2D Rutherford-Like Scattering in Ballistic Nanodevices

Ballistic injection in a nanodevice is a complex process where electrons can either be transmitted or reflected, thereby introducing deviations from the otherwise quantized conductance. In this context, quantum rings (QRs) appear as model geometries: in a semiclassical view, most electrons bounce against the central QR antidot, which strongly reduces injection efficiency. Thanks to an analogy with Rutherford scattering, we show that a local partial depletion of the QR close to the edge of the antidot can counter-intuitively ease ballistic electron injection. On the contrary, local charge accumulation can focus the semi-classical trajectories on the hard-wall potential and strongly enhance reflection back to the lead. Scanning gate experiments on a ballistic QR, and simulations of the conductance of the same device are consistent, and agree to show that the effect is directly proportional to the ratio between the strength of the perturbation and the Fermi energy. Our observation surprisingly fits the simple Rutherford formalism in two-dimensions in the classical limit

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

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

Locked and Unlocked Polygonal Chains in 3D

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D with a polynomial number of moves.Comment: To appear in Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 199

A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Hadron Spectrum in QCD with Valence Wilson Fermions and Dynamical Staggered Fermions at $6/g^2=5.6

We present an analysis of hadronic spectroscopy for Wilson valence quarks with dynamical staggered fermions at lattice coupling $6/g^2 = \beta=5.6$ at sea quark mass $am_q=0.01$ and 0.025, and of Wilson valence quarks in quenched approximation at $\beta=5.85$ and 5.95, both on $16^3 \times 32$ lattices. We make comparisons with our previous results with dynamical staggered fermions at the same parameter values but on $16^4$ lattices doubled in the temporal direction.Comment: 32 page

Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Correlated Percolation in the Damage Zone

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture process being a correlated percolation process in a self-generated quadratic damage gradient. We use the quasi-static two-dimensional fuse model as a paradigm of a fracture model. We measure for this model, that exhibits a correlated percolation process, the correlation length exponent nu approximately equal to 1.35 and conjecture it to be equal to that of uncorrelated percolation, 4/3. We then show that the roughness exponent in the fuse model is zeta = 2 nu/(1+2 nu)= 8/11. This is in accordance with the numerical value zeta=0.75. As for three-dimensional brittle fractures, a mean-field theory gives nu=2, leading to zeta=4/5 in full accordance with the universally observed value zeta =0.80.Comment: 4 pages RevTeX

Fracturing and Porosity Channeling in Fluid Overpressure Zones in the Shallow Earth’s Crust

At the time of energy transition, it is important to be able to predict the effects of fluid overpressures in different geological scenarios as these can lead to the development of hydrofractures and dilating high-porosity zones. In order to develop an understanding of the complexity of the resulting effective stress fields, fracture and failure patterns, and potential fluid drainage, we study the process with a dynamic hydromechanical numerical model. The model simulates the evolution of fluid pressure buildup, fracturing, and the dynamic interaction between solid and fluid. Three different scenarios are explored: fluid pressure buildup in a sedimentary basin, in a vertical zone, and in a horizontal layer that may be partly offset by a fault. Our results show that the geometry of the area where fluid pressure is successively increased has a first-order control on the developing pattern of porosity changes, on fracturing, and on the absolute fluid pressures that sustained without failure. If the fluid overpressure develops in the whole model, the effective differential and mean stress approach zero and the vertical and horizontal effective principal stresses flip in orientation. The resulting fractures develop under high lithostatic fluid overpressure and are aligned semihorizontally, and consequently, a hydraulic breccia forms. If the area of high fluid pressure buildup is confined in a vertical zone, the effective mean stress decreases while the differential stress remains almost constant and failure takes place in extensional and shear modes at a much lower fluid overpressure. A horizontal fluid pressurized layer that is offset shows a complex system of effective stress evolution with the layer fracturing initially at the location of the offset followed by hydraulic breccia development within the layer. All simulations show a phase transition in the porosity where an initially random porosity reduces its symmetry and forms a static porosity wave with an internal dilating zone and the presence of dynamic porosity channels within this zone. Our results show that patterns of fractures, hence fluid release, that form due to high fluid overpressures can only be successfully predicted if the geometry of the geological system is known, including the fluid overpressure source and the position of seals and faults that offset source layers and seals

Roughness and multiscaling of planar crack fronts

We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $\xi$. The problem is shown to have two important length scales, $\xi$ and the Larkin length $L_c$. Multiscaling of the crack front is observed for scales below $\xi$, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent $\zeta \approx 0.39$ is recovered for scales larger than both $\xi$ and $L_c$. If $L_c > \xi$, these regimes are separated by a third regime characterized by the Larkin exponent $\zeta_L \approx 0.5$. We discuss the experimental implications of our results.Comment: 8 pages, two figure