scholarly journals Steady-State Density of Reactants in Diffusion-Limited Reaction A+B->0 with Source

1988 ◽  
Vol 80 (6) ◽  
pp. 999-1004 ◽  
Author(s):  
S. Kanno ◽  
K.-i. Tainaka
Keyword(s):  
Steady State ◽  
State Density ◽  
Diffusion Limited ◽  
Diffusion Limited Reaction

Local Reaction Probability Effects in Non-Classical Kinetics: Batch and Steady State

1992 ◽  
Vol 290 ◽  
Author(s):  
Zhong-You Shi ◽  
Raoul Kopelman
Keyword(s):  
Steady State ◽  
Nearest Neighbor ◽  
Local Reaction ◽  
Reaction Order ◽  
Reaction Probability ◽  
Neighbor Distance ◽  
Reaction Conditions ◽  
Diffusion Limited ◽  
Diffusion Limited Reaction ◽  
Effective Reaction

AbstractThe reaction A+A→0 is simulated in 1-D and 2-D square lattices with various local reaction probabilities, P. The effective reaction order, X, and the nearest neighbor distance distribution (NNDD), are evaluated in all these reactions. For batch reactions, sharp increases in X with increasing P occur at early times. Classical reaction limited kinetics is obtained at early times only when P→0. At long times, all reactions are in the non-classical, diffusion limited regime, regardless of P. For steady state reactions, our results demonstrate a similar behavior of X with P. The NNDD at steady state in 1-D media at P=1.0, i.e. diffusion limited reaction, follows the previously reported skewed exponential shape. This is no longer true for P<I. Finally, at P→0, as expected, an exponential (Poissonian) distribution is obtained for both reaction conditions.

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

Glancing Angle X-Ray Study of Crystallization of Amorphous Ge at the Ge-A1 Interface

1990 ◽  
Vol 202 ◽  
Author(s):  
S. M. Heald ◽  
J. K. D. Jayanetti ◽  
R. C. Budhani
Keyword(s):  
Initial Period ◽  
Time Characteristic ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffusion Limited ◽  
Glancing Angle ◽  
Lower Temperature ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Good Agreement

ABSTRACTThe amorphous to crystalline transformation of Ge in Al/Ge thin film couples has been studied using glancing angle EXAFS, x-ray reflectivity and diffraction. It was found that crystallization occurs at a much lower temperature (118-150 °C) than for bulk Ge, and initiates at the Al/Ge interface. X-ray diffraction studies were made at 152 °C to study the kinetics of the reaction. After an initial period we find good agreement with a square root dependence of the time, characteristic of a diffusion limited reaction.

scholarly journals Iterative solutions to the steady-state density matrix for optomechanical systems

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
P. D. Nation ◽  
J. R. Johansson ◽  
M. P. Blencowe ◽  
A. J. Rimberg
Keyword(s):  
Steady State ◽  
Density Matrix ◽  
State Density ◽  
Optomechanical Systems ◽  
Iterative Solutions
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