Two methods for molecular dynamics simulations are given for systems under shear-stress. In the first method, the system evolves under constant volume, while the second method treats systems with constant pressure applied against the plane parallel to the applied shear. We demonstrate the first method by simulating a system of soft spherocylinders in smectic liquid crystal phase. We observe a change in the orientation of the molecules, along with a rotation of the smectic layers such that they become normal with respect to the initial condition. Normal-stress simulation methods are also given.

Spontaneous formation of structures with ‘cubic symmetry’ is observed by molecular dynamics simulation. We show that many phases with cubic symmetry with planes of edge dislocations appear when the Sm layers are allowed to break up at relatively low pressures. The phases obtained can be interpreted as bend-grain-boundary phases consisting of edge dislocations, the counterpart of the twist-grain-boundary phase consisting of screw dislocations.

Smectic liquid crystal phases are investigated using systems of parallel spherocylinders by canonical hydrostatic molecular dynamics simulations which keep the volume constant without non-hydrostatic stress. Simulation cell lengths undergo bifurcations when the temperature is increased. At certain temperatures, elastic instability occurs which do not decay for long. The six fold bond orientation order, distinctive of hexatic smectic B phase, shows reentrant behavior, where higher order reappears after a drop at higher temperatures. In spite of the complex responses to temperature, systems of different volume with same anisotropy scale on each other, as well on systems with different anisotropy.

We discuss deterministic molecular dynamics (MD) simulation methods in relation to non-equilibrium thermodynamics. The MD method uses a barostat and a thermostat which is solved through explicit symplectic algorithm. The time scaling factor ??, common to Nos?? thermostat and Poincar?? time transformation, is shown to be the coefficient of entropy production rate. Evolution toward equilibrium as well as non-equilibrium steady states are both calculated and we show that ?? reflects the microscopic structure and dynamics and disseminates them to macroscopic thermodynamic properties.

By a molecular dynamics (MD) simulation method which ensures the system will be under hydrostatic pressure, dynamic and elastic properties of glassy metatstable states are investigated. In the MD method, the simulation cell fluctuates not only in volume but also in shape under constant hydrostatic pressure and temperature. As observed in experiments for many glass forming materials, metastable states in our simulation show a sharp increase in mean-square-displacement at certain temperatures TD. Dynamic heterogeneity is also observed at TD. Elastic properties are calculated from stress and strain relations obtained from the spontaneous fluctuation of internal stress tensor and simulation cell parameters. Each investigated state shows distinctive dynamics while maintaining solid-like elastic properties. The elastic properties stay intact even above TD. It has been shown that the rigidity and mobility of glassy metastable states are compatible under dynamic heterogeneity.

The pressure distribution under heaps has found to be dependent on the building history of the heap both in experiments and in simulations. Up to now, theoretical models and analysis assume that the packing of the heap is homogeneous. We show new experimental and simulational results which indicate that the packing is inhomogeneous and that this packing property is likely causing the pressure minimum under the heap.

Molecular dynamics (MD) methods suitable for treating anisotropic fluctuations in condensed matter are discussed. Barostats with two anisotropic factors to control the simulation cell dynamics are introduced in three MD simulation methods; constant pressure, constant surface tension, and canonical hydrostatic. To demonstrate the possibilities of these methods, calculations of two systems, one consisting of anisotropic particles and other consisting of isotropic particles, are presented.

By constant surface tension molecular dynamics simulation method, we show that the structural transformation of smectic liquid crystals can be caused by surface tension. Comparison with systems under hydrostatic pressure is discussed.

Systems of hexatic smectic B liquid crystal are investigated by constant-pressure and constant-temperature molecular dynamics simulations. By using a symplectic integrator designed for soft-matter under a condition where the fluctuation of the system is large, spontaneous transfer among the metastable states is observed. By analyzing the transfer in both directions, distributions of work values corresponding to the forward and reverse processes are obtained.

Origin of hopping dynamics in liquid crystals is investigated by constant-pressure and constant-temperature molecular dynamics simulations. Hopping dynamics is observed in both hexatic smectic B (HexB) and smectic A (SmA) liquid crystals, however in different directions. At the crystal-Hex B transition, a second order transtition occurs where the layer thickness increases continuously. At the HexB-SmA transition, melting inside the layers is observed. The hopping occurs in the direction normal to the direction with loose density, i.e., xy-direction in HexB and z-direction in SmA.

Entropy S is a fundamental quantity in physics. In molecular simulations, S has been estimated through statistical physics approach calculating S = −kB ∑ pB ln pB. The value of Boltzmann probability pB depends not only on each configuration but also on the entire ensemble through the partition function, thus the sampling quality is always crucial. A different approach to calculate S through absorption/production of heat in the system, i.e., thermodynamic approach, has been proposed [1, 2]. This method has an advantage that the thermodynamic quantities are obtained at each temperature by a simple function of the calculated canonical variables. Precise calculation of the change in heat is possible due to the extended Hamiltonian structure which yield constant pressure and temperature.

The topology of the free-energy landscape of a model system, which gives rise to multiple metastable states of hexatic smectic B (HexB) liquid crystals, is investigated using network theory. Directed and weighted networks of HexB states are constructed from a series of dynamical data calculated by constant-pressure and constant-temperature molecular dynamics simulations. The k-shell decomposition is extended to directed networks, and the networks of HexB metastable states are analyzed. Singular values of the weighted adjacency matrix, with elements consisting of the weight of the directed edge, are used to distinguish important vertices for evolution.

K. M. Aoki1,2,3, S. Fujiwara4, K. Sogo5, S. Ohnishi2, and T. Yamamoto6 1 iCFD, 1-16-5 Haramachi, Meguro-ku, Tokyo 152-0011, Japan 2 Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan 3 Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Tokyo 169-8555, Japan 4 Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan 5 Kitasato University, 1-15-1 Sagamihara, Kanagawa 228-8555, Japan 6 1-19-8 Shin-Yokohama, Kohoku-ku, Yokohama 222-0033, Japan

Hopping dynamics in glass has been known for quite a long time. In contrast, hopping dynamics in smectic-A (SmA) and hexatic smectic-B (HexB) liquid crystals (LC) has been observed only recently. The hopping in SmA phase occurs among the smectic layers (one-dimensionally), while hopping in HexB phase occurs inside the layers (two-dimensionally). The hopping dynamics in SmA and HexB liquid crystal phases is investigated by parallel soft-core spherocylinders, while three-dimensional hopping dynamics in inherent glassy states is investigated by systems of Weeks–Chandler–Andersen (WCA) spheres. The temperature dependence of diffusion coefficients of hopping in SmA phase can be described by the Arrhenius equation characteristic of activation process. In HexB LC phase, the diffusion coefficients saturate at higher temperatures. In a system of WCA spheres, the values and temperature dependence of diffusion coefficients depend on the observed states.

Hexatic smectic B liquid crystal (HexB) is studied by molecular dynamics simulations for a wide range of temperatures. In addition to the thermodynamic equilibrium HexB phase, there exist multiple metastable states with a smaller sixfold bond orientational order C 6 than the thermodynamic equilibrium phase. The values of C 6 are discrete, with each metastable state having different thermodynamic characteristics. 12- and 18-fold bond orientational orders C 6 n ( n = 2, 3) satisfy the scaling relation C 6 n = C 6 σ n for a wide range. The metastable HexB states are nested and each layer also has a discrete value of bond order forming these discrete states as a whole.

A random walk model is formulated and examined which gives the correlated anomalous diffusion found in molecular dynamics simulations. The mean square displacement (MSD) shows a logarithmic behavior in one dimension. Corresponding Langevin equation is constructed by solving the inverse problem which gives a procedure to derive random impulse correlation from MSD function.

Entropy and heat capacity are calculated in phase sequence of crystal, hexatic smectic- B , and smectic- A liquid crystals through constant pressure and temperature molecular-dynamics simulations of parallel soft spherocylinders. The transition from crystal to hexatic smectic- B phase is continuous while the transition to smectic- A phase is first order. The dependence of the phase sequence against the molecular shape anisotropy is investigated and there exists a triple point at a rather small anisotropy. Hopping diffusion of molecules is observed in the hexatic smectic- B phase.

We propose a simulation method for liquid-liquid interface under constant surface tension and constant normal pressure. The method introduces an anisotropic factor in the cell dynamics which avoids artifacts such as continuous expansion or contraction of the cell lengths. This allows simulation of a full range of surface tensions including when the value is 0, i. e, hydrostatic pressure.