We calculate the parameter that governs the width of the transition zone by molecular dynamics (MD) simulation and use it in a phase-field crack (PFC) simulation with the mechanical properties of iron. First, a quantitative evaluation of intactness is conducted by examining the change in atomic conformation induced by crack propagation, whose numerical data are taken from the result of the MD simulation. The spatial distribution of the intactness is fitted to the same function as the damage parameter in the PFC model, namely, an exponential function, by the least-squares method. From this distribution, the transition zone parameter is estimated. The result of the PFC simulation using this newly determined transition zone parameter is discussed in terms of the crack path by comparison with the result of crack propagation analysis based on the MD simulation.
We propose a new random number generation method, which is the fastest and the simplest of its kind, for use with molecular simulation. We also discuss the possibility of using this method with various other numerical calculations. To demonstrate the significant increases in calculation speeds that can be gained by using our method, we present a comparison with prior methods for dissipative particle dynamics (DPD) simulations. The DPD method uses random numbers to reproduce thermal fluctuations of molecules. As such, an efficient method to generate random numbers in parallel computing environments has been widely sought after. Several random number generation methods have been developed that use encryption. In this study, we establish for the first time that random numbers with desirable properties exist in the particle coordinates used in DPD calculations. We propose a method for generating random numbers without encryption that utilizes this source of randomness. This is an innovative method with minimal computational cost, since it is not dependent on a complicated random number generation algorithm or an encryption process. Furthermore, our method may lead to faster random number generation for many other physical and chemical simulations.
The tiny encryption algorithm (TEA) is widely used when performing dissipative particle dynamics (DPD) calculations in parallel, usually on distributed memory systems. In this research, we reduced the computational cost of the TEA hash function and investigated the influence of the quality of the random numbers generated on the results of DPD calculations. It has already been established that the randomness, or quality, of the random numbers depend on the number of processes from internal functions such as SHIFT, XOR and ADD, which are commonly referred to as “rounds”. Surprisingly, if we choose seed numbers from high entropy sources, with a minimum number of rounds, the quality of the random numbers generated is sufficient to successfully perform accurate DPD simulations. Although it is well known that using a minimal number of rounds is insufficient for generating high-quality random numbers, the combination of selecting good seed numbers and the robustness of DPD simulations means that we can reduce the random number generation cost without reducing the accuracy of the simulation results.
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