Copula-based modeling and simulation of 3D systems of curved fibers by isolating intrinsic fiber properties and external effects.

In this paper we lay the foundation for data-driven 3D analysis of virtual fiber systems with respect to their microstructure and functionality. In particular, we develop a stochastic 3D model for systems of curved fibers similar to nonwovens, which is fitted to tomographic image data. By systematic variations of model parameters, efficient computer-based scenario analyses can be performed to get a deeper insight how effective properties of this type of functional materials depend on their 3D microstructure. In a first step, we consider single fibers as polygonal tracks which can be modeled by a third-order Markov chain. For constructing the transition function of the Markov chain, we formalize the intuitive notions of intrinsic fiber properties and external effects and build a copula-based transition function such that both aspects can be varied independently. Using this single-fiber model, in a second step we derive a model for the entire fiber system observed in a bounded sampling window and fit it to two different 3D datasets of nonwovens measured by CT imaging. Considering various geometric descriptors of the 3D microstructure related to effective properties of the pore space, we evaluate the goodness of model fit by comparing geometric descriptors of the 3D morphology of model realizations with those of tomographic image data.

Delay-sustained pattern formation in subexcitable media.

The influence of time-delayed feedback on pattern formation in subexcitable media represented by a net of FitzHugh-Nagumo elements, a minimal model of neuronal dynamics, is studied. Without feedback, wave fronts die out after a short propagation length (subexcitable net dynamics). Applying time-delayed feedback with appropriate feedback parameters, pattern formation is sustained and the wave fronts may propagate through the whole net (signature of excitable behavior). The coherence of noise-induced patterns is significantly enhanced if feedback with appropriately chosen parameters is applied, and shows a resonancelike dependency on the delay time. In a next step, the transition to the excitable regime is investigated in dependence on the quota of elements, which get the feedback signal. It is sufficient to control approximately half of the elements to achieve excitable behavior. Regarding a medical application, where the external control of a neural tissue would affect not single neurons but clusters of neurons, the spatial correlation of the controlled elements is of importance. The selection of the elements, which get the feedback signal, is based on a spatially correlated random distribution. It is shown that the correlation length of this distribution affects the pattern formation.

Doubly diversity-induced resonance.

The influence of variability on the response of a net of bistable FitzHugh-Nagumo elements to a weak signal is investigated. The response of the net undergoes a resonancelike behavior due to additive variability. For an intermediate strength of additive variability the external signal is optimally enhanced in the output of the net (diversity-induced resonance). Furthermore, we show that additive noise strongly influences the diversity-induced resonance. Afterwards the interplay of additive and multiplicative variability on the response of the net is investigated. Starting with asymmetric bistable elements the enhancement of the signal is not very pronounced in the presence of additive variability. Via symmetry restoration by multiplicative variability the resonance is further enhanced. We call this phenomenon doubly diversity-induced resonance, because the interplay of both, additive and multiplicative variability, is essential to achieve the optimal enhancement of the signal. The restoration of symmetry can be explained by a systematic effect of the multiplicative variability, which changes the thresholds for the transitions between the two stable fixed points. We investigate the response to variability for globally and diffusively coupled networks and in dependency on the coupling strength.

Variability-sustained pattern formation in subexcitable media.

Starting with a subexcitable net of FitzHugh-Nagumo elements it is shown that parameter variability (diversity) is able to induce pattern formation. These patterns are most coherent for an intermediate variability strength. This effect is similar to the well-known spatiotemporal stochastic resonance generated by additive noise in subexcitable media. Furthermore, variability is able to induce a transition to an excitable behavior of the net. This transition strongly depends on the coupling strength between the elements and it is found only for strong coupling. For weaker coupling one observes a lifetime lengthening of waves propagating through the medium, but the net stays subexcitable.

Variability-induced transition in a net of neural elements: From oscillatory to excitable behavior.

Starting with an oscillatory net of neural elements, increasing variability induces a phase transition to excitability. This transition is explained by a systematic effect of the variability, which stabilizes the formerly unstable, spatially uniform, temporally constant solution of the net. Multiplicative noise may also influence the net in a systematic way and may thus induce a similar transition. Adding noise into the model, the interplay of noise and variability with respect to the reported transition is investigated. Finally, pattern formation in a diffusively coupled net is studied, because excitability implies the ability of pattern formation and information transmission.

Noise-memory induced excitability and pattern formation in oscillatory neural models.

We report a noise-memory induced phase transition in an array of oscillatory neural systems, which leads to the suppression of synchronous oscillations and restoration of excitable dynamics. This phenomenon is caused by the systematic contributions of temporally correlated parametric noise, i.e., possessing a memory, which stabilizes a deterministically unstable fixed point. Changing the noise correlation time, a reentrant phase transition to noise-induced excitability is observed in a globally coupled array. Since noise-induced excitability implies the restoration of the ability to transmit information, associated spatiotemporal patterns are observed afterwards. Furthermore, an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations.