Takahiro Murashima

Molecular dynamics and Monte Carlo hybrid simulation for fuzzy tungsten nanostructure formation

For the purposes of long-term use of tungsten divertor walls, the formation process of the fuzzy tungsten nanostructure induced by exposure to the helium plasma was studied. In the present paper, the fuzzy nanostructures formation has been successfully reproduced by the new hybrid simulation method in which the deformation of the tungsten material due to pressure of the helium bubbles was simulated by the molecular dynamics and the diffusion of the helium atoms was simulated by the random walk based on the Monte Carlo method. By the simulation results, the surface height of the fuzzy nanostructure increased only when helium retention was under the steady state. It was proven that the growth of the fuzzy nanostructure was brought about by bursting of the helium bubbles. Moreover, we suggest the following key formation mechanisms of the fuzzy nanostructure: (1) lifting in which the surface lifted up by the helium bubble changes into a convexity, (2) bursting by which the region of the helium bubble changes into a concavity, and (3) the difference of the probability of helium retention by which the helium bubbles tend to appear under the concavity. Consequently, the convex-concave surface structure was enhanced and grew to create the fuzzy nanostructure.

Multiscale simulation of history-dependent flow in entangled polymer melts

Predicting the flow of an entangled polymer melt is still difficult because of its multiscale characteristics. We have developed a novel multiscale simulation technique to investigate the history-dependent flow behavior of entangled polymer melts. The technique involves using a smoothed particle hydrodynamics simulation that is coupled at each fluid element to microscopic simulators that can accurately account for the dynamics of entangled polymers. The multiscale simulation is used to investigate the flow of an entangled polymer melt around a cylindrical obstacle subject to periodic boundary conditions. It is found that the macroscopic flow behavior is dependent on the history of the microscopic states of the polymers and that this memory causes nonlinear behavior even in the regions where the local Weissenberg number defined using the local strain-rate is less than unity. The spatial distribution of the entanglements Z suggests that, in a region around the obstacle, a slight depletion of the entanglements is observed and that this region broadens along the downstream direction. The totality of the presented results suggests that we have succeeded in describing the entangled polymer melt flow without using any constitutive equation.

Multiscale Lagrangian fluid dynamics simulation for polymeric fluid

We have developed a simulation technique of multiscale Lagrangian fluid dynamics to tackle hierarchical problems relating to historical dependency of polymeric fluid. We investigate flow dynamics of dilute polymeric fluid by using the multiscale simulation approach incorporating Lagrangian particle fluid dynamics technique (the modified smoothed particle hydrodynamics) with stochastic coarse-grained polymer simulators (the dumbbell model). We have confirmed that our approach is nicely in agreement with the macroscopic results obtained by a constitutive equation corresponding to the dumbbell model, and observed microscopic thermal fluctuation appears in macroscopic fluid dynamics as dispersion phenomena.

Multiscale Modeling for Polymeric Flow: Particle-Fluid Bridging Scale Methods

Multiscale simulation methods have been developed based on the local stress sampling strategy and applied to three flow problems with different difficulty levels: (a) general flow problems of simple fluids, (b) parallel (one-dimensional) flow problems of polymeric liquids, and (c) general (two- or three-dimensional) flow problems of polymeric liquids. In our multiscale methods, the local stress of each fluid element is calculated directly by performing microscopic or mesoscopic simulations according to the local flow quantities instead of using any constitutive relations. For simple fluids (a), such as the Lenard-Jones liquid, a multiscale method combining molecular dynamics (MD) and computational fluid dynamics (CFD) simulations is developed rather straightforwardly based on the local stationarity assumption without memories of the flow history. For polymeric liquids in parallel flows (b), the multiscale method is extended to take into account the memory effects that arise in hydrodynamic stress due to the slow relaxation of polymer-chain conformations. The memory of polymer dynamics on each fluid element is thus resolved by performing MD simulations in which cells are fixed at the mesh nodes of the CFD simulations. The complicated viscoelastic flow behaviors of a polymeric liquid confined between oscillating plates are simulated using the multiscale method. For general (two- or three-dimensional) flow problems of polymeric liquids (c), it is necessary to trace the history of microscopic information such as polymer-chain conformation, which carries the memories of past flow history, along the streamline of each fluid element. A Lagrangian-based CFD is thus implemented to correctly advect the polymerchain conformation consistently with the flow. On each fluid element, coarse-grained polymer simulations are carried out to consider the dynamics of entangled polymer chains that show extremely slow relaxation compared to microscopic time scales. This method is successfully applied to simulate a flow around a cylindrical obstacle.

Incommensurability and edge states in the one-dimensional S= 1 bilinear-biquadratic model

Commensurate-incommensurate change on the one-dimensional S = 1 bilinear-biquadratic model (H(�) = P i {SiSi+1 + �(SiSi+1) 2 }) is examined. The gapped Haldane phase has two sub- phases (the commensurate Haldane subphase and the incommensurate Haldane subphase) and the commensurate-incommensurate change point (the Affleck-Kennedy-Lieb-Tasaki point, � = 1/3). There have been two different analytical predictions about the static structure factor in the neigh- borhood of this point. By using the Sorensen-Affleck prescription, these static structure factors are related to the Green functions, and also to the energy gap behaviors. Numerical calculations sup- port one of the predictions. Accordingly, the commensurate-incommensurate change is recognized as a motion of a pair of poles in the complex plane.

Thinning Approximation for Two-Dimensional Scattering Patterns from Coarse-Grained Polymer Melts under Shear Flow

We proposed a thinning approximation (TA) for estimation of the two-dimensional (2D) wide-angle scattering patterns from Kremer–Grest polymer melts under shear. In the TA, extra particles are inserted at the middle of bonds for fine-graining of the coarse-grained polymers. For the case without the TA, spots corresponding to the orientation of bonds at a high shear rate are difficult to observe because the bond length of successive particles is comparable to the distance between neighboring particles. With the insertion of the extra particles, a ring pattern originating from the neighboring particles can be moved to a wide-angle region. Thus, we can observe the spots at high shear rates. We also examined the relationship between 2D scattering patterns and the Weissenberg number, which is defined as the product of the shear rate and the longest relaxation time. It is confirmed that the relationship for coarse-grained polymers with the TA is consistent with that of the all-atomistic model of polyethylene.

Multiscale simulation for soft matter: Application to wormlike micellar solution

Macroscopic flow behavior of wormlike micellar solution confined to a channel is analyzed with multiscale simulation that is composed of the fluid dynamics simulation describing the macroscopic flow behavior and the coarse-grained micellar dynamics simulation describing the microscopic states of micelles. To decrease the noise coming from the thermal fluctuation of the microscopic simulator, we have compared two different noise reduction techniques (ensemble averaging and time averaging). We have selected the ensemble averaging noise reduction technique that is rather suitable to utilize the high performance of parallel computers. Startup flow profile of wormlike micellar solution analyzed with the multiscale simulation has shown an elastic flow that is caused by a microscopic structure in a fluid element.

Phase Diagram of S ¼ 1 XXZ Chain with Next-Nearest-Neighbor Interaction

The one dimensional S =1 XXZ model with next-nearest-neighbor interaction α and Ising-type anisotropy Δ is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the Neel phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear σ model and analyze the phase diagram in the α≪-1 and Δ∼1 region by using the renormalization group method.

Incommensurability and Edge State in Quantum Spin Chain

In quantum spin chains, it has been observed that the incommensurability occurs near valence-bond-solid (VBS) type points. It was difficult to study the commensurate–incommensurate (C–IC) change. On the one hand field theoretical approaches are not justified because of the short correlation length. On the other hand numerical calculations are not suitable to study the incommensurability since it is needed to treat the large size data. We discuss the relation between the edge state and the incommensurability, partially using the previous our study on the C–IC change.

Simulation of 3D food printing extrusion and deposition

In our 3D food printer, gel food such as gelatin is extruded from syringe and deposited to make a shape. Low viscosity is reasonable when the food is injected. On the other hand, high viscosity or solid state is desirable to keep the food shape after the food is deposited. The selection of the food viscoelastic property is difficult to succeed in the food printing. In general, we need trial and error to appropriate food viscosity. To avoid the trial and error, we are developing a simulation system of 3D food printing using Smoothed Particle Hydrodynamics (SPH) which is a kind of particle based simulation method.