tests at constant rate of elongation and constant stress.

scholarly journals Phloem transport limitation in Huanglongbing affected sweet orange is dependent on phloem-limited bacteria and callose

2021 ◽  
Author(s):  
Stacey Welker ◽  
Myrtho Pierre ◽  
James Patrick Santiago ◽  
Manjul Dutt ◽  
Christopher Vincent ◽  
...  
Keyword(s):  
Genetic Material ◽  
Sugar Transport ◽  
Phloem Transport ◽  
Microbial Infection ◽  
Transport Pathway ◽  
Callose Deposition ◽  
Citrus Production ◽  
Candidatus Liberibacter ◽  
Phloem Translocation ◽  
Translocation Speed

Huanglongbing (HLB), caused by Candidatus Liberibacter asiaticus (CLas), is a phloem-limited disease which disrupts citrus production in affected areas. In HLB-affected plants, phloem sieve plate pores accumulate callose, and leaf carbohydrate export is reduced. However, whether HLB causes a reduction in carbohydrate phloem translocation speed, and the quantitative relationships among callose, CLas population, and phloem translocation are still unknown. In this work, a procedure was developed to concurrently measure sugar transport, callose deposition, and relative pathogen population at different locations throughout the stem. Increasing quantities of CLas genetic material were positively correlated with quantity and density of callose deposits, and negatively correlated with phloem translocation speed. Callose deposit quantity was site- and rootstock dependent, and were negatively correlated with phloem translocation speed, suggesting a localized relationship. Remarkably, callose accumulation and phloem translocation disruption in the scion was dependent on rootstock genotype. Regression results suggested that the interaction of Ct values and number of phloem callose depositions, but not their size or density, explained the effects on translocation speed. Sucrose, starch, and sink 14C label allocation data support the interpretation of a transport pathway limitation by CLas infection. This work shows that the interaction of local accumulation of callose and CLas affect phloem transport. Further, the extent of this accumulation is attenuated by the rootstock and provides important information about the disease mechanism of phloem-inhabiting bacteria. Together, these results constitute the first example of a demonstrated transport limitation of phloem function by a microbial infection.

scholarly journals Sieve tube structural variation in Austrobaileya scandens and its significance for lianescence

2021 ◽  
Author(s):  
Juan Losada ◽  
Zhe He ◽  
Noel Holbrook
Keyword(s):  
Resource Allocation ◽  
Hydraulic Resistance ◽  
Structural Variation ◽  
Vascular System ◽  
Sieve Tube ◽  
Sink Strength ◽  
Sieve Plate ◽  
Vascular Elements ◽  
Microscopy Analysis ◽  
Sieve Plates

Lianas combine large leaf areas with slender stems, features that require an efficient vascular system. The only extant member of the Austrobaileyaceae is an endemic twining liana of the tropical Australian forests with well-known xylem hydraulics, but the vascular phloem continuum aboveground remains understudied. Microscopy analysis across leaf veins and stems of A. scandens revealed a low foliar xylem to phloem ratio, with isodiametric vascular elements along the midrib, but tapered across vein orders. Small sieve plate pore radii increased from 0.08 µm in minor veins to 0.12 µm in the petiole, but only to 0.20 µm at the stem base, tens of meters away. In searcher branches, phloem conduits contained a pectin-rich wall and simple plates, whereas in twinning stems, conduits connected through highly-angled-densely populated sieve plates. Twisted and elongated stems of A. scandens display a high hydraulic resistance of phloem conduits, which decreases from leaves to stems, efficiently delivering photoassimilate from sources under Münch predictions. Sink strength of a continuously growing canopy might be stronger than in self-supporting understory plants, favoring resource allocation to aerial organs in angiosperms that colonized the vertical niche.

Constant-Rate Feed Device. A Reply to Comment

1950 ◽  
Vol 22 (7) ◽  
pp. 956-956 ◽  
Author(s):  
Lester Lundsted
Keyword(s):  
Constant Rate ◽  
Feed Device
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