Multiscale Molecular Dynamics Approach to Energy Transfer in Nanomaterials.

After local transient fluctuations are dissipated, in an energy transfer process, a system evolves to a state where the energy density field varies slowly in time relative to the dynamics of atomic collisions and vibrations. Furthermore, the energy density field remains strongly coupled to the atomic scale processes (collisions and vibrations), and it can serve as the basis of a multiscale theory of energy transfer. Here, a method is introduced to capture the long scale energy density variations as they coevolve with the atomistic state in a way that yields insights into the basic physics and implies an efficient algorithm for energy transfer simulations. The approach is developed based on the N-atom Liouville equation and an interatomic force field and avoids the need for conjectured phenomenological equations for energy transfer and other processes. The theory is demonstrated for sodium chloride and silicon dioxide nanoparticles immersed in a water bath via molecular dynamics simulations of the energy transfer between a nanoparticle and its aqueous host fluid. The energy density field is computed for different sets of symmetric grid densities, and the multiscale theory holds when slowly varying energy densities at the nodes are obtained. Results strongly depend on grid density and nanoparticle constituent material. A nonuniform temperature distribution, larger thermal fluctuations in the nanoparticle than in the bath, and enhancement of fluctuations at the surface, which are expressed due to the atomic nature of the systems, are captured by this method rather than by phenomenological continuum energy transfer models.

Multiscale time-dependent density functional theory: Demonstration for plasmons.

Plasmon properties are of significant interest in pure and applied nanoscience. While time-dependent density functional theory (TDDFT) can be used to study plasmons, it becomes impractical for elucidating the effect of size, geometric arrangement, and dimensionality in complex nanosystems. In this study, a new multiscale formalism that addresses this challenge is proposed. This formalism is based on Trotter factorization and the explicit introduction of a coarse-grained (CG) structure function constructed as the Weierstrass transform of the electron wavefunction. This CG structure function is shown to vary on a time scale much longer than that of the latter. A multiscale propagator that coevolves both the CG structure function and the electron wavefunction is shown to bring substantial efficiency over classical propagators used in TDDFT. This efficiency follows from the enhanced numerical stability of the multiscale method and the consequence of larger time steps that can be used in a discrete time evolution. The multiscale algorithm is demonstrated for plasmons in a group of interacting sodium nanoparticles (15-240 atoms), and it achieves improved efficiency over TDDFT without significant loss of accuracy or space-time resolution.

Reverse Coarse-Graining for Equation-Free Modeling: Application to Multiscale Molecular Dynamics.

Constructing atom-resolved states from low-resolution data is of practical importance in many areas of science and engineering. This problem is addressed in this article in the context of multiscale factorization methods for molecular dynamics. These methods capture the crosstalk between atomic and coarse-grained scales arising in macromolecular systems. This crosstalk is accounted for by Trotter factorization, which is used to separate the all-atom from the coarse-grained phases of the computation. In this approach, short molecular dynamics runs are used to advance in time the coarse-grained variables, which in turn guide the all-atom state. To achieve this coevolution, an all-atom microstate consistent with the updated coarse-grained variables must be recovered. This recovery is cast here as a nonlinear optimization problem that is solved with a quasi-Newton method. The approach yields a Boltzmann-relevant microstate whose coarse-grained representation and some of its fine-scale features are preserved. Embedding this algorithm in multiscale factorization is shown to be accurate and scalable for simulating proteins and their assemblies.

Implicit Time Integration for Multiscale Molecular Dynamics Using Transcendental Padé Approximants.

Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Padé approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations.

Prospective on multiscale simulation of virus-like particles: Application to computer-aided vaccine design.

Simulations of virus-like particles needed for computer-aided vaccine design highlight the need for new algorithms that accelerate molecular dynamics. Such simulations via conventional molecular dynamics present a practical challenge due to the millions of atoms involved and the long timescales of the phenomena of interest. These phenomena include structural transitions, self-assembly, and interaction with a cell surface. A promising approach for addressing this challenge is multiscale factorization. The approach is distinct from coarse-graining techniques in that it (1) avoids the need for conjecturing phenomenological governing equations for coarse-grained variables, (2) provides simulations with atomic resolution, (3) captures the cross-talk between disturbances at the atomic and the whole virus-like particle scale, and (4) achieves significant speedup over molecular dynamics. A brief review of multiscale factorization method is provided, as is a prospective on its development.

Alternating metastable/stable pattern in the mercuric iodide crystal formation outside the Ostwald Rule of Stages.

We report a reaction-diffusion system in which two initially separated electrolytes, mercuric chloride (outer) and potassium iodide (inner), interact in a solid hydrogel media to produce a propagating front of mercuric iodide precipitate. The precipitation process is accompanied by a polymorphic transformation of the kinetically favored (unstable) orange, (metastable) yellow, and (thermodynamically stable) red polymorphs of HgI2. The sequence of crystal transformation is confirmed to agree with the Ostwald Rule of Stages. However, a region is found of initial inner iodide concentration, where a stationary pattern of alternating metastable/stable crystals is formed. A theoretical model based on reaction diffusion coupled to a special nucleation and growth mechanism is proposed. Its numerical solution is shown to reproduce the experimental results.

Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision.

Mesoscopic N-atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. A multiscale method for simulating these systems in the friction dominated regime from the underlying N-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate to coarse-grained variables constitute a stationary process on the time scale of coarse-grained dynamics. The method is demonstrated for lactoferrin, nudaurelia capensis omega virus, and human papillomavirus to assess its accuracy.

Scaling and crossover dynamics in the hyperbolic reaction-diffusion equations of initially separated components.

In this paper we investigate the dynamics of front propagation in the family of reactions (nA + mB (k)→ C) with initially segregated reactants in one dimension using hyperbolic reaction-diffusion equations with the mean-field approximation for the reaction rate. This leads to different dynamics than those predicted by their parabolic counterpart. Using perturbation techniques, we focus on the initial and intermediate temporal behavior of the center and width of the front and derive the different time scaling exponents. While the solution of the parabolic system yields a short time scaling as t(1/2) for the front center, width, and global reaction rate, the hyperbolic system exhibits linear scaling for those quantities. Moreover, those scaling laws are shown to be independent of the stoichiometric coefficients n and m. The perturbation results are compared with the full numerical solutions of the hyperbolic equations. The crossover time at which the hyperbolic regime crosses over to the parabolic regime is also studied. Conditions for static and moving fronts are also derived and numerically validated.