scholarly journals Improvements to the Sink Strength Theory Used in Multi-Scale Rate Equation Simulations of Defects in Solids

Materials ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2621
Author(s):  
Tommy Ahlgren ◽  
Kalle Heinola
Keyword(s):  
Interaction Parameter ◽  
Rate Equation ◽  
Mean Field ◽  
Interaction Parameters ◽  
Rate Theory ◽  
Sink Strength ◽  
Strength Theory ◽  
Dissociation Process ◽  
Multi Scale ◽  
Defect Interaction

The application of mean-field rate theory equations have proven to be a versatile method in simulating defect dynamics and temporal changes in the microstructure of materials. The reliability and usefulness of the method, however, depends critically on the defect interaction parameters used. In this study, we show that the main interaction parameter, the sink strength, intrinsically depends on the detrapping, or the dissociation process itself. We present a theory on how to determine the appropriate sink strengths. The correct sink strength required for a detrapping defect, is considerably larger than the values commonly used, and thus should not be neglected.

scholarly journals Multi-scale dynamic mean field model (MDMF) relates resting-state brain dynamics with local cortical excitatory–inhibitory neurotransmitter homeostasis

2021 ◽  
pp. 1-55
Author(s):  
Amit Naskar ◽  
Anirudh Vattikonda ◽  
Gustavo Deco ◽  
Dipanjan Roy ◽  
Arpan Banerjee
Keyword(s):  
Resting State ◽  
Computational Models ◽  
Field Model ◽  
Diffusion Tensor ◽  
Brain Activity ◽  
Mean Field ◽  
Clustering Coefficient ◽  
Brain Dynamics ◽  
Mean Field Model ◽  
Multi Scale

Abstract Previous computational models have related spontaneous resting-state brain activity with local excitatory−inhibitory balance in neuronal populations. However, how underlying neurotransmitter kinetics associated with E-I balance governs resting state spontaneous brain dynamics remains unknown. Understanding the mechanisms by virtue of which fluctuations in neurotransmitter concentrations, a hallmark of a variety of clinical conditions relate to functional brain activity is of critical importance. We propose a multi-scale dynamic mean field model (MDMF) – a system of coupled differential equations for capturing the synaptic gating dynamics in excitatory and inhibitory neural populations as a function of neurotransmitter kinetics. Individual brain regions are modelled as population of MDMF and are connected by realistic connection topologies estimated from Diffusion Tensor Imaging data. First, MDMF successfully predicts resting-state functionalconnectivity. Second, our results show that optimal range of glutamate and GABA neurotransmitter concentrations subserve as the dynamic working point of the brain, that is, the state of heightened metastability observed in empirical blood-oxygen-level dependent signals. Third, for predictive validity the network measures of segregation (modularity and clustering coefficient) and integration (global efficiency and characteristic path length) from existing healthy and pathological brain network studies could be captured by simulated functional connectivity from MDMF model.

scholarly journals A Multi-scale Spin-Glass Mean-Field Model

2019 ◽  
Vol 368 (3) ◽  
pp. 1323-1344 ◽  
Author(s):  
Pierluigi Contucci ◽  
Emanuele Mingione
Keyword(s):  
Spin Glass ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
Multi Scale

Mean field rate theory and object kinetic Monte Carlo: A comparison of kinetic models

2008 ◽  
Vol 382 (2-3) ◽  
pp. 77-90 ◽  
Author(s):  
R.E. Stoller ◽  
S.I. Golubov ◽  
C. Domain ◽  
C.S. Becquart
Keyword(s):  
Monte Carlo ◽  
Kinetic Models ◽  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Rate Theory ◽  
Object Kinetic Monte Carlo

Significance of thermodynamic interaction parameters in guiding the optimization of polymer:nonfullerene solar cells

2020 ◽  
Vol 56 (83) ◽  
pp. 12463-12478
Author(s):  
Mengyuan Gao ◽  
Ziqi Liang ◽  
Yanhou Geng ◽  
Long Ye
Keyword(s):  
Solar Cells ◽  
Interaction Parameter ◽  
Polymer Solar Cells ◽  
Interaction Parameters ◽  
Recent Advances ◽  
Thermodynamic Interaction

Recent advances in analysing the morphology of nonfullerene polymer solar cells are discussed with an effective thermodynamic interaction parameter.

A rate equation for atomic ordering in mean field theory. II. General considerations

1991 ◽  
Vol 3 (17) ◽  
pp. 2975-2986 ◽  
Author(s):  
S Dattagupta ◽  
V Heine ◽  
S Marais ◽  
E Salje
Keyword(s):  
Field Theory ◽  
Rate Equation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Atomic Ordering

scholarly journals Randomized longest-queue-first scheduling for large-scale buffered systems

2015 ◽  
Vol 47 (04) ◽  
pp. 1015-1038 ◽  
Author(s):  
A. B. Dieker ◽  
T. Suk
Keyword(s):  
Limit Theorems ◽  
Large Scale ◽  
Scheduling Algorithm ◽  
Queueing Systems ◽  
Mean Field ◽  
Diffusion Approximations ◽  
Mean Field Limit ◽  
Multi Scale ◽  
Noteworthy Feature ◽  
Longest Queue First

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling (LQF) algorithm by establishing new mean-field limit theorems as the number of buffers n → ∞. We achieve this by allowing the number of sampled buffers d = d(n) to depend on the number of buffers n, which yields an asymptotic 'decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of n and d(n). To the best of the authors' knowledge, this is the first derivation of diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized LQF algorithm emulates the LQF algorithm, yet is computationally more attractive. The analysis of the system performance as a function of d(n) is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized LQF scheduling algorithm.

Pressure and Temperature Effects in Homopolymer Blends and Diblock Copolymers

1997 ◽  
Vol 30 (5) ◽  
pp. 696-701 ◽  
Author(s):  
H. Frielinghaus ◽  
D. Schwahn ◽  
K. Mortensen ◽  
L. Willner ◽  
K. Almdal
Keyword(s):  
Interaction Parameter ◽  
Diblock Copolymers ◽  
Mean Field ◽  
Three Dimensional ◽  
Thermal Fluctuation ◽  
Thermal Fluctuations ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Phase Boundaries ◽  
Composition Fluctuations

Thermal composition fluctuations in a homogeneous binary polymer blend and in a diblock copolymer were measured by small-angle neutron scattering as a function of temperature and pressure. The experimental data were analyzed with theoretical expressions, including the important effect of thermal fluctuations. Phase boundaries, the Flory–Huggins interaction parameter and the Ginzburg number were obtained. The packing of the molecules changes with pressure. Therefore, the degree of thermal fluctuation as a function of packing and temperature was studied. While in polymer blends packing leads, in some respects, to a universal behaviour, such behaviour is not found in diblock copolymers. It is shown that the Ginzburg number decreases with pressure sensitively in blends, while it is constant in diblock copolymers. The Ginzburg number is an estimation of the transition between the universality classes of the `mean-field' approximation and the three-dimensional Ising model. The phase boundaries in blends increase with pressure, while the phase boundary of the studied block copolymer shows an unusual shape: with increasing pressure it first decreases and then increases. Its origin is an increase of the entropic and of the enthalpic parts, respectively, of the Flory–Huggins interaction parameter.

A simple model of burst nucleation

2015 ◽  
Vol 17 (32) ◽  
pp. 20846-20852 ◽  
Author(s):  
Alexandr Baronov ◽  
Kevin Bufkin ◽  
Dan W. Shaw ◽  
Brad L. Johnson ◽  
David L. Patrick
Keyword(s):  
Simple Model ◽  
Induction Period ◽  
Rate Equation ◽  
Self Assembly ◽  
Mean Field ◽  
Equation Model ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Rate Equation Model ◽  
Quantitative Treatment

We introduce a comprehensive quantitative treatment for burst nucleation (BN), a kinetic pathway toward self-assembly or crystallization defined by an extended post-supersaturation induction period, followed by a burst of nucleation, and finally the growth of existing stable assemblages absent the formation of new ones, based on a hybrid mean field rate equation model incorporating thermodynamic treatment of the saturated solvent from classical nucleation theory.

Role of Interstitial and Interstitial-Impurity Interaction on Irradiation-Induced Segregation in Austenitic Steels

1997 ◽  
Vol 481 ◽  
Author(s):  
M. Nastar ◽  
P. Bellon ◽  
G. Martin ◽  
J. Ruste
Keyword(s):  
Mean Field ◽  
Tracer Diffusion ◽  
Austenitic Steels ◽  
Rate Theory ◽  
Fitting Procedure ◽  
Surfaces And Interfaces ◽  
Total Inhibition ◽  
Impurity Interaction ◽  
Jump Frequencies

ABSTRACTSegregation under irradiation in austenitic steels is due to a permanent flux of vacancies and interstitials produced by irradiation towards sinks like surfaces and interfaces. A model based on a mean field lattice rate theory is proposed where kinetics and thermodynamics are treated in a mutually consistent way. For a Fe-Ni-Cr ternary alloy, the 15 parameters defining the jump frequencies of vacancies were fitted on equilibrium properties including ordering energies and tracer diffusion experiments with no use of segregation data. Measurements of RIS by Auger Electron Spectroscopy (AES) were used in the last step of the fitting procedure in order to choose the best set of the 27 interstitial jump frequencies. This fitting procedure strongly supports the idea that the interstitials are contributing to RIS in Fe-Cr-Ni alloys. We also simulate the trapping of interstitials by an impurity model and reproduce the total inhibition of RIS by this impurity as observed experimentally [1].

Interaction Parameters and Heats of Dilution for Ethylene Propylene Rubber in Various Solvents

1966 ◽  
Vol 39 (5) ◽  
pp. 1451-1459 ◽  
Author(s):  
Earl D. Holly
Keyword(s):  
Interaction Parameter ◽  
Polymer Concentration ◽  
Interaction Parameters ◽  
Temperature Dependent ◽  
Heat Of Dilution ◽  
Ethylene Propylene ◽  
Thermodynamic Criterion ◽  
Heats Of Dilution ◽  
Ethylene Propylene Rubber ◽  
Polymer Interaction

Abstract Crosslinked ethylene propylene rubber gels were swollen in five solvents at 25–100° C. The solvent polymer interaction parameter μ for each system was determined as a function of temperature and polymer concentration. A thermodynamic criterion of the sign of the heat of dilution, ΔH1, was pointed out. For three of the systems ΔH1 was negative. The entropy contribution to the interaction parameter was found to be smaller than usual for systems having a temperature-dependent heat of dilution. The heats of dilution and the entropy terms may be consistently interpreted in terms of Prigogine's theory of solutions.

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