Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is computed in small patches spread across the space-time domain, with patch coupling conditions bridging the unsimulated space. For accurate simulations, care must be taken in designing the patch coupling conditions. Here we construct novel coupling conditions which preserve translational invariance, rotational invariance, and self-adjoint symmetry, thus guaranteeing that conservation laws associated with these symmetries are preserved in the macroscale simulation. Spectral and algebraic analyses of the proposed scheme in both one and two dimensions reveal mechanisms for further improving the accuracy of the simulations. Consistency of the patch scheme's macroscale dynamics with the original microscale model is proved. This new self-adjoint patch scheme provides an efficient, flexible, and accurate computational homogenisation in a wide range of multiscale scenarios of interest to scientists and engineers

Machine learning–driven multiscale modeling reveals lipid-dependent dynamics of RAS signaling proteins

RAS is a signaling protein associated with the cell membrane that is mutated in up to 30% of human cancers. RAS signaling has been proposed to be regulated by dynamic heterogeneity of the cell membrane. Investigating such a mechanism requires near-atomistic detail at macroscopic temporal and spatial scales, which is not possible with conventional computational or experimental techniques. We demonstrate here a multiscale simulation infrastructure that uses machine learning to create a scale-bridging ensemble of over 100,000 simulations of active wild-type KRAS on a complex, asymmetric membrane. Initialized and validated with experimental data (including a new structure of active wild-type KRAS), these simulations represent a substantial advance in the ability to characterize RAS-membrane biology. We report distinctive patterns of local lipid composition that correlate with interfacially promiscuous RAS multimerization. These lipid fingerprints are coupled to RAS dynamics, predicted to influence effector binding, and therefore may be a mechanism for regulating cell signaling cascades

A statistical approach for fracture property realization and macroscopic failure analysis of brittle materials

Lacking the energy dissipative mechanics such as plastic deformation to rebalance localized stresses, similar to their ductile counterparts, brittle material fracture mechanics is associated with catastrophic failure of purely brittle and quasi-brittle materials at immeasurable and measurable deformation scales respectively. This failure, in the form macroscale sharp cracks, is highly dependent on the composition of the material microstructure. Further, the complexity of this relationship and the resulting crack patterns is exacerbated under highly dynamic loading conditions. A robust brittle material model must account for the multiscale inhomogeneity as well as the probabilistic distribution of the constituents which cause material heterogeneity and influence the complex mechanisms of dynamic fracture responses of the material. Continuum-based homogenization is carried out via finite element-based micromechanical analysis of a material neighbor which gives is geometrically described as a sampling windows (i.e., statistical volume elements). These volume elements are well-defined such that they are representative of the material while propagating material randomness from the inherent microscale defects. Homogenization yields spatially defined elastic and fracture related effective properties, utilized to statistically characterize the material in terms of these properties. This spatial characterization is made possible by performing homogenization at prescribed spatial locations which collectively comprise a non-uniform spatial grid which allows the mapping of each effective material properties to an associated spatial location. Through stochastic decomposition of the derived empirical covariance of the sampled effective material property, the Karhunen-Loeve method is used to generate realizations of a continuous and spatially-correlated random field approximation that preserve the statistics of the material from which it is derived. Aspects of modeling both isotropic and anisotropic brittle materials, from a statistical viewpoint, are investigated to determine how each influences the macroscale fracture response of these materials under highly dynamic conditions. The effects of modeling a material both explicitly by representations of discrete multiscale constituents and/or implicitly by continuum representation of material properties is studies to determine how each model influences the resulting material fracture response. For the implicit material representations, both a statistical white noise (i.e., Weibull-based spatially-uncorrelated) and colored noise (i.e., Karhunen-Loeve spatially-correlated model) random fields are employed herein