Dynamics of interacting system

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Segregation in a binary mixture

Jump rules for small particles. The external bias b affects the jump rates of small particles only.

Process of stripe formation is analyzed numerically in the mixture of binary system of particles. System consists of particles of two sizes, with no direct interactions between particles of the same or different types. The model is build on lattice, sites of which can be occupied by up to four neighboring large particles at the same time. Smaller objects cannot overlap. System orders, forming stripes, under external, constant or oscillating driving force, if its density is large enough. It is shown that this process happens with logarithmic like time dependence.

Jump rules for small particles. The external bias b affects the jump rates of small particles only.

Rescaled mean stripe width $d=l\kappa$ as a function of rescaled time for closed, open, and interacting systems in log-linear main panel and log-log plots. This figure contains results grouped in seven data sets. Six of them refer to the presently studied two-component systems and the seventh one, shown for comparison, is for the one component interacting system. The main panel shows the mean width of stripes l as a function of log(t) . Three lower data sets, labeled with $\ast$ , +, and $\times$ , represent results obtained for systems with a fixed number of small and large particles. The remaining data sets labeled with $\blacksquare$ , $\circ$ , $\bullet$ and $\bigtriangledown$ represent results for open systems, with fixed external potential. In each of these graphs the stripe width l was rescaled by a factor $\kappa$ chosen such that each data set lies on the same line $d=\kappa l=log(\frac{t}{\alpha L_{||}})$ where $L_{||}=25$ is the system width, parallel to stripes Two different values of the coefficient a were used to shift the data without changing the slope of the plot. We have chosen a = 10 for closed and a = 1.4 for open systems. The scaling factor ? depends on the density of the free sites $m=N_V/L_{||}L_{\bot}$ . Since for open systems NV changes in time we have used for m its mean value from the second stage of the stripe growth. For closed systems $\kappa=\sqrt{m_{averaged}}/4$ and for open systems: $\kappa=\sqrt{m_{averaged}}/2.8$ In all our simulations we have used systems with different sizes labeled with (*) (100 × 50), (+) (100 × 25), and (×) (250 × 25). The number of large particles were N = 600, 300, and 781, respectively. At the beginning of simulation small particles occupy 99% of available space. The upper set labeled by inverted triangles $\bigtriangledown$ represents the stripe growth for a one-component interacting driven system at a temperature 0.8Tc , where Tc = 3.18J / kB (where J = 1 is interaction strength).

Successive stages of separation of large orange and small green particles. The biasing field is parallel to the shorter side of the system. System size is 25 $\times$ 250. It is populated by 500 large and 3972 small particles and closed, i.e., number of particles, both large and small, does not change during simulation. The initial free sites fraction is 0.01.

Articles:

Segregation in a noninteracting binary mixture.

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