Related papers: Spatially-extended hybrid methods: a review
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…
Multiscale modeling of material properties has emerged as one of the grand challenges in material science and engineering. We provide a comprehensive, though not exhaustive, overview of the current status of multiscale simulations of…
Environmental and climate processes are often distributed over large space-time domains. Their complexity and the amount of available data make modelling and analysis a challenging task. Statistical modelling of environment and climate data…
Many biological phenomena are inherently multiscale, i.e. they are characterized by interactions involving different spatial and temporal scales simultaneously. Though several approaches have been proposed to provide "multilayer" models,…
The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which address this problem by keeping the…
Particle Swarm Optimization (PSO) has emerged as a powerful metaheuristic global optimization approach over the past three decades. Its appeal lies in its ability to tackle complex multidimensional problems that defy conventional…
Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs…
Both discrete and continuum models have been widely used to study rapid granular flow, discrete model is accurate but computationally expensive, whereas continuum model is computationally efficient but its accuracy is doubtful in many…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
3D spatial perception is the problem of building and maintaining an actionable and persistent representation of the environment in real-time using sensor data and prior knowledge. Despite the fast-paced progress in robot perception, most…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
Quantum computing has shown significant potential to address complex optimization problems; however, its application remains confined to specific problems at limited scales. Spatial regionalization remains largely unexplored in quantum…
We describe some scaling issues that arise when using lattice Boltzmann methods to simulate binary fluid mixtures -- both in the presence and in the absence of colloidal particles. Two types of scaling problem arise: physical and…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
Hybrid systems are complex dynamical systems that combine discrete and continuous components. Reachability questions, regarding whether a system can run into a certain subset of its state space, stand at the core of verification and…
Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural…