Scalings of A + B Reaction Kinetics due to Anisotropic Confinements

1998 ◽  
Vol 543 ◽  
Author(s):  
Panos Argyrakis ◽  
Jaewook Ahn ◽  
Anna Lin ◽  
Raoul Kopelman
Keyword(s):  
Monte Carlo ◽  
Initial Conditions ◽  
Late Time ◽  
Dimensional Crossover ◽  
Elementary Reactions ◽  
3 Dimensional ◽  
Diffusion Limited ◽  
Reaction Regime ◽  
Classical Behavior ◽  
Anisotropic Spaces

We report on the diffusion-limited A + B reaction in highly anisotropic spaces. In addition to the highly non-classical behavior of the density of reactants predicted for isotropic spaces, we observe a dimensional crossover in A + B → 0 reactions due to the geometrical compactness of the tubular 2- and 3-dimensional spaces (baguettelike structures). For slabs, we find the crossover time Tc. = Wα, which scales as , where a, b and β are given by the earlier and the late time inverse density scalings of ρ− 1 ˜-, ta and ρ−1 - tbWβ, respectively. We also obtain a critical width W, below which the chemical reaction progresses without traversing a 2- or 3-dimensional Ovchinnikov-Zeldovich reaction regime. We find that there exist different hierarchies of dimensionally forced crossovers, depending on the initial conditions and geometric restrictions. Kinetic phase diagrams are employed and exponents are given for the A + B elementary reactions in various euclidean geometries. Monte-Carlo simulations illustrate some of the kinetic hierarchies.

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.

scholarly journals Automated Search-Based Robustness Testing for Autonomous Vehicle Software

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Kevin M. Betts ◽  
Mikel D. Petty
Keyword(s):  
Monte Carlo ◽  
Performance Metrics ◽  
Initial Conditions ◽  
Autonomous Vehicle ◽  
Vehicle Control ◽  
Test Case ◽  
Test Cases ◽  
Control Software ◽  
Robustness Testing ◽  
Testing Techniques

Autonomous systems must successfully operate in complex time-varying spatial environments even when dealing with system faults that may occur during a mission. Consequently, evaluating the robustness, or ability to operate correctly under unexpected conditions, of autonomous vehicle control software is an increasingly important issue in software testing. New methods to automatically generate test cases for robustness testing of autonomous vehicle control software in closed-loop simulation are needed. Search-based testing techniques were used to automatically generate test cases, consisting of initial conditions and fault sequences, intended to challenge the control software more than test cases generated using current methods. Two different search-based testing methods, genetic algorithms and surrogate-based optimization, were used to generate test cases for a simulated unmanned aerial vehicle attempting to fly through an entryway. The effectiveness of the search-based methods in generating challenging test cases was compared to both a truth reference (full combinatorial testing) and the method most commonly used today (Monte Carlo testing). The search-based testing techniques demonstrated better performance than Monte Carlo testing for both of the test case generation performance metrics: (1) finding the single most challenging test case and (2) finding the set of fifty test cases with the highest mean degree of challenge.

scholarly journals Implicit large eddy simulation of shock-driven material mixing

2013 ◽  
Vol 371 (2003) ◽  
pp. 20120217 ◽  
Author(s):  
F. F. Grinstein ◽  
A. A. Gowardhan ◽  
J. R. Ristorcelli
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Mixing ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Late Time ◽  
Eddy Simulation ◽  
Geometrical Complexity ◽  
Planar Shock ◽  
Large Eddy ◽  
Implicit Large Eddy Simulation

Under-resolved computer simulations are typically unavoidable in practical turbulent flow applications exhibiting extreme geometrical complexity and a broad range of length and time scales. An important unsettled issue is whether filtered-out and subgrid spatial scales can significantly alter the evolution of resolved larger scales of motion and practical flow integral measures. Predictability issues in implicit large eddy simulation of under-resolved mixing of material scalars driven by under-resolved velocity fields and initial conditions are discussed in the context of shock-driven turbulent mixing. The particular focus is on effects of resolved spectral content and interfacial morphology of initial conditions on transitional and late-time turbulent mixing in the fundamental planar shock-tube configuration.

scholarly journals Characterization and Prediction of Texture in Laser Annealed NiTi Shape Memory Thin Films

2010 ◽  
Author(s):  
Gen Satoh ◽  
Y. Lawrence Yao ◽  
Xu Huang ◽  
Ainissa Ramirez
Keyword(s):  
Thin Film ◽  
Monte Carlo ◽  
Shape Memory ◽  
Grain Growth ◽  
Electron Backscatter Diffraction ◽  
Laser Crystallization ◽  
3 Dimensional ◽  
Shape Memory Properties ◽  
Melting Regime ◽  
Grain Growth Model

Thin film shape memory alloys are a promising material for use in micro-scale devices for actuation and sensing due to their strong actuating force, substantial displacements, and large surface to volume ratios. NiTi, in particular, has been of great interest due to its biocompatibility and corrosion resistance. Effort has been directed toward adjusting the microstructure of as-deposited films in order to modify their shape memory properties for specific applications. The anisotropy of the shape memory and superelastic effects suggests that inducing preferred orientations could allow for optimization of shape memory properties. Limited work, however, has been performed on adjusting the crystallographic texture of these films. In this study, thin film NiTi samples are processed using excimer laser crystallization and the effect on the overall preferred orientation is analyzed through the use of electron backscatter diffraction and x-ray diffraction. A 3-dimensional Monte Carlo grain growth model is developed to characterize textures formed through surface energy induced abnormal grain growth during solidification. Furthermore, a scaling factor between Monte Carlo steps and real time is determined to aid in the prediction of texture changes during laser crystallization in the partial melting regime.

scholarly journals New Results on the Motions of Asteroids in Resonances

1992 ◽  
Vol 152 ◽  
pp. 145-152 ◽  
Author(s):  
R. Dvorak
Keyword(s):  
Initial Conditions ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Close Approach ◽  
Integration Time ◽  
Time Interval ◽  
Time Intervals ◽  
3 Dimensional ◽  
Special Cases ◽  
Good Agreement

In this article we present a numerical study of the motion of asteroids in the 2:1 and 3:1 resonance with Jupiter. We integrated the equations of motion of the elliptic restricted 3-body problem for a great number of initial conditions within this 2 resonances for a time interval of 104 periods and for special cases even longer (which corresponds in the the Sun-Jupiter system to time intervals up to 106 years). We present our results in the form of 3-dimensional diagrams (initial a versus initial e, and in the z-axes the highest value of the eccentricity during the whole integration time). In the 3:1 resonance an eccentricity higher than 0.3 can lead to a close approach to Mars and hence to an escape from the resonance. Asteroids in the 2:1 resonance with Jupiter with eccentricities higher than 0.5 suffer from possible close approaches to Jupiter itself and then again this leads in general to an escape from the resonance. In both resonances we found possible regions of escape (chaotic regions), but only for initial eccentricities e > 0.15. The comparison with recent results show quite a good agreement for the structure of the 3:1 resonance. For motions in the 2:1 resonance our numeric results are in contradiction to others: high eccentric orbits are also found which may lead to escapes and consequently to a depletion of this resonant regions.

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