Takenobu Nakamura

Hierarchical structures of amorphous solids characterized by persistent homology

Significance Persistent homology is an emerging mathematical concept for characterizing shapes of data. In particular, it provides a tool called the persistence diagram that extracts multiscale topological features such as rings and cavities embedded in atomic configurations. This article presents a unified method using persistence diagrams for studying the geometry of atomic configurations in amorphous solids. The method highlights hierarchical structures that conventional techniques could not have treated appropriately. This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the PDs is given by an atomic configuration and the output is expressed as 2D histograms. Then, specific distributions such as curves and islands in the PDs identify meaningful shape characteristics of the atomic configuration. Although the method can be applied to a wide variety of disordered systems, it is applied here to silica glass, the Lennard-Jones system, and Cu-Zr metallic glass as standard examples of continuous random network and random packing structures. In silica glass, the method classified the atomic rings as short-range and medium-range orders and unveiled hierarchical ring structures among them. These detailed geometric characterizations clarified a real space origin of the first sharp diffraction peak and also indicated that PDs contain information on elastic response. Even in the Lennard-Jones system and Cu-Zr metallic glass, the hierarchical structures in the atomic configurations were derived in a similar way using PDs, although the glass structures and properties substantially differ from silica glass. These results suggest that the PDs provide a unified method that extracts greater depth of geometric information in amorphous solids than conventional methods.

Persistent homology and many-body atomic structure for medium-range order in the glass

The characterization of the medium-range (MRO) order in amorphous materials and its relation to the short-range order is discussed. A new topological approach to extract a hierarchical structure of amorphous materials is presented, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. This method is called the persistence diagram (PD) and introduces scales to many-body atomic structures to facilitate size and shape characterization. We first illustrate the representation of perfect crystalline and random structures in PDs. Then, the MRO in amorphous silica is characterized using the appropriate PD. The PD approach compresses the size of the data set significantly, to much smaller geometrical summaries, and has considerable potential for application to a wide range of materials, including complex molecular liquids, granular materials, and metallic glasses.

Free energy analysis of vesicle-to-bicelle transformation

A lipid assembly composed of a finite number of lipid molecules can have multiple metastable structures. Using a series of coarse-grained molecular dynamics simulations, we evaluate the free energy profile for the transformation of a small vesicle to a disk-like structure called a bicelle. This free energy is found to be lower than that predicted from continuum elastic theory. For small unilamellar vesicles, the relaxation of the internal structure of the membrane is suggested to play an important role in lowering the free energy barrier for the vesicle-to-bicelle transformation.

Novel numerical method for calculating the pressure tensor in spherical coordinates for molecular systems

We propose a novel method for computing the pressure tensor along the radial axis of a molecular system with spherical symmetry. The proposed method uses the slice averaged pressure to improve the numerical stability and precision significantly. Simplified expressions of the local pressure are derived for a conventional molecular force field including non-bond, bond stretching, angle bending, and torsion interactions; these expressions are advantageous in terms of the computational cost. We also discuss an algorithm to avoid numerical singularity. Finally, the method is successfully applied to three different molecular systems, i.e., a water droplet in oil, a spherical micelle, and a liposome.

Method of evaluating curvature-dependent elastic parameters for small unilamellar vesicles using molecular dynamics trajectory.

A numerical method is proposed for evaluating the curvature dependency of elastic parameters of a spherical vesicle based on a calculation of the pressure profile across the membrane. The proposed method is particularly useful for small unilamellar vesicles (SUVs), in which the internal structure of the membrane is asymmetric owing to the high curvature. In this case, the elastic energy is insufficiently described as a perturbation from a planar membrane. The calculated saddle-splay curvature modulus of SUVs, which is about 16 nm in diameter, is found to be much higher than that of a planar membrane. A comparison of the free energy change in the initial stage of vesicle-to-bicelle transformation with the Fromherz theory demonstrates that the elastic parameters estimated for SUVs provide better estimation of the free energy than those estimated for a planar membrane.

Derivation of the nonlinear fluctuating hydrodynamic equation from the underdamped Langevin equation

We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki–Dean formula in the underdamped case. The steady-state probability distribution of the number and momentum densities field can be expressed by the kinetic and potential energies. In the massless limit, the obtained fluctuating hydrodynamic equation reduces to the Kawasaki–Dean equation. Moreover, the derived equation corresponds to the field equation derived from the canonical equation when the friction coefficient is zero.

A guiding potential method for evaluating the bending rigidity of tensionless lipid membranes from molecular simulation.

A new method is proposed to estimate the bending rigidity of lipid membranes from molecular dynamics simulations. An external cylindrical guiding potential is used to impose a sinusoidal deformation to a planar membrane. The bending rigidity is obtained from the mean force acting on the cylinder by calibrating against a discretized Helfrich model that accounts for thermal fluctuations of the membrane surface. The method has been successfully applied to a dimyristoyl phosphatidylcholine bilayer simulated with a coarse-grained model. A well-converged bending rigidity was obtained for the tension-free membrane and showed reasonable agreement with that obtained from the height fluctuation spectrum.

Fluctuation-response relation of many Brownian particles under nonequilibrium conditions.

We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In equilibrium cases, the linear response coefficient is related to the intensity of density fluctuations in a universal manner, which is called a fluctuation-response relation. We then report numerical evidence that this relation holds even in nonequilibrium cases. This result suggests that Einsteins formula on density fluctuations can be extended to driven diffusive systems when the slowly varying potential is applied in a direction transversal to the driving force.

Far‐wing excitation study of the reactions in the Hg–H2 collisional quasimolecules. I. Transit‐state selectivity in HgH formation and three‐body dissociation

Laser‐pump/probe and double‐beam absorption/dispersion approaches have been applied to the far wings of the Hg 3P1–1S0 resonance line broadened by collisions with H2. Absolute reduced absorption coefficients of the Hg–H2 quasimolecules have been determined as a function of the wave‐number shift Δ from the resonance‐line center both in the red and blue wings. Decay probabilities of the excited Hg*(3P1)–H2 quasimolecule into the reactive channel (hGH formation) or into the elastic channel (Hg*(3P1) formation) have been determined as a function of Δ both for the red‐wing excited Ai and blue‐wing excited B states. The rest of these decay probabilities have been attributed to three‐body dissociation Hg(1S0)+H+H. These results indicate that (a) the A‐state surface serves more effectively in HgH formation than the B‐state surface by a factor of about 2.3; but (b) three‐body dissociation, in turn, proceeds far more efficiently on the B‐state surface than on the A‐state surface. Discussions about the energy bar...

Precise calculation of the local pressure tensor in Cartesian and spherical coordinates in LAMMPS

An accurate and efficient algorithm for calculating the 3D pressure field has been developed and implemented in the open-source molecular dynamics package, LAMMPS. Additionally, an algorithm to compute the pressure profile along the radial direction in spherical coordinates has also been implemented. The latter is particularly useful for systems showing a spherical symmetry such as micelles and vesicles. These methods yield precise pressure fields based on the Irving–Kirkwood contour integration and are particularly useful for biomolecular force fields. The present methods are applied to several systems including a buckled membrane and a vesicle.