Essential Constraints of Edge-Constrained Proximity Graphs

Given a plane forest $F = (V, E)$ of $|V| = n$ points, we find the minimum set $S \subseteq E$ of edges such that the edge-constrained minimum spanning tree over the set $V$ of vertices and the set $S$ of constraints contains $F$. We present an $O(n \log n )$-time algorithm that solves this problem. We generalize this to other proximity graphs in the constraint setting, such as the relative neighbourhood graph, Gabriel graph, $\beta$-skeleton and Delaunay triangulation. We present an algorithm that identifies the minimum set $S\subseteq E$ of edges of a given plane graph $I=(V,E)$ such that $I \subseteq CG_\beta(V, S)$ for $1 \leq \beta \leq 2$, where $CG_\beta(V, S)$ is the constraint $\beta$-skeleton over the set $V$ of vertices and the set $S$ of constraints. The running time of our algorithm is $O(n)$, provided that the constrained Delaunay triangulation of $I$ is given.Comment: 24 pages, 22 figures. A preliminary version of this paper appeared in the Proceedings of 27th International Workshop, IWOCA 2016, Helsinki, Finland. It was published by Springer in the Lecture Notes in Computer Science (LNCS) serie

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism investigation of size effects on field-induced N\'eel-cap reversal

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism is used to investigate the influence of an applied magnetic field on N\'eel caps (i.e., surface terminations of asymmetric Bloch walls). Self-assembled micron-sized Fe(110) dots displaying a moderate distribution of size and aspect ratios serve as model objects. Investigations of remanent states after application of an applied field along the direction of N\'eel-cap magnetization give clear evidence for the magnetization reversal of the N\'eel caps around 120 mT, with a $\pm$20 mT dispersion. No clear correlation could be found between the value of the reversal field and geometrical features of the dots

Demonstration of an optical-coherence converter

Studying the coherence of an optical field is typically compartmentalized with respect to its different optical degrees of freedom (DoFs) -- spatial, temporal, and polarization. Although this traditional approach succeeds when the DoFs are uncoupled, it fails at capturing key features of the field's coherence if the DOFs are indeed correlated -- a situation that arises often. By viewing coherence as a `resource' that can be shared among the DoFs, it becomes possible to convert the entropy associated with the fluctuations in one DoF to another DoF that is initially fluctuation-free. Here, we verify experimentally that coherence can indeed be reversibly exchanged -- without loss of energy -- between polarization and the spatial DoF of a partially coherent field. Starting from a linearly polarized spatially incoherent field -- one that produces no spatial interference fringes -- we obtain a spatially coherent field that is unpolarized. By reallocating the entropy to polarization, the field becomes invariant with regards to the action of a polarization scrambler, thus suggesting a strategy for avoiding the deleterious effects of a randomizing system on a DoF of the optical field.Comment: 7 pages; 6 figure

Third type of domain wall in soft magnetic nanostrips

Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The associated phase diagram is now well established and often used to predict the low-energy magnetic configuration in a given magnetic nanostructure. However, besides the transverse and vortex walls, we find numerically that another type of wall exists in permalloy nanostrips. This third type of DW is characterised by a three-dimensional, flux closure micromagnetic structure with an unusual length and three internal degrees of freedom. Magnetic imaging on lithographically-patterned permalloy nanostrips confirms these predictions and shows that these DWs can be moved with an external magnetic field of about 1mT. An extended phase diagram describing the regions of stability of all known types of DWs in permalloy nanostrips is provided.Comment: 19 pages, 7 figure

Angular-dependence of magnetization switching for a multi-domain dot: experiment and simulation

We have measured the in-plane angular variation of nucleation and annihilation fields of a multi-domain magnetic single dot with a microsquid. The dots are Fe/Mo(110) self-assembled in UHV, with sub-micron size and a hexagonal shape. The angular variations were quantitatively reproduced by micromagnetic simulations. Discontinuities in the variations are observed, and shown to result from bifurcations related to the interplay of the non-uniform magnetization state with the shape of the dot.Comment: 4 pages, 4 figures, for submission as a regular articl

Phase diagram of magnetic domain walls in spin valve nano-stripes

We investigate numerically the transverse versus vortex phase diagram of head-to-head domain walls in Co/Cu/Py spin valve nano-stripes (Py: Permalloy), in which the Co layer is mostly single domain while the Py layer hosts the domain wall. The range of stability of the transverse wall is shifted towards larger thickness compared to single Py layers, due to a magnetostatic screening effect between the two layers. An approached analytical scaling law is derived, which reproduces faithfully the phase diagram.Comment: 4 page

Downscaling of fracture energy during brittle creep experiments

We present mode 1 brittle creep fracture experiments along fracture surfaces that contain strength heterogeneities. Our observations provide a link between smooth macroscopic time-dependent failure and intermittent microscopic stress-dependent processes. We find the large-scale response of slow-propagating subcritical cracks to be well described by an Arrhenius law that relates the fracture speed to the energy release rate. At the microscopic scale, high-resolution optical imaging of the transparent material used (PMMA) allows detailed description of the fracture front. This reveals a local competition between subcritical and critical propagation (pseudo stick-slip front advances) independently of loading rates. Moreover, we show that the local geometry of the crack front is self-affine and the local crack front velocity is power law distributed. We estimate the local fracture energy distribution by combining high-resolution measurements of the crack front geometry and an elastic line fracture model. We show that the average local fracture energy is significantly larger than the value derived from a macroscopic energy balance. This suggests that homogenization of the fracture energy is not straightforward and should be taken cautiously. Finally, we discuss the implications of our results in the context of fault mechanics

Revolving rivers in sandpiles: from continuous to intermittent flows

In a previous paper [Phys. Rev. Lett. 91, 014501 (2003)], the mechanism of "revolving rivers" for sandpile formation is reported: as a steady stream of dry sand is poured onto a horizontal surface, a pile forms which has a river of sand on one side owing from the apex of the pile to the edge of the base. For small piles the river is steady, or continuous. For larger piles, it becomes intermittent. In this paper we establish experimentally the "dynamical phase diagram" of the continuous and intermittent regimes, and give further details of the piles topography, improving the previous kinematic model to describe it and shedding further light on the mechanisms of river formation. Based on experiments in Hele-Shaw cells, we also propose that a simple dimensionality reduction argument can explain the transition between the continuous and intermittent dynamics.Comment: 8 pages, 11 figures, submitted to Phys Rev

Interplay of seismic and aseismic deformations during earthquake swarms: An experimental approach

Observations of earthquake swarms and slow propagating ruptures on related faults suggest a close relation between the two phenomena. Earthquakes are the signature of fast unstable ruptures initiated on localized asperities while slow aseismic deformations are experienced on large stable segments of the fault plane. The spatial proximity and the temporal coincidence of both fault mechanical responses highlight the variability of fault rheology. However, the mechanism relating earthquakes and aseismic processes is still elusive due to the difficulty of imaging these phenomena of large spatiotemporal variability at depth. Here we present laboratory experiments that explore, in great detail, the deformation processes of heterogeneous interfaces in the brittle-creep regime. We track the evolution of an interfacial crack over 7 orders of magnitude in time and 5 orders of magnitude in space using optical and acoustic sensors. We explore the response of the system to slow transient loads and show that slow deformation episodes are systematically accompanied by acoustic emissions due to local fracture energy disorder. Features of acoustic emission activities and deformation rate distributions of our experimental system are similar to those in natural faults. On the basis of an activation energy model, we link our results to the Rate and State friction model and suggest an active role of local creep deformation in driving the seismic activity of earthquake swarms