Coarse-Grained Analysis of Microscopic Neuronal Simulators on Networks: Bifurcation and Rare-events computations

We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of neurons that interact on complex networks. In particular we show how the Equation-Free approach can be exploited to perform system-level tasks such as bifurcation, stability analysis and estimation of mean appearance times of rare events, bypassing the need for obtaining analytical approximations, providing an "on-demand" model reduction. Using the detailed simulator as a black-box timestepper, we compute the coarse-grained equilibrium bifurcation diagrams, examine the stability of the solution branches and perform a rare-events analysis with respect to certain characteristics of the underlying network topology such as the connectivity degre

Synthesis and Characterization of Greener Ceramic Materials with Lower Thermal Conductivity Using Olive Mill Solid Byproduct

In the current research, the valorization of olive mill solid waste as beneficial admixture into clay bodies for developing greener ceramic materials with lower thermal conductivity, thus with increased thermal insulation capacity towards energy savings, is investigated. Various clay/waste mixtures were prepared. The raw material mixtures were characterized and subjected to thermal gravimetric analysis, in order to optimize the mineral composition and maintain calcium and magnesium oxides content to a minimum. Test specimens were formed employing extrusion and then sintering procedure at different peak temperatures. Apparent density, water absorption capability, mechanical strength, porosity and thermal conductivity were determined on sintered specimens and examined in relation to the waste percentage and sintering temperature. The experimental results showed that ceramic production from clay/olive-mill solid waste mixtures is feasible. In fact, the mechanical properties are not significantly impacted with the incorporation of the waste in the ceramic body. However, the thermal conductivity decreases significantly, which can be of particular interest for thermal insulating materials development. Furthermore, the shape of the produced ceramics does not appear to change with the sintering temperature increase

Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables

A bifurcation analysis of dislocation patterning in the one-dimensional finite domain

© 2015 AIP Publishing LLC. We study the celebrated Walgraef-Aifantis (W-A) model of dislocation patterning in one dimensional finite domain. The system consists of two partial differential equations of reaction diffusion type, which describes one dimensional dislocation dynamics. We give both analytical and numerical results for the system\u27s behavior. The analysis shows rich non linear dynamics including hysteresis and periodic solutions, which are characteristics of dislocation-induced plastic deformation under cyclic loading

Coarse-scale PDEs from fine-scale observations via machine learning

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through, e.g., atomistic, agent-based, or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using, e.g., partial differential equations (PDEs) describing the evolution of the right few macroscopic observables (e.g., concentration and momentum fields). Deriving good macroscopic descriptions (the so-called "closure problem") is often a time-consuming process requiring deep understanding/intuition about the system of interest. Recent developments in data science provide alternative ways to effectively extract/learn accurate macroscopic descriptions approximating the underlying microscopic observations. In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine-learning algorithms. Specifically, using Gaussian processes, artificial neural networks, and/or diffusion maps, the proposed framework uncovers the relation between the relevant macroscopic space fields and their time evolution (the right-hand side of the explicitly unavailable macroscopic PDE). Interestingly, several choices equally representative of the data can be discovered. The framework will be illustrated through the data-driven discovery of macroscopic, concentration-level PDEs resulting from a fine-scale, lattice Boltzmann level model of a reaction/transport process. Once the coarse evolution law is identified, it can be simulated to produce long-term macroscopic predictions. Different features (pros as well as cons) of alternative machine-learning algorithms for performing this task (Gaussian processes and artificial neural networks) are presented and discussed

The effect of the diffusion on the bifurcation behavior of dislocation patterns in the one-dimensional finite domain

© 2016 Author(s). We study the pattern formation in dislocation dynamics of solid materials through bifurcation analysis. The model under study is the celebrated Walgraef-Aifantis (W-A) model of dislocation patterning in one dimensional finite domain. The model describes the evolution of the patterns along the domain and it consists of a couple of partial diffusion equations. The system is a reaction diffusion type with two different diffusion coefficients, one for the mobile (free to move due to stress in the slip plane) dislocations and the second for the immobile dislocations (slow movement or trapped ones). We analytically study the onset of instabilities as the diffusion coefficients are varied. We finally construct the bifurcation diagram with respect to the diffusion coefficients

Analytical and numerical bifurcation analysis of dislocation pattern formation of the Walgraef–Aifantis model

© 2018 We analyze the pattern formation due to dislocations under cyclic loading resulting from the Walgraef–Aifantis model. The model consists of a set of partial differential equations of the reaction–diffusion type in the one dimensional finite space with two different diffusion-like coefficients, for the mobile (free to move when the applied resolved shear stress in the slip plane exceeds a certain threshold) and for the immobile (of slow movement or trapped) dislocations. We derive analytically the Turing spatial and Andronov–Hopf temporal instabilities emanating from the homogeneous solutions and construct the complete bifurcation diagram of the far-from-equilibrium spatio-temporal patterns, with respect to the applied stress and the size of the domain. Finally, we analyze the symmetric properties of all branches of both steady and oscillating far-from-equilibrium regimes