Reduced computations for nematic-liquid crystals: A timestepper approach for systems with continuous symmetries

A timestepper-based approach for the coarse-grained analysis of microscopic neuronal simulators on networks: Bifurcation and rare-events micro- to macro-computations

“…However, these functionals, due to complexity of the underlying multiscale evolution of the dynamics, are unavailable or extremely difficult to derive. In fact, the Equation Free methodology provides these closures "on demand"; relatively short bursts of fine scale simulations establish naturally this slaving relation [11,26,35,17,18,38,36,28,24,32].…”

“…In this paper, we show how the so-called "Equation-free" approach [11,26,35,17,18,38,12,27,28,36,24,40] a computational framework for multi-scale computations, can be used to efficiently extract "systems-level" information from detailed individualistic based neuronal-models with respect to certain topology characteristics of the underlying networks.…”

Detection of coarse-grained unstable states of microscopic/stochastic systems: a timestepper-based iterative protocol

“…What a coarse timestepper does, in fact, is providing such closures on demand: relatively short calls of the fine scale simulation can establish this "slaving" relation (refer to [51,55,53,56,58,59] for more detailed discussions). Briefly, once the appropriate macroscopic observables have been identified, the coarse timestepper consists of the following essential components ( (d) Obtain the coarse-grained variables using a restriction operator M : The sequence should converge to zero for deterministic systems (or within a small tolerance, 1 tol , that can be defined with respect to the system's relative noise for stochastic/ microscopic systems), i.e.…”

“…In this paper, we address a new iterative procedure based on the concept of coarse-timestepping [51,55,53,56,58,59] that can be used to drive microscopic simulators -and potentially physical experimentsdirectly to their own open-loop unstable hyperbolic stationary points in a "vicinity" of a regular turning point. The approach does not require the implementation of a branch tracing method, such as the pseudo-arc length continuation, in order to reach the desired saddle point.…”

Ανάπτυξη Παραλληλοποιήσιμων Υπολογιστικών Μεθοδολογιών Χρονο-Βηματισμού Για Την Ανάλυση Και Τον Σχεδιασμό Δικτύων Νευρώνων Πολλαπλών Χωροχρονικών Κλιμάκων Και Πολύ Μεγάλης Κλίμακας

“…στάσιμα σημεία, διακλαδώσεις, οδεύοντα κύματα, και χωροχρονικό χάος [Kopel & Ermetrout, 1986;Kaneko, 1992;Chow, 1998;Freeman, 1999;Bressloff &Coombes, 1999;Chow & Koppel, 2000;Coombes & Osbaldestin, 2000;Haskell et ah, 2001;Roxin et ah, 2004;Coombes, 2005] [Treves, 1993;Bressloff et al, 1997;Bressloff, 1999;Haskell et al, 2001;Casti et al, 2002;Cai et al, 2004;Rangan & Cai, 2006] Siettos, 2007Siettos, , 2009 Κύριο μέρος αυτής της εργασίας βασίζεται στην χρήση και την επιπλέον ανάπτυξη μεθοδολογιών βασισμένων στην μέθοδο «Ελεύθερη Εξισώσεων» (Equation free) [Gear et al, 2002;Makeev et al, 2002;Runborg et al, 2002;Kevrekidis et al, 2003;Siettos et al, 2003;Kevrekidis et al, 2004;Haataja et al, 2004;Mooller et al, 2005;Moon et al, 2005;Russo et al, 2007;Laing & Kevrekidis, 2008] [Fitzhugh, 1961;Morris & Lecar, 1981Izhikevich, 2004Ermentrout &Chow, 2002]. Ένα μοντέλο επομένως, μπορεί να παρουσιάζει:…”