Random walk simulations

In order to examine the current response to the imposition of the potential step on the self-affine fractal interface, the current transients were calculated theoretically by random walk simulation.153 The simulation cell was taken as the square area bottom boundary which is replaced by one of the self-affine fractal profiles in Figure 7. The details of the simulation condition were described in their publication.43... 

J.B. Anderson, A random-walk simulation of the Schrodinger equation H3+. J. Chem. Phys. 63, 1499-1503 (1975)... 

Figure 8. Double logarithmic plot of the ratio of the normalized correlation time i[tp)/xi as a function of the normalized evolution time tp, determined from random walk simulations for different jump angle aj. (From Ref. 12 cf. also Ref. 189.)...

Figure 56. (a) Results from random walk simulations for different solid-echo delay times 7, the... 

Probing highly hindered motion by 2H NMR theoretical background and random walk simulations... 

Studies carried out with the aim of developing models to estimate migration include a study by Aurela and Ketoja (2002). They estimated the diffusion rate of model compounds (butanol, ethanol, butyl acetate and tetrahydrofuran) in air at room temperature. They then measured the diffusion of these substances through papers with different grammages (and hence, porosities) produced from birch Kraft pulp. The model compounds were not in contact with the test papers and hence transferred via the gas phase. They concluded that the diffusion constants determined in air could be used in random walk simulation to predict migration in a fibre network. Random walk simulations are a mathematical means of modelling processes based on probability distribution and are often applied to investigate diffusion processes. 

AURELA B and KETOJA j A (2002), Diffusion of volatile compounds in fibre networks experiments and modelling by random walk simulation . Food Addit Contam, 19, suppl, 56-62. 

In random walk simulations with configurational temperature, the calculations are started with a convergence factor / = exp(O.l). When / > exp(10 ), the density of states calculated from the temperature is used as the initial density of states for the next stage, the convergence factor is reduced by and the temperature accumulators are reset to zero... 

J. B. Anderson (1975) Random-walk simulation of Schrodinger equation - H- -3. J. Chem,. Phys. 63, pp. 1499-1503 ibid. (1976) Quantum chemistry by random-walk. 65, pp. 4121-4127... 

The orthogonal space random walk simulation method... 

Fig. 25. Random walk simulations for static 2H NMR powder lineshapes arising from a quadrupole echo 90°x-t-90°v-t-FID pulse sequence for the model of an isotropic 3° jump.36 (a) Jump correlation time, tj = 411 gs correlation time for the motion, xc = 100 ms, echo delays x as given in the figure. Dotted line is the spectrum for an isotropic random jump with xj = xc = 100 ms and an echo delay x — 200 gs. (b) Jump correlation times xj and motional correlation times xc as given in the figure, echo delay x = 100 gs.

D. Betteridge, C.Z. Marczewski, A.P. Wade, A random walk simulation of flow injection analysis, Anal. Chim. Acta 165 (1984) 227. 

Figure 2. Distribution of particle positions in one-dimensional random-walk simulations. The solid line shows the results with an uncorrelated sequence the bold dashed line, sequences with correlation coefficient = 0.2 and the dashed-dotted line for sequences with correlation coefficient = 0.2.

Random walk simulations assuming a smooth surface and allowing for surface relaxation have derived the following equation for short A times ... 

Figure 7.11 summarizes the results obtained from (7.42) (lines) and compares it with random walk simulations on the Peano basin up to order Q = 10 (open circles) and OCNs (full circles). In the simulations, all the walkers were initially on the left side of the lattice and the front advanced to the right. A logistic growth rp(l — p) was introduced at every site at every time step to simulate the reaction process. For the OCNs, we averaged over 10 different 200 x 200 networks. 

A random walk simulation thus provides the structure factor for any geometry that one defines. This technique has been used to examine the structure factor for an infinitely small solute within random arrays of freely overlapping cylinders with various orientation distributions [61], to study the effect of the distribution of reactive sites within a porous catalyst [62], and to study the effect of solute size on the structure factor within ordered assemblies of spherical colloids [31]. 

Baur JE, Motsegood PN (2004) Diffusional interactions at dual disk microelectrodes comparison of experiment with three-dimensional random walk simulations. J Electroanal Chem 572 29 0... 

Nagy G, Sugimoto Y, Denuault G (1997) Three-dimensional random walk simulation of diffusion controlled electrode processes (I) a hemisphere, disc and growing hemisphere. J Electroanal Chem 433 167-173... 

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