No abstract

First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the Péclet number (Pe) -the ratio between the rates of advective and diffusive transport. When Pe > 1 the process is drift-controlled and restart can only hinder its completion. In contrast, when 0 ≤ Pe < 1 the process is diffusion-controlled and restart can speed-up its completion by a factor of ∼ 1/Pe. Such speedup occurs when the process is restarted at an optimal rate r r 0 (1 − Pe), where r 0 stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions -some of its central features are completely generic. arXiv:1811.08239v4 [cond-mat.stat-mech]

Patients with advanced corneal disease do poorly with conventional corneal transplantation and require a keratoprosthesis (KPro) for visual rehabilitation. The most widely used KPro is constructed using poly(methyl methacrylate) (PMMA) in the central optical core and a donor cornea as skirt material. In many cases, poor adherence between the PMMA and the soft corneal tissue is responsible for device "extrusion" and bacterial infiltration. The interfacial adhesion between the tissue and the PMMA was therefore critical to successful implantation and device longevity. In our approach, we modified the PMMA surface using oxygen plasma (plasma group); plasma followed by calcium phosphate (CaP) coating (p-CaP); dopamine followed by CaP coating (d-CaP); or plasma followed by coating with (3-aminopropyl)triethoxysilane (3-APTES). To create a synthetic KPro model, we constructed and attached 500 μm thick collagen type I hydrogel on the modified PMMA surfaces. Surface modifications produced significantly improved interfacial adhesion strength compared to untreated PMMA (p < 0.001). The p-CaP group yielded the best interfacial adhesion with the hydrogel (177 ± 27 mN/cm(2)) followed by d-CaP (168 ± 31 mN/cm(2)), 3-APTES (145 ± 12 mN/cm(2)), and plasma (119 ± 10 mN/cm(2)). Longer-term stability of the adhesion was achieved by d-CaP, which, after 14 and 28 days of incubation in phosphate buffered saline, yielded 164 ± 25 mN/cm(2) (p = 0.906 compared to adhesion at day 1) and 131 ± 20 mN/cm(2) (p = 0.053), respectively. In contrast, significant reduction of adhesion strength was observed in p-CaP group over time (p < 0.001). All surface coatings were biocompatible to human corneal stromal fibroblasts, except for the 3-APTES group, which showed no live cells at 72 h of culture. In contrast, cells on d-CaP surface showed good anchorage, evidenced by the expression of focal adhesion complex (paxillin and vinculin), and prominent filopodia protrusions. In conclusion, d-CaP can not only enhance and provide stability to the adhesion of collagen hydrogel on the PMMA surface but also promote biointegration.