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In this contribution we investigate the application of phase-field fracture models on non-linear multiscale computational homogenization schemes. In particular, we introduce different phase-fields on a two-scale problem and develop a thermodynamically consistent model. This allows on the one hand for the prediction of local micro-fracture patterns, which effectively acts as an anisotropic damage model on the macroscale. On the other and, the macro-fracture phase-field model allows to predict complex fracture pattern with regard to local microstructures. Both phase-fields are introduced in a common framework, such that a joint consistent linearization for the Newton-Raphson iteration can be developed. Finally, the limits of both models as well as the applicability are shown in different numerical examples.

In this contribution, we derive a consistent variational formulation for computational homogenization methods and show that traditional FE2 and IGA2 approaches are special discretization and solution techniques of this most general framework. This allows us to enhance dramatically the numerical analysis as well as the solution of the arising algebraic system. In particular, we expand the dimension of the continuous system, discretize the higher dimensional problem consistently and apply afterwards a discrete null-space matrix to remove the additional dimensions. A benchmark problem, for which we can obtain an analytical solution, demonstrates the superiority of the chosen approach aiming to reduce the immense computational costs of traditional FE2 and IGA2 formulations to a fraction of the original requirements. Finally, we demonstrate a further reduction of the computational costs for the solution of general non-linear problems.

Shared automated mobility-on-demand promises efficient, sustainable, and flexible transportation. Nevertheless, security concerns, resilience, and their mutual influence - especially at night - will likely be the most critical barriers to public adoption since passengers have to share rides with strangers without a human driver on board. As related work points out that information about fellow travelers might mitigate passengers' concerns, we designed two user interface variants to investigate the role of this information in an exploratory within-subjects user study (N = 24). Participants experienced four automated day and night rides with varying personal information about co-passengers in a simulated environment. The results of the mixed-method study indicate that having information about other passengers (e.g., photo, gender, and name) positively affects user experience at night. In contrast, it is less necessary during the day. Considering participants' simultaneously raised privacy demands poses a substantial challenge for resilient system design.

The popularity of concurrent transmissions (CT) has soared after recent studies have shown their feasibility on the four physical layers specified by BLE 5, hence providing an alternative to the use of IEEE 802.15.4 for the design of reliable and efficient low-power wireless protocols. However, to date, the extent to which physical layer properties affect the performance of CT has not yet been investigated in detail. This paper fills this gap and provides an extensive study on the impact of the physical layer on CT-based solutions using IEEE 802.15.4 and BLE 5. We first highlight through simulation how the impact of errors induced by relative carrier frequency offsets on the performance of CT highly depends on the choice of the underlying physical layer. We then confirm these observations experimentally on real hardware and with varying environmental conditions through an analysis of the bit error distribution across received packets, unveiling possible techniques to effectively handle these errors. We further study the performance of CT-based data collection and dissemination protocols in the presence of RF interference on a large-scale testbed, deriving insights on how the employed physical layer affects their dependability., Comment: arXiv admin note: substantial text overlap with arXiv:2005.13816

Flooding protocols based on concurrent transmissions are regarded as the most reliable way to collect or disseminate data across a multi-hop low-power wireless mesh network. Recent works have shown that such protocols are effective for narrowband communication not only over IEEE 802.15.4, but also over the BLE 5 physical layers (PHYs). However, to date, existing literature has only built synchronous flooding solutions on top of a single PHY, and there has been no attempt to leverage different PHYs at runtime to increase performance. This paper fills this gap and presents OSF, an open-source framework that enables the design of multi-PHY synchronous flooding solutions thanks to a novel radio driver and middle-ware architecture capable of dynamically switching the underlying physical layer. This allows exploitation of the specific benefits of each PHY (e.g., higher data-rate, increased robustness) on-demand during each flood, increasing performance. We tailor OSF to the off-the-shelf nRF52840 platform, and showcase its benefits by comparing single-PHY and multi-PHY synchronous flooding solutions on a real-world testbed.

A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain decomposition approach. From a computational point of view, this is motivated by the fact that matrix and fibers can easily meshed independently. Our main interest is in fiber reinforce polymers where the Young's modulus are quite different. Thus the modeling error from the overlapping approach is of no significance. The coupling conditions acknowledge both, the forces and the moments of the beam model and transfer them to the background material. A suitable static condensation procedure is applied to remove the beam balance equations. The condensed system then forms our starting point for a numerical approximation in terms of isogeometric analysis. The choice of our discrete basis functions of higher regularity is motivated by the fact, that as a result of the static condensation, we obtain second gradient terms in fiber direction. Eventually, a series of benchmark tests demonstrate the flexibility and robustness of the proposed methodology. As a proof-of-concept, we show that our new model is able to capture bending, torsion and shear dominated situations.

Targeting dependable communications for industrial Internet of Things applications, IETF 6TiSCH provides mechanisms for efficient scheduling, routing, and forwarding of IPv6 traffic across low-power mesh networks. Yet, despite an overwhelming body of literature covering both centralized and distributed scheduling schemes for 6TiSCH, an effective control solution for large-scale multi-hop mesh networks remains an open challenge. This paper addresses this with a novel approach that eliminates much of the routing and link-layer overhead incurred by centralized schedulers, and provides a robust mechanism for data dissemination synchronization within 6TiSCH. Specifically, we leverage the physical layer (PHY) switching capabilities of modern low-power wireless platforms to build on recent work demonstrating the viability of Concurrent Transmission (CT)-based flooding protocols across the Bluetooth 5 (BT 5) PHYs. By switching the PHY and MAC layer at runtime, we inject a BT 5-based CT flood within a standard IEEE 802.15.4 TSCH slotframe, thereby providing a reliable, low-latency scheme for 6TiSCH control messaging. We present an analytical model and experimental evaluation showing how our solution not only exploits the BT 5 high data-rate PHY layers for rapid data dissemination, but can also provide reliable 6TiSCH association and synchronization even under external radio interference. We further discuss how the proposed technique can be used to address other open challenges within the standard.

The popularity of concurrent transmissions (CT) has soared after recent studies have shown their feasibility on the four physical layers specified by BLE 5, hence providing an alternative to the use of IEEE 802.15.4 for the design of reliable and efficient low-power wireless protocols. However, to date, the extent to which physical layer properties affect the performance of CT has not yet been investigated in detail. This paper fills this gap and provides the first extensive study on the impact of the physical layer on CT-based solutions using IEEE 802.15.4 and BLE 5. We first highlight through simulation how the impact of errors induced by de-synchronization and beating on the performance of CT highly depends on the choice of the underlying physical layer. We then confirm these observations experimentally on real hardware through an analysis of the bit error distribution across received packets, unveiling possible techniques to effectively handle these errors. We further study the performance of CT-based flooding protocols in the presence of radio interference on a large-scale, and derive important insights on how the used physical layer affects their dependability., Comment: Paper submitted at ICNP 2020

What is the path associated with the fastest Brownian particle that reaches a narrow window located on the boundary of a domain? Although the distribution of the fastest arrival times has been well studied in dimension 1, much less is known in higher dimensions. Based on the Wiener path-integral, we derive a variational principle for the path associated with the fastest arrival particle. Specifically, we show that in a large ensemble of independent Brownian trajectories, the first moment of the shortest arrival time is associated with the minimization of the energy-action and the optimal trajectories are geodesics. Escape trajectories concentrate along these geodesics, as confirmed by stochastic simulations when an obstacle is positioned in front of the narrow window. To conclude paths in stochastic dynamics and their time scale can differ significantly from the mean properties, usually at the basis of the Smoluchowski's theory of chemical reactions., Comment: After Narrow Escape, Here is Extreme Narrow Escape

We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is liner in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behavior, quantum absorption, time of arrival, quantum measurements, and more, as will be discussed separately., Comment: 7 pages, 1 figures.Spelling and typo corrected. The appendix was removed and for further mathematical detail A. Friedman's book was referred to. Both sections (introduction and summary) have been extended (as the referee suggested). Accepted for publication at Physics Letters A

Do biological cells sense time by the number of their divisions, a process that ends at senescence? We consider the question "can the cell's perception of time be expressed through the length of the shortest telomere?" The answer is that the absolute time before senescence cannot be expressed by the telomere's length and that a cell can survive many more divisions than intuitively expected. This apparent paradox is due to shortening and elongation of the telomere, which suggests a random walk model of the telomere's length. The model indicates two phases, first, a determinist drift of the length toward a quasi-equilibrium state, and second, persistence of the length near an attracting state for the majority of divisions prior to senescence. The measure of stability of the latter phase is the expected number of divisions at the attractor ("lifetime") prior to crossing a threshold to senescence. The telomerase regulates stability by creating an effective potential barrier that separates statistically the shortest lifetime from the next shortest. The random walk has to overcome the barrier in order to extend the range of the first regime. The model explains how random telomere dynamics underlies the extension of cell survival time., Comment: No comments

The first of $N$ identical independently distributed (i.i.d.) Brownian trajectories that arrives to a small target, sets the time scale of activation, which in general is much faster than the arrival to the target of only a single trajectory. Analytical asymptotic expressions for the minimal time is notoriously difficult to compute in general geometries. We derive here asymptotic laws for the probability density function of the first and second arrival times of a large number of i.i.d. Brownian trajectories to a small target in 1,2, and 3 dimensions and study their range of validity by stochastic simulations. The results are applied to activation of biochemical pathways in cellular transduction., Comment: 6 figs

We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP) equations for charge concentration and electric potential as a model of electro-diffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. As the number of charge increases, they concentrate at the end of cusp-shaped funnel. These results can be used in the design of nano-pipettes and help to understand the local voltage changes inside dendrites and axons with heterogenous local geometry., Comment: To appear in Journal of Nonlinear Science

100 years after Smoluchowski introduces his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from large number (tens of thousands) of single molecular trajectories or to study the diffusive motion of molecules, proteins or receptors. Stochastic modeling is a new step in large data analysis that serves extracting cell biology concepts. We review here the Smoluchowski's approach to stochastic processes and provide several applications for coarse-graining diffusion, studying polymer models for understanding nuclear organization and finally, we discuss the stochastic jump dynamics of telomeres across cell division and stochastic gene regulation., Comment: 65 pages, J. Phys A 2016

Voltage and charge distributions in cellular microdomains regulate communications, excitability, and signal transduction. We report here new electrical laws in a cell, which follow from a nonlinear electro-diffusion model. These newly discovered relations derive from the geometrical cell-membrane properties, such as membrane curvature, volume, and surface area. These electro-diffusion laws can now be used to predict and interpret voltage distribution in cellular microdomains., Comment: submitted in PRL 2016

Theoretically, the coordinate measurement of two identical particles at a point by two narrowly separated narrow detectors, is interpreted in the limit of shrinking width and separation, as the detection of two particles by a single narrow detector. { Ordinarily, the ratio between probabilities of point measurements is independent of the width of the narrow detectors.} We show here that not only this is not the case, but that in some scenarios the results depend on the way the dimensions shrink to zero. The ratio between the width and the separation determines the detection result. { In particular, it is shown that the bunching parameter of bosons is not a well-defined physical property. Moreover, it may suggests that } there is a difficulty in quantum measurement theory in the interpretation of coordinate measurement of two particles., Comment: 15 pages, 2 figures,to be published in Phys. Lett. A

The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratu-type equation with the difference that the boundary condition is Neumann, not Dirichlet and there a minus sign in the exponent of the exponential term. The entire boundary is impermeable to the ions and the electric field satisfies the compatibility condition of Poisson's equation. We construct a steady radial solution and find that the potential is maximal in the center and decreases toward the boundary. We study the limit of large charge in dimension 1,2 and 3. For the case of a small absorbing window in the sphere, we find the escape rate of an ion from the steady density., Comment: 20 pages in SIAP 2015

To recover the long-time behavior and the statistics of molecular trajectories from the large number (tens of thousands) of their short fragments, obtained by super-resolution methods at the single molecule level, data analysis based on a stochastic model of their non-equilibrium motion is required. Recently, we characterized the local biophysical properties underlying receptor motion based on coarse-grained long-range interactions, corresponding to attracting potential wells of large sizes. The purpose of this letter is to discuss optimal estimators and show what happens when thing goes wrong., Comment: 4 pages