Simulation studies of diffusion-limited coarsening in two dimensions

AIChE Journal ◽  
1991 ◽  
Vol 37 (7) ◽  
pp. 1053-1064 ◽  
Author(s):  
Tang H. Wong ◽  
James A. O'Brien
Keyword(s):  
Two Dimensions ◽  
Simulation Studies ◽  
Diffusion Limited

scholarly journals Fractal and Dendritic Growth of Surface Aggregates

1995 ◽  
Vol 407 ◽  
Author(s):  
H. Brune ◽  
K. Bromann ◽  
K. Kern ◽  
J. Jacobsen ◽  
P. Stoltze ◽  
...  
Keyword(s):  
Dendritic Growth ◽  
Kinetic Monte Carlo ◽  
Variable Temperature ◽  
Two Dimensions ◽  
Present System ◽  
Diffusion Limited Aggregation ◽  
Microscopic Mechanism ◽  
Diffusion Limited ◽  
Kinetic Monte Carlo Simulations ◽  
Equilibrium Growth

ABSTRACTThe similarity of patterns formed in non-equilibrium growth processes in physics, chemistry and biology is conspicuous and many attempts have been made to discover common mechanisms underlying their growth. The central question in this context is what causes some patterns to be dendritic, as e.g. snowflakes, while others grow fractal (randomly ramified). Here we report a crossover from fractal to dendritic patterns for growth in two dimensions: the diffusion limited aggregation of Ag atoms on a Pt(111) surface as observed by means of variable temperature STM. The microscopic mechanism of dendritic growth can be analyzed for the present system. It originates from the anisotropy of the diffusion of adatoms at corner sites which is linked to the trigonal symmetry of the substrate. This corner diffusion is observed to be active as soon as islands form, therefore, the classical DLA clusters with the hit and stick mechanism do not form. The ideas on the mechanism for dendritic growth have been verified by kinetic Monte-Carlo simulations which are in excellent agreement with experiment.

scholarly journals Dynamics and Patterning of Screw Dislocations in Two Dimensions

2000 ◽  
Vol 653 ◽  
Author(s):  
Robin L. B. Selinger ◽  
Brian B. Smith ◽  
Wei-Dong Luo
Keyword(s):  
Defect Density ◽  
Model Simulation ◽  
Two Dimensions ◽  
Xy Model ◽  
Shear Strain Rate ◽  
Simulation Studies ◽  
Ordered Structures ◽  
Screw Dislocations ◽  
Thermodynamic Forces ◽  
Computer Simulation Studies

AbstractTo understand how dislocations form ordered structures during the deformation of metals, we perform computer simulation studies of the dynamics and patterning of screw dislocations in two dimensions. The simulation is carried out using an idealized atomistic model with anti-plane displacements only; we show that this system is an analog of the two-dimensional XY rotor model. Simulation studies show that under a constant applied shear strain rate, the flow of dislocations spontaneously coalesces to form narrow dislocation-rich channels separated by wide dislocation-free regions, so that the applied strain is localized into slip bands. We argue that this pattern formation represents a phase separation into low/high defect density phases associated with the XY model, and conjecture that thermodynamic forces drive strain localization.

The Anomalous Diffusion-limited Reaction Kinetics of a Phototrapping Reaction

1996 ◽  
Vol 464 ◽  
Author(s):  
Eric Monson ◽  
Anna L. Lin ◽  
Raoul Kopelman
Keyword(s):  
Laser Beam ◽  
Two Dimensions ◽  
One Dimensional ◽  
Rate Laws ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Classical Constant

AbstractA focused laser beam acts as both a “phototrap”, bleaching fluorophore molecules which diffuse into the beam path, and as a confocal probe, detecting the excited, unbleached fluorophore molecules still present in the trap. With this focused laser beam, we observe anomalous asymptotic rate laws similar to those predicted for a diffusion-controlled elementary trapping reaction, A + T → T, in one and two dimensions. One dimensional diffusion-limited trapping kinetics are approached in capillaries with 10 μm diameters while two dimensional diffusion limited trapping kinetics are observed with unstirred samples having a quasi 2-D geometry. In the presence of stirring, the 2-D samplesexhibit the classical, constant trapping rate over time.

scholarly journals Integrability-preserving regularizations of Laplacian Growth

2020 ◽  
Vol 15 ◽  
pp. 9
Author(s):  
Razvan Teodorescu
Keyword(s):  
Universality Class ◽  
Two Dimensions ◽  
Laplacian Growth ◽  
Boundary Singularity ◽  
Diffusion Limited Aggregation ◽  
Scaling Properties ◽  
Scale Free ◽  
Diffusion Limited ◽  
Long Time ◽  
Discrete Counterpart

The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA.

A Method for Elasticity Modulus Calculation in Porous Media with Known Geometry Using the Monte Carlo Technique

2009 ◽  
Vol 423 ◽  
pp. 75-82 ◽  
Author(s):  
Liz Añez ◽  
Juan Primera ◽  
Anwar Hasmy ◽  
Pedro Franceschini ◽  
Néstor Sánchez ◽  
...  
Keyword(s):  
Porous Media ◽  
Monte Carlo ◽  
Elasticity Modulus ◽  
Two Dimensions ◽  
Monte Carlo Technique ◽  
Computational Method ◽  
Diffusion Limited ◽  
Minimum Strain Energy ◽  
And Diffusion ◽  
Central Forces

This study introduces a method for a computational calculus of the Elasticity Modulus (E) of simulated porous media using the Monte Carlo technique. The porous media of known geometry is simulated as an elastic network of central forces, to which a known deformation is applied. The minimum strain energy is calculated applying the Monte Carlo technique. The Elasticity Modulus is obtained from the theoretical relations between the elastic energy of a system and its deformation. The computational method is validated by applying it in systems of known analytic solution and over porous media generated through aggregation algorithm in two dimensions i.e. Random Sequential Aggregation and Diffusion Limited Cluster-Cluster Aggregation (RSA and DLCA respectively). The latter used to simulate the structure of silica aerogels. As for the range of concentrations studied for the DLCA and RSA systems, it was found that the elasticity modulus E decreases as the porosity of the system increases, being the E value higher for the DLCA system with respect to RSA. The method used is able to differentiate the elastic properties for two different aggregation models. Being E values different for equal porosities, the coordination number (Z) was the geometric parameter that best explains the behavior of the Elasticity Modulus.

Dimensional Crossover in the Growth of Depletion Zone in a Rectangular Capillary: Experiments and Monte Carlo Simulations

2003 ◽  
Vol 790 ◽  
Author(s):  
Sung Hyun Park ◽  
Hailin Peng ◽  
Panos Argyrakis ◽  
Haim Taitelbaum ◽  
Raoul Kopelman
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Reaction Zone ◽  
Two Dimensions ◽  
Finite Width ◽  
Dimensional Crossover ◽  
Depletion Zone ◽  
Diffusion Limited ◽  
Boundary Information ◽  
Specific Fraction

ABSTRACTThe diffusion-limited kinetics of the growth of depletion zone around a static point trap in a thin, long stripe geometry was studied using a laser photobleaching experiment of fluorescein dye inside a rectangular capillary. The dynamics of the depletion zone was monitored by the θ-distance, defined as the distance from the trap to the point where the reactant concentration has been depleted to the specific fraction of its initial bulk value. A dimensional crossover from two dimensions to one dimension, due to the finite width of the reaction zone, was observed. The crossover seems to occur for all θ values concurrently when the depletion zone touches the boundary for the first time, suggesting that the boundary information spreads faster than diffusion. Monte Carlo simulations were performed to support the experimental results. The crossover time (τc) is found to scale with the width (L) of the rectangular reaction zone as τc ∼ L2, as expected from the Einstein's diffusion law.

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