Multiscale Modeling of Ductile Iron Solidification With Continuous Nucleation by a Cellular Automaton

2010 ◽  
Author(s):  
Andriy A. Burbelko ◽  
Daniel Gurgul ◽  
Edward Fras´ ◽  
Edward Guzik
Keyword(s):  
Chemical Composition ◽  
Cellular Automaton ◽  
Source Function ◽  
Distribution Curve ◽  
Heat Diffusion ◽  
Cumulative Distribution ◽  
Microstructure Formation ◽  
Time Step ◽  
Solid Phases ◽  
Continuous Nucleation

The solidification of metals and alloys is a typical example of multiphysics and multiscale engineering systems. The phenomenon of different time and spatial scales should be taken into consideration in the modeling of a microstructure formation: heat diffusion, the components diffusion in the liquid and solid phases, the thermodynamics of phase transformation under a condition of inhomogeneous chemical composition of growing and vanishing phases, phase interface kinetics, and grains nucleation. The results of a two-dimensional modeling of the microstructure formation in a ductile cast iron are presented. The cellular automaton model (CA) was used for the simulation. The model takes into account the nucleation of two kinds of grains that appear inside of the liquid during solidification: austenite and graphite. The six states of CA cells correspond to the above-mentioned three phases (liquid, austenite and graphite) and to the three two-phase interfaces. A numerical solution was used for the modeling of concentration and temperature fields. The parabolic nonlinear differential equations with a source function were solved by using the finite element method and explicit scheme. In the mono-phase cells the source function is equal to zero. In the interface cells the value of the source function varies depending on the local undercooling. The undercooling value depends on the front curvature, the local temperature and the local chemical composition of the phases. Overlapping lattices with the same spatial step were used for concentration field modeling and for the CA. The time scale of the temperature field for this lattice is about 104 times shorter. Due to the above reasons, another lattice was used with a multiple spatial step and the same time step. The new grain nucleation of solid phases from a liquid is a phenomenon which must be taken into account for correct simulation of a polycrystalline structure formation. The cumulative distribution curve approach was used to calculate the number of substrates on which nucleation takes place as a function of under-cooling below the equilibrium temperature. An algorithm of continuous nucleation modeling during solidification is presented. The undercooling of solid phase grain nucleation was calculated on the basis of the inverse function of the above-mentioned cumulative distribution curve (fractile) with the argument equal to the random number generated in the interval 0…1 with uniform density. The domain of correct usage of this algorithm was analyzed.

scholarly journals A 2-DIMENSIONAL CELLULAR AUTOMATON FOR AGENTS MOVING FROM ORIGINS TO DESTINATIONS

2005 ◽  
Vol 16 (12) ◽  
pp. 1849-1860 ◽  
Author(s):  
NAJEM MOUSSA
Keyword(s):  
Cellular Automaton ◽  
Cluster Size ◽  
Bimodal Distribution ◽  
Minimal Distance ◽  
Time Step ◽  
Neighbor Site ◽  
Model Dynamics ◽  
Long Time ◽  
Freely Moving ◽  
Small Clusters

We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The stochasticity or noise (p) is introduced in the model dynamics, through the uncertainty in estimating the distance from the destination. The friction parameter "μ" is also introduced to control the probability that movement of all involved agents to the same site (conflict) is denied at each time step. This model displays two states; namely the freely moving and the jamming state. If μ is large and p is low, the system is in the jamming state even if the density is low. However, if μ is large and p is high, a freely moving state takes place whenever the density is low. The cluster size and the travel time distributions in the two states are studied in detail. We find that only very small clusters are present in the freely moving state, while the jamming state displays a bimodal distribution. At low densities, agents can take a very long time to reach their destinations if μ is large and p is low (jamming state); but long travel times are suppressed if p becomes large (freely moving state).

scholarly journals Analytical results for the distribution of cover times of random walks on random regular graphs

2021 ◽  
Author(s):  
Ido Tishby ◽  
Ofer Biham ◽  
Eytan Katzav
Keyword(s):  
Random Walks ◽  
Cumulative Distribution ◽  
Large Network ◽  
Regular Graphs ◽  
Time Step ◽  
Single Node ◽  
Initial Node ◽  
Analytical Results ◽  
Partial Cover ◽  
Cover Times

Abstract We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of N nodes of degree c (c ≥ 3). Starting from a random initial node at time t = 1, at each time step t ≥ 2 an RW hops into a random neighbor of its previous node. In some of the time steps the RW may visit a new, yet-unvisited node, while in other time steps it may revisit a node that has already been visited before. The cover time TCis the number of time steps required for the RW to visit every single node in the network at least once. We derive a master equation for the distribution Pt(S = s) of the number of distinct nodes s visited by an RW up to time t and solve it analytically. Inserting s = N we obtain the cumulative distribution of cover times, namely the probability P (TC ≤ t) = Pt(S = N) that up to time t an RW will visit all the N nodes in the network. Taking the large network limit, we show that P (TC ≤ t) converges to a Gumbel distribution. We calculate the distribution of partial cover (PC) times P (TPC,k = t), which is the probability that at time t an RW will complete visiting k distinct nodes. We also calculate the distribution of random cover (RC) times P (TRC,k = t), which is the probability that at time t an RW will complete visiting all the nodes in a subgraph of k randomly pre-selected nodes at least once. The analytical results for the distributions of cover times are found to be in very good agreement with the results obtained from computer simulations.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata and Cellular Automata With Inhomogeneous Cells

2017 ◽  
pp. 127-138
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Local State ◽  
Active Cell ◽  
State Function ◽  
Local Function ◽  
Time Step ◽  
Random Number Generators ◽  
Asynchronous Cellular Automata ◽  
A Cell

The sixth chapter deals with the construction of pseudo-random number generators based on a combination of two cellular automata, which were considered in the previous chapters. The generator is constructed based on two cellular automata. The first cellular automaton controls the location of the active cell on the second cellular automaton, which realizes the local state function for each cell. The active cell on the second cellular automaton is the main cell and from its output bits of the bit sequence are formed at the output of the generator. As the first cellular automaton, an asynchronous cellular automaton is used in this chapter, and a synchronous cellular automaton is used as the second cellular automaton. In this case, the active cell of the second cellular automaton realizes another local function at each time step and is inhomogeneous. The algorithm for the work of a cell of a combined cellular automaton for implementing a generator and its hardware implementation are presented.

scholarly journals Supergene gold transformation in technogenic mineral formations

2019 ◽  
Vol 98 ◽  
pp. 01028
Author(s):  
Alfiia Khusainova ◽  
Vladimir Naumov ◽  
Oksana Naumova
Keyword(s):  
Chemical Composition ◽  
Mine Wastes ◽  
Supergene Zone ◽  
Physical Chemical ◽  
Solid Phases

This article is about the research on gold obtained from mine wastes and other technogenic mineral formations. The authors investigated how solid phases of gold in supergene zone transform from various deposits. Results show the following supergene gold transformations by various physical, chemical, biological and mechanical processes occurring in the wastes. Transformations result in changes in morphology and chemical composition, and special redistribution of gold in wastes.

Simulation of High-Resolution Precipitable Water Data by a Stochastic Model with a Random Trigger

2016 ◽  
Vol 08 (02) ◽  
pp. 1650006 ◽  
Author(s):  
Kimberly Leung ◽  
Max Velado ◽  
Aneesh Subramanian ◽  
Guang J. Zhang ◽  
Richard C. J. Somerville ◽  
...  
Keyword(s):  
Stochastic Model ◽  
Climate Models ◽  
Time Window ◽  
Model Simulation ◽  
Precipitable Water ◽  
Cumulative Distribution ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Ice Period

We use a stochastic differential equation (SDE) model with a random precipitation trigger for mass balance to simulate the 20 s temporal resolution column precipitable water vapor (PWV) data during the tropical warm pool international cloud experiment (TWP-ICE) period of January 20 to February 15, 2006 at Darwin, Australia. The trigger is determined by an exponential cumulative distribution function, the time step size in the SDE simulation, and a random precipitation indicator uniformly distributed over [0, 1]. Compared with the observed data, the simulations have similar means, extremes, skewness, kurtosis, and overall shapes of probability distribution, and are temporally well synchronized for increasing and decreasing, but have about 20% lower standard deviation. Based on a 1000-day run, the correlations between the model data and the observations in TWP-ICE period were computed in a moving time window of 25 days and show quasi-periodic variations between (−0.675, 0.697). This shows that the results are robust for the stochastic model simulation of the observed PWV data, whose fractal dimension is 1.9, while the dimension of the simulated data is also about 1.9. This agreement and numerous sensitivity experiments form a test on the feasibility of using an SDE model to simulate precipitation processes in more complex climate models.

scholarly journals THE CUMULATIVE DISTRIBUTION CURVE FOR DRAINAGE AREAS

2011 ◽  
Vol 67 (4) ◽  
pp. I_649-I_654
Author(s):  
Hitoshi MIYAMOTO ◽  
Tsubasa HASHIMOTO ◽  
Kohji MICHIOKU
Keyword(s):  
Distribution Curve ◽  
Cumulative Distribution

scholarly journals Modelling of base cation emissions, concentrations and deposition in the UK

2010 ◽  
Vol 10 (9) ◽  
pp. 21989-22018 ◽  
Author(s):  
M. Werner ◽  
M. Kryza ◽  
A. J. Dore ◽  
M. Błaś ◽  
S. Hallsworth ◽  
...  
Keyword(s):  
Chemical Composition ◽  
Wet Deposition ◽  
Fine Particles ◽  
Sea Water ◽  
Monitoring Network ◽  
Base Cations ◽  
Base Cation ◽  
Sea Surface ◽  
Time Step ◽  
The Uk

Abstract. Base cations exerts a large impact on various geochemical and geophysical processes both in the atmosphere and at the Earth surface. One of the essential roles of these compounds is impact on surface pH causing an increase in alkalinity and neutralizing the effects of acidity generated by sulphur and nitrogen deposition. During recent years anthropogenic emissions of base cations in the UK have decreased substantially, by about 70% for Na+, 78% for Mg2+, 75% for Ca2+ and about 48% for K+ for the period 1990–2006. For the island regions, such as the is UK, the main source of base cation particles is the aerosol produced from the sea surface. Here, the sea salt aerosol (SSA) emissions are calculated with parameterisations proposed by Maårtensson et al. (2003); ultra fine particles, Monahan et al. (1986); fine particles and Smith and Harisson (1998); coarse particles continuously with a 0.1 μ m size step using WRF-modelled wind speed data at a 5 km × 5 km grid square resolution with a 3 h time step for two selected years 2003 and 2006. SSA production has been converted into base cation emissions, with the assumption that the chemical composition of the particle emitted from the sea surface is equal to the chemical composition of sea water, and used as input data in the Fine Resolution Atmospheric Multi-pollutant Exchange Model (FRAME). FRAME model results, yearly mean concentrations and total wet deposition at a 5 km × 5 km grid resolution, are compared with concentrations in air and wet deposition from the National Monitoring Network and measurements based estimates of UK deposition budget. The correlation coefficient for wet deposition achieves high values for Na+ and Mg2+, and for Ca2+ there is significant scattering. Base cation concentration is also represented well, with some overestimations on the west coast and underestimations in the centre of the land.

Effects of Cellulosic and Basic Flux on the Structure, Composition and Hardness of SMAW Welds on Steel X42

2016 ◽  
Vol 27 ◽  
pp. 11-19 ◽  
Author(s):  
Farida Khamouli ◽  
Mosbah Zidani ◽  
Hichem Farh ◽  
Adel Saoudi ◽  
L'hadi Atoui
Keyword(s):  
Chemical Composition ◽  
Carbon Content ◽  
Acicular Ferrite ◽  
Mass Concentration ◽  
Chemical Compositions ◽  
Low Carbon ◽  
Micro Hardness ◽  
Microstructure Formation ◽  
Basic Flux ◽  
Metallic Inclusions

This paper studied the effects of cellulosic and basic flux on the chemical composition, microstructure, formation of inclusions and micro hardness of X42 steel SMAW welds. The commercialized chemical compositions of flux used are: E6010, E8010-P1 and E8018-G, with electrodes of low carbon content. Welding conditions are not constant. The microstructure of the fusion zone for each flux consists mainly of acicular ferrite. It is found that manganese increases in the fusion zones (C, B and A) respectively .The change in mass concentration of manganese is homogeneous through the three points with all the used flux. Regardless of the flux used, the non-metallic inclusions observed are of two types: white and black. The micro-hardness decreasing values were obtained in the fusion zones (C, B and A).

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