scholarly journals Solution of a one-dimensional stochastic model with branching and coagulation reactions

2001 ◽  
Vol 64 (4) ◽  
Author(s):  
Mauro Mobilia ◽  
Pierre-Antoine Bares
Keyword(s):  
Stochastic Model ◽  
One Dimensional

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Stochastic Model of Non-Isothermal Flow Chemical Reactor

1996 ◽  
Vol 61 (2) ◽  
pp. 242-258 ◽  
Author(s):  
Vladimír Kudrna ◽  
Libor Vejmola ◽  
Pavel Hasal
Keyword(s):  
Stochastic Model ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Dispersion Model ◽  
Chemical Reactor ◽  
Segregation Index ◽  
One Dimensional ◽  
A Value ◽  
Isothermal Case ◽  
Flow Through

Recently developed stochastic model of a one-dimensional flow-through chemical reactor is extended in this paper also to the non-isothermal case. The model enables the evaluation of concentration and temperature profiles along the reactor. The results are compared with the commonly used one-dimensional dispersion model with Danckwerts' boundary conditions. The stochastic model also enables to evaluate a value of the segregation index.

Stochastic model of a one-dimensional fluid

1975 ◽  
Vol 12 (2) ◽  
pp. 153-162 ◽  
Author(s):  
Sezar Fesciyan ◽  
H. L. Frisch
Keyword(s):  
Stochastic Model ◽  
One Dimensional

scholarly journals Stochastic model of a one-dimensional fluid

1975 ◽  
Vol 13 (3) ◽  
pp. 277-278
Author(s):  
Sezar Fesciyan ◽  
H. L. Frisch
Keyword(s):  
Stochastic Model ◽  
One Dimensional

scholarly journals Transitional Channel Flow: A Minimal Stochastic Model

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1348
Author(s):  
Paul Manneville ◽  
Masaki Shimizu
Keyword(s):  
Laminar Flow ◽  
Stochastic Model ◽  
Channel Flow ◽  
Lateral Spreading ◽  
Critical Properties ◽  
Von Neumann ◽  
One Dimensional ◽  
Longitudinal Splitting ◽  
Thermodynamic Phase ◽  
Single Orientation

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

Anomalous transport: A one-dimensional stochastic model

1990 ◽  
Vol 146 (3) ◽  
pp. 433-444 ◽  
Author(s):  
G. Zumofen ◽  
J. Klafter ◽  
A. Blumen
Keyword(s):  
Stochastic Model ◽  
Anomalous Transport ◽  
One Dimensional

scholarly journals Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210214
Author(s):  
Matthew J. Simpson ◽  
Alexander P. Browning ◽  
Christopher Drovandi ◽  
Elliot J. Carr ◽  
Oliver J. Maclaren ◽  
...  
Keyword(s):  
Stochastic Model ◽  
Heterogeneous Media ◽  
Profile Likelihood ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Likelihood Analysis ◽  
Approximate Likelihood ◽  
Profile Likelihoods ◽  
Parameter Values ◽  
The Continuum

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether these data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second, we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods, we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.

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