We discuss recent progress in hybrid atomistic-continuum methods with particular emphasis on developments in boundary condition imposition in molecular simulations, an essential ingredient of hybrid methods. Both Dirichlet (state variable) and flux boundary conditions are discussed. We also briefly review various coupling approaches and discuss the effects of compressibility and molecular fluctuations on the choice of coupling method. Common elements between hybrid methods and related multiscale simulation approaches are also briefly discussed.

The paper contains a description of a multiscale algorithm based on the boundary element method (BEM) coupled with a discrete atomistic model. The atomic model uses empirical pair-wise potentials to describe interactions between atoms. The Newton-Raphson method is applied to solve a nanoscale model. The continuum domain is modelled by using BEM. The application of BEM reduces the total number of degrees of freedom in the multiscale model. Some numerical results of simulations

at the nanoscale are shown to examine the presented algorithm.

The article reviews the results of experimental tests assessing the impact of process parameters of additive manufacturing technologies on the geometric structure of free-form surfaces. The tests covered surfaces manufactured with the Selective Laser Melting additive technology, using titanium-powder-based material (Ti6Al4V) and Selective Laser Sintering from polyamide PA2200. The evaluation of the resulting surfaces was conducted employing modern multiscale analysis, i.e., wavelet transformation. Comparative studies using selected forms of the mother wavelet enabled determining the character of irregularities, size of morphological features and the indications of manufacturing process errors. The tests provide guidelines and allow to better understand the potential in manufacturing elements with complex, irregular shapes.

Effects of microstructure factors on the acoustic performance of open-cell foams can be characterized numerically by a microstructure-based approach. To this regard, the numerical homogenization approach and the equivalent-fluid theory are employed to study the acoustic behavior of random open-cell foams within their Voronoi tessellation-based Representative Volume Elements (RVE). As a validation step, the numerical predictions are compared with the reference findings to either verify the finite element procedure or demonstrate that the constructed RVE can capture both the local geometrical characteristics and the acoustic macrobehavior of cellular solid foams. It can be seen from the obtained results that the morphological characteristics of open-cell foams could be controlled to achieve the desired sound absorbing behavior. In addition, the analytical expressions, formulating the relationship between the geometry of foam absorbers and their target absorption performance, are established to design sound absorbing foam layers.

Exploring the drivers of changes in ecosystem services is crucial to maintain ecosystem functionality, especially in the diverse Central Citarum watershed. This study utilises the integrated valuation of ecosystem service and trade-offs (InVEST) model and multiscale geographically weighted regression (MGWR) model to examine ecosystem services patterns from 2006 to 2018. The InVEST is a hydrological model to calculate water availability and evaluate benefits provided by nature through simulating alterations in the amount of water yields driven by land use/cover changes. Economic, topographic, climate, and vegetation factors are considered, with an emphasis on their essential components. The presence of a geographical link between dependent and explanatory variables was investigated using a multiscale geographic weighted regression model. The MGWR model is employed to analyse spatial impacts. The integration of both models simplified the process and enhanced its understanding. The findings reveal the following patterns: 1) decreasing land cover and increasing ecosystem services demand in the watershed, along with a decline in water yield, e.g. certain sub-districts encounter water scarcity, while others have abundant water resources; 2) the impact of natural factors on water yield shifts along vegetation > climate > topography (2006) changes to climate > vegetation > topography (2018).