Kinetics of diffusive phase transformations: From local equilibrium to mobility-driven migration of thick interfaces

2011 ◽  
Vol 83 (5) ◽  
pp. 1105-1112
Author(s):  
Ernst Gamsjäger
Keyword(s):  
Steady State ◽  
Phase Transformations ◽  
Evolution Equations ◽  
Local Equilibrium ◽  
Time Dependent ◽  
Dependent Development ◽  
Principle Of Maximum Entropy ◽  
Kinetics Of ◽  
Principle Of Maximum ◽  
Satisfactory Manner

It is a prerequisite for the occurrence of diffusive phase transformations that the system is in an off-equilibrium condition. The time-dependent development of the variables until equilibrium or steady-state conditions are reached can be calculated by solving the evolution equations that can be derived from the principle of maximum entropy production. These equations provide the theoretical framework for the kinetics of diffusive phase transformations. In this work, the development from sharp interface-local equilibrium (SI-LE) models to thick interface-finite mobility (TI-FM) models is reviewed and presented in the light of the above-mentioned principle. Experimental results indicate that the kinetics of diffusive solid-state phase transformations can, at least in certain ranges of composition and temperature, be modeled in a satisfactory manner by the TI-FM approach only.

scholarly journals Determinants of mRNA stability in Dictyostelium discoideum amoebae: differences in poly(A) tail length, ribosome loading, and mRNA size cannot account for the heterogeneity of mRNA decay rates.

1988 ◽  
Vol 8 (5) ◽  
pp. 1957-1969 ◽  
Author(s):  
R A Shapiro ◽  
D Herrick ◽  
R E Manrow ◽  
D Blinder ◽  
A Jacobson
Keyword(s):  
Steady State ◽  
Dictyostelium Discoideum ◽  
Mrna Decay ◽  
Decay Rates ◽  
Time Dependent ◽  
Translational Efficiency ◽  
Cdna Clones ◽  
Dependent Manner ◽  
Significant Difference ◽  
Kinetics Of

As an approach to understanding the structures and mechanisms which determine mRNA decay rates, we have cloned and begun to characterize cDNAs which encode mRNAs representative of the stability extremes in the poly(A)+ RNA population of Dictyostelium discoideum amoebae. The cDNA clones were identified in a screening procedure which was based on the occurrence of poly(A) shortening during mRNA aging. mRNA half-lives were determined by hybridization of poly(A)+ RNA, isolated from cells labeled in a 32PO4 pulse-chase, to dots of excess cloned DNA. Individual mRNAs decayed with unique first-order decay rates ranging from 0.9 to 9.6 h, indicating that the complex decay kinetics of total poly(A)+ RNA in D. discoideum amoebae reflect the sum of the decay rates of individual mRNAs. Using specific probes derived from these cDNA clones, we have compared the sizes, extents of ribosome loading, and poly(A) tail lengths of stable, moderately stable, and unstable mRNAs. We found (i) no correlation between mRNA size and decay rate; (ii) no significant difference in the number of ribosomes per unit length of stable versus unstable mRNAs, and (iii) a general inverse relationship between mRNA decay rates and poly(A) tail lengths. Collectively, these observations indicate that mRNA decay in D. discoideum amoebae cannot be explained in terms of random nucleolytic events. The possibility that specific 3'-structural determinants can confer mRNA instability is suggested by a comparison of the labeling and turnover kinetics of different actin mRNAs. A correlation was observed between the steady-state percentage of a given mRNA found in polysomes and its degree of instability; i.e., unstable mRNAs were more efficiently recruited into polysomes than stable mRNAs. Since stable mRNAs are, on average, "older" than unstable mRNAs, this correlation may reflect a translational role for mRNA modifications that change in a time-dependent manner. Our previous studies have demonstrated both a time-dependent shortening and a possible translational role for the 3' poly(A) tracts of mRNA. We suggest, therefore, that the observed differences in the translational efficiency of stable and unstable mRNAs may, in part, be attributable to differences in steady-state poly(A) tail lengths.

A NEW METHOD FOR SUPERSATURATION MEASUREMENT: IDEA, IMPLEMENTATION AND RESULTS

2002 ◽  
Vol 16 (01n02) ◽  
pp. 391-398 ◽  
Author(s):  
M. LÖFFELMANN ◽  
A. MERSMANN
Keyword(s):  
Crystal Growth ◽  
Physical Properties ◽  
Crystallization Process ◽  
Measurement Methods ◽  
Time Dependent ◽  
Sensor Surface ◽  
Dependent Development ◽  
Starting Time ◽  
Metastable Zone ◽  
Kinetics Of

Up to now supersaturation measurement can be generalized as using physical properties that show a dependence on concentration as measurands for supersaturation. Impurities, foreign particles or ions influence the metastable zone width as well as the kinetics of nucleation and crystal growth, but most of the existing measurement methods are not able to incorporate those disturbances in the measured supersaturation. Therefore, a supersaturation sensor considering the actual crystallization process itself has been developed. The idea of the new supersaturation sensor is to induce crystallization on the sensor surface by generating an additional supersaturation by cooling and to observe the time-dependent development of the incrustation. Assuming a constant cooling rate and constant properties of the sensor surface the starting time of the incrustation on the sensor surface depends only on the prevailing supersaturation in the process solution. Experimental results obtained for inorganic ( KNO 3) and organic (Adipicacid) crystallizing solutes proved the applicability of the new sensor.

The growth kinetics of ledges during phase transformations: multistep interactions

1982 ◽  
Vol 384 (1786) ◽  
pp. 107-133 ◽  
Keyword(s):  
Steady State ◽  
Phase Transformations ◽  
Growth Kinetics ◽  
Volume Diffusion ◽  
Asymptotic Methods ◽  
Parent Phase ◽  
Growth Characteristics ◽  
Controlling Factor ◽  
Kinetics Of ◽  
Equal Height

An analysis of the growth characteristics of a train of ledges is presented, where volume diffusion in the parent phase is assumed to be the rate­- controlling factor. First a train of steps of unequal height is considered where the step heights are assumed to be consistent with a steady-state motion so that each step moves with the same speed. It is possible to analyse this situation by asymptotic methods when the steps are either far apart or close together. Explicit results are given for both two- and three-step trains and it is shown how the step heights must vary if a given train is to move steadily at a specified speed. Trains of steps of equal height are also considered and an analysis is made of the relative velocities of such steps due to their interaction.

On the thermodynamic stability of steady-state adiabatic systems

1988 ◽  
Vol 189 ◽  
pp. 509-529 ◽  
Author(s):  
L. F. Henderson
Keyword(s):  
Steady State ◽  
Local Thermodynamic Equilibrium ◽  
Equilibrium System ◽  
Adiabatic Flow ◽  
Total Enthalpy ◽  
Principle Of Maximum Entropy ◽  
System A ◽  
The Subject ◽  
Principle Of Maximum ◽  
Oblique Shocks

This paper begins by reviewing Bethe's (1942) work on the subject. He considered the propagation of a normal shock wave in a medium with an arbitrary equation of state. Difficulties arise if one attempts to extend his theory to systems containing plane oblique shocks or the reflection or refraction of such shocks. The object of the present paper is to resolve these difficulties. General conditions for the local thermodynamic equilibrium and thermodynamie stability, of a non-equilibrium system in steady-state, adiabatic, flow are summarized by the principle of maximum entropy production, which gives \[ \Delta s\geqslant 0;\quad {\rm d}(\Delta s)= 0;\quad {\rm d}^2(\Delta s) < 0, \] for ht, constant, where s is the specific entropy and ht is the specific total enthalpy; it is deduced from the second law. Conversely the consequences of Δs < 0, d(Δs) ≠ 0, d2(Δs) = 0, are discussed and may lead to either an impossibility or to some form of instability such as unsteadiness, or a change in the structure of the system (a catastrophe).

scholarly journals Approximation of the steady state system state distribution of the M/G/1 retrial queue with impatient customers

2012 ◽  
Vol 22 (2) ◽  
pp. 285-296 ◽  
Author(s):  
Nadjet Stihi ◽  
Natalia Djellab
Keyword(s):  
Steady State ◽  
Retrial Queue ◽  
Mean Value ◽  
Retrial Queues ◽  
System State ◽  
Impatient Customers ◽  
State Distribution ◽  
Information Theoretic ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

For M/G/1 retrial queues with impatient customers, we review the results, concerning the steady state distribution of the system state, presented in the literature. Since the existing formulas are cumbersome (so their utilization in practice becomes delicate) or the obtaining of these formulas is impossible, we apply the information theoretic techniques for estimating the above mentioned distribution. More concretely, we use the principle of maximum entropy which provides an adequate methodology for computing a unique estimate for an unknown probability distribution based on information expressed in terms of some given mean value constraints.

scholarly journals Dynamic Maximum Entropy Reduction

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 715 ◽  
Author(s):  
Václav Klika ◽  
Michal Pavelka ◽  
Petr Vágner ◽  
Miroslav Grmela
Keyword(s):  
Maximum Entropy ◽  
Evolution Equations ◽  
Hyperbolic Heat Conduction ◽  
State Variables ◽  
Principle Of Maximum Entropy ◽  
Reduced Equations ◽  
Explicit Recognition ◽  
Entropy Reduction ◽  
Principle Of Maximum ◽  
Different Levels

Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of conjugate variables guarantees that the reduced equations are closed. Moreover, an infinite chain of consecutive DynMaxEnt approximations can be constructed. The method is demonstrated on a particle with friction, complex fluids (equipped with conformation and Reynolds stress tensors), hyperbolic heat conduction and magnetohydrodynamics.

scholarly journals Determinants of mRNA stability in Dictyostelium discoideum amoebae: differences in poly(A) tail length, ribosome loading, and mRNA size cannot account for the heterogeneity of mRNA decay rates

1988 ◽  
Vol 8 (5) ◽  
pp. 1957-1969
Author(s):  
R A Shapiro ◽  
D Herrick ◽  
R E Manrow ◽  
D Blinder ◽  
A Jacobson
Keyword(s):  
Steady State ◽  
Dictyostelium Discoideum ◽  
Mrna Decay ◽  
Decay Rates ◽  
Time Dependent ◽  
Translational Efficiency ◽  
Cdna Clones ◽  
Dependent Manner ◽  
Significant Difference ◽  
Kinetics Of

As an approach to understanding the structures and mechanisms which determine mRNA decay rates, we have cloned and begun to characterize cDNAs which encode mRNAs representative of the stability extremes in the poly(A)+ RNA population of Dictyostelium discoideum amoebae. The cDNA clones were identified in a screening procedure which was based on the occurrence of poly(A) shortening during mRNA aging. mRNA half-lives were determined by hybridization of poly(A)+ RNA, isolated from cells labeled in a 32PO4 pulse-chase, to dots of excess cloned DNA. Individual mRNAs decayed with unique first-order decay rates ranging from 0.9 to 9.6 h, indicating that the complex decay kinetics of total poly(A)+ RNA in D. discoideum amoebae reflect the sum of the decay rates of individual mRNAs. Using specific probes derived from these cDNA clones, we have compared the sizes, extents of ribosome loading, and poly(A) tail lengths of stable, moderately stable, and unstable mRNAs. We found (i) no correlation between mRNA size and decay rate; (ii) no significant difference in the number of ribosomes per unit length of stable versus unstable mRNAs, and (iii) a general inverse relationship between mRNA decay rates and poly(A) tail lengths. Collectively, these observations indicate that mRNA decay in D. discoideum amoebae cannot be explained in terms of random nucleolytic events. The possibility that specific 3'-structural determinants can confer mRNA instability is suggested by a comparison of the labeling and turnover kinetics of different actin mRNAs. A correlation was observed between the steady-state percentage of a given mRNA found in polysomes and its degree of instability; i.e., unstable mRNAs were more efficiently recruited into polysomes than stable mRNAs. Since stable mRNAs are, on average, "older" than unstable mRNAs, this correlation may reflect a translational role for mRNA modifications that change in a time-dependent manner. Our previous studies have demonstrated both a time-dependent shortening and a possible translational role for the 3' poly(A) tracts of mRNA. We suggest, therefore, that the observed differences in the translational efficiency of stable and unstable mRNAs may, in part, be attributable to differences in steady-state poly(A) tail lengths.

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