2018
DOI: 10.1098/rsif.2017.0931
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Spatially extended hybrid methods: a review

Abstract: Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentratio… Show more

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Cited by 37 publications
(38 citation statements)
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References 117 publications
(339 reference statements)
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“…Evaluating dissipative properties of molecules is a task that is becoming essential in computational chemistry, especially in molecular dynamics (MD) simulations of macromolecules and ensembles of macromolecules . Coarse‐graining (CG) techniques prefer, when possible, to treat the medium implicitly as a thermal bath that contributes to the energetics in a mean field fashion and to the dynamics by imposing fluctuation‐dissipation to the momenta associated with the coordinates of the relevant part of the system, which is described explicitly.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Evaluating dissipative properties of molecules is a task that is becoming essential in computational chemistry, especially in molecular dynamics (MD) simulations of macromolecules and ensembles of macromolecules . Coarse‐graining (CG) techniques prefer, when possible, to treat the medium implicitly as a thermal bath that contributes to the energetics in a mean field fashion and to the dynamics by imposing fluctuation‐dissipation to the momenta associated with the coordinates of the relevant part of the system, which is described explicitly.…”
Section: Introductionmentioning
confidence: 99%
“…Evaluating dissipative properties of molecules is a task that is becoming essential in computational chemistry, especially in molecular dynamics (MD) simulations of macromolecules and ensembles of macromolecules. [1][2][3][4][5][6][7][8][9][10] Coarse-graining (CG) techniques prefer, when possible, to treat the medium implicitly as a thermal bath that contributes to the energetics in a mean field fashion and to the dynamics by imposing fluctuation-dissipation to the momenta associated with the coordinates of the relevant part of the system, which is described explicitly. Under these assumptions, the time evolution of the relevant coordinates is stochastic and in the diffusive regime (which is a reasonable assumption for most molecules in room temperature solvents), the dynamics is Brownian, and described by a diffusion tensor.…”
Section: Introductionmentioning
confidence: 99%
“…The stretching method will be particularly useful when developing spatially extended hybrid methods on growing domains. These methods split the spatial domain into subdomains, in which different modelling paradigms are used, separated by an interface or overlap region [22]. We envisage that the stretching method can be used in the compartment-based subdomain of a hybrid model for reaction-diffusion on a growing domain, without causing a build-up of particles at the interface.…”
Section: Discussionmentioning
confidence: 99%
“…The population dynamics resulting from such interactions will depend on the types of spatial structure examined in this work. Another extension would be to consider spatial processes such as moving fronts that are relevant to many biological processes including malignant invasion and developmental morphogenesis 38 . In this study, we consider the movement of individuals in a two-dimensional spatial domain.…”
Section: /19mentioning
confidence: 99%