New PDF release: Introduction to practice of molecular simulation : molecular

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Additional info for Introduction to practice of molecular simulation : molecular dynamics, Monte Carlo, Brownian dynamics, Lattice Boltzmann, dissipative particle dynamics

Sample text

As shown 22 Introduction to Practice of Molecular Simulation later, these constants are related to the system temperature and friction coefficients. The FijD acts such that the relative motion of particles i and j relaxes, and FijR functions such that the thermal motion is activated. Since the actionÀreaction law is satisfied by FijR, the conservation of the total momentum is not violated by FijR. By substituting Eqs. 71) into Eq. 69), the equation of motion of particles can be written as m X X X dvi 5 FCij ðrij Þ 2 γwD ðrij Þðeij Uvij Þeij 1 σwR ðrij Þeij ζ ij dt jð6¼iÞ jð6¼iÞ jð6¼iÞ ð1:73Þ The integral of this equation with respect to the time from t to (t 1 Δt) leads to the finite difference equations specifying the motion of the simulation particles: Δri 5 vi Δt ð1:74Þ !

78) and is sampled from a normal distribution or from a uniform distribution. The DPD dynamics method simulates the motion of the dissipative particles according to Eqs. 83). For actual simulations, we show the method of nondimensionalizing quantities. The following representative values are used for nondimensionalization: (kT/m)1/2 for velocities, rc for distances, rc(m/kT)1/2 for time, (1/rc3) for number densities. Using these representative values, Eqs. 83) are nondimensionalized as ΔrÃi 5 vÃi Δtà ð1:84Þ X wR ðrijà Þeij Δtà 2 γ à w2R ðrijà Þðeij UvÃij Þeij Δtà jð6¼iÞ jð6¼iÞ X p ffiffiffiffiffiffiffiffi à 1=2 à 1 ð2γ Þ wR ðrij Þeij θij Δtà ΔvÃi 5 αà X ð1:85Þ jð6¼iÞ in which wR ðrijÃ Þ 5 & 1 2 rijà 0 for rijà # 1 for rijà .

Particle within the cutoff radius. 10C corresponds to case 3, in which the two particles are proximate enough to give rise to a possibility of four pairs of magnetic charges being within the cutoff range. Hence, if case 1 holds, the calculation of energies or forces between particles is unnecessary, and for case 2, if two pairs of magnetic charges are found to be within the cutoff range, the further calculation of energies or forces is unnecessary. Finally, it should be noted that the introduction of the cutoff radius by itself does not necessarily lead to a significant reduction in the computational time, since the N(N 2 1)/2 calculations have to be conducted in order to evaluate the distances between particles.

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