An operational procedure is presented to compute explicitly the different terms in the generalized Langevin equation (GLE) for a few relevant variables obtained within Mori-Zwanzig formalism. The procedure amounts to introducing an artificial controlled parameter which can be tuned in such a way that the so-called projected dynamics becomes explicit and the GLE reduces to a Markovian equation. The projected dynamics can be realised in practice by introducing constraints, and it is shown that the Green-Kubo formulae computed with these dynamics do not suffer from the plateau problem. The methodology is illustrated in the example of star polymer molecules in a melt using their center of mass as relevant variables. Through this example, we show that not only the effective potentials, but also the friction forces and the noise play a very important role in the dynamics.

Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well defined statistical ensembles can be generated making use of all standard Molecular Dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.

Two-dimensional perovskites, in which inorganic layers are stabilized by organic spacer molecules, are attracting increasing attention as a more robust analogue to the conventional three-dimensional metal-halide perovskites. However, reducing the perovskite dimensionality alters their optoelectronic properties dramatically, yielding excited states that are dominated by bound electron-hole pairs known as excitons, rather than by free charge carriers common to their bulk counterparts. Despite the growing interest in two-dimensional perovskites for both light harvesting and light emitting applications, the full impact of the excitonic nature on their optoelectronic properties remains unclear, particularly regarding the spatial dynamics of the excitons within the two-dimensional (2D) plane.Here, we present direct measurements of in-plane exciton transport in single-crystalline layered perovskites. Using time-resolved fluorescence microscopy, we show that excitons undergo an initial fast, intrinsic normal diffusion through the crystalline plane, followed by a transition to a slower subdiffusive regime as excitons get trapped. Interestingly, the early intrinsic exciton diffusivity depends sensitively on the choice of organic spacer. We find a clear correlation between the stiffness of the lattice and the diffusivity, suggesting exciton-phonon interactions to be dominant in determining the spatial dynamics of the excitons in these materials. Our findings provide a clear design strategy to optimize exciton transport in these systems. lead, tin), X is a halide anion (chloride, bromide, iodide), L is a long organic spacer molecule, and n is the number of octahedra that make up the thickness of the inorganic layer. The separation into fewatom thick inorganic layers yields strong quantum and dielectric confinement effects. 38 As a result, the exciton binding energies in 2D perovskites can be as high as several hundreds of meVs, which is around an order of magnitude larger than those found in bulk perovskites. [39][40][41] The excitonic character of the excited state is accompanied by an effective widening of the bandgap, an increase in the oscillator strength, and a narrowing of the emission spectrum. [40][41][42] The strongest confinement effects are observed for n = 1, where the excited state is confined to a single B-X-octahedral layer (see Figure 1a).Light harvesting using 2D perovskites relies on the efficient transport of excitons and their subsequent separation into free charges. 43 This stands in contrast to bulk perovskites in which free charges are generated instantaneously thanks to the small exciton binding energy. 39 Particularly, with excitons being neutral quasi-particles, the charge extraction becomes significantly more challenging as they cannot be guided to the electrodes through an external electric field. 44 Excitons need to diffuse to an interface before the electron and hole can be efficiently separated into free charges. 45 On the other hand, for light emitting applications the spatial displacement is ...

We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions "on the fly." Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid dynamics. The matching of both descriptions of matter is made across an overlapping region and, in general, consists of a two-way coupling scheme (C-->P and P-->C) that conveys mass, momentum, and energy fluxes. The contribution of the hybrid scheme hereby presented is twofold. First, it treats unsteady flows and, more importantly, it handles energy exchange between both C and P regions. The implementation of the C-->P coupling is tested here using steady and unsteady flows with different rates of mass, momentum and energy exchange. In particular, relaxing flows described by linear hydrodynamics (transversal and longitudinal waves) are most enlightening as they comprise the whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the onset of an initial perturbation, the cell-averaged Fourier components of the flow variables in the P region (velocity, density, internal energy, temperature, and pressure) evolve in excellent agreement with the hydrodynamic trends. It is also shown that the scheme preserves the correct rate of entropy production. We discuss some general requirements on the coarse-grained length and time scales arising from both the characteristic microscopic and hydrodynamic scales.