Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

We study the dynamics of vortices in an inhomogeneous Gross--Pitaevskii equation iδtu = Δu + 1/ε²(ρ² ε(ᵡ) - |u|²). For a unique scaling regime |ρε(ᵡ) - 1 = O(logε¯¹), it is shown that vortices can interact both with the background perturbation and with each other. Results for associated parabolic and elliptic problems are discussed

Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur

Halfvortices in flat nanomagnets

We discuss a new type of topological defect in XY systems where the O(2) symmetry is broken in the presence of a boundary. Of particular interest is the appearance of such defects in nanomagnets with a planar geometry. They are manifested as kinks of magnetization along the edge and can be viewed as halfvortices with winding numbers \pm 1/2. We argue that halfvortices play a role equally important to that of ordinary vortices in the statics and dynamics of flat nanomagnets. Domain walls found in experiments and numerical simulations are composite objects containing two or more of these elementary defects. We also discuss a closely related system: the two-dimensional smectic liquid crystal films with planar boundary condition.Comment: 7 pages, 8 figures, To appear as a chapter in Les Houches summer school on Quantum Magnetis

Ginzburg-Landau vortex dynamics with pinning and strong applied currents

We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected to an applied electric current and electromagnetic field and containing impurities. Such a current is expected to set the vortices in motion, while the pinning term drives them toward minima of the pinning potential and "pins" them there. We derive the limiting dynamics of a finite number of vortices in the limit of a large Ginzburg-Landau parameter, or \ep \to 0, when the intensity of the electric current and applied magnetic field on the boundary scale like \lep. We show that the limiting velocity of the vortices is the sum of a Lorentz force, due to the current, and a pinning force. We state an analogous result for a model Ginzburg-Landau equation without magnetic field but with forcing terms. Our proof provides a unified approach to various proofs of dynamics of Ginzburg-Landau vortices.Comment: 48 pages; v2: minor errors and typos correcte

Feasibility and acceptance of electronic quality of life assessment in general practice: an implementation study

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

The mimetic politics of lone-wolf terrorism

Written at a time of crisis in the project of social and political modernity, Fyodor Dostoevsky’s 1864 novel Notes from Underground offers an intriguing parallel for the twenty-first century lone-wolf; it portrays an abject, outcast, spiteful unnamed anti-hero boiling with rage, bitter with resentment and on the verge of radicalisation. A Girardian reading of the poetic truths contained in Dostoevsky’s work is able to provide important keys to explain the contemporary transformation from ‘fourth-wave’ religious terrorism to ‘fifth-wave’ lone-wolf terrorism. Such a reading argues that it is mimetic rivalry – rather than much-trumpeted forms of religious violence or cultural differences – that fuels the triangular relation between governments, terrorists and civilian victims at heart of terrorist acts. This approach is further able to blend social inquiry with an account of the individual, in fact anthropological, conditions of lone-wolf terrorism by tracing the globalisation of resentment and the individualisation of violence to the hyper-mimeticism characterising the globalisation of late modernity. Finally, a mimetic reading of ‘fifth-wave’ terrorism accounts for the turbulence of a global politics in which victimhood and scapegoating no longer have the ability to stabilise social order and warns against a future where violence proliferates and escalates unchecked

Dynamics for Ginzburg-Landau vortices under a mixed flow

Abstract. We consider a complex Ginzburg-Landau equation that contains a Schrödinger term and a damping term that is proportional to the time derivative. Given well-prepared initial conditions that correspond to quantized vortices, we establish the vortex motion law until collision time. 1. introduction We study the asymptotic behavior of the complex Ginzburg-Landau equation (αε + i)∂tuε = ∆uε + 1 ε2 uε(1 − |uε | 2 (1.1) uε(·, 0) = u 0 (1.2) ε(·) as ε → 0, where uε(t) : Ω → C, Ω ⊂ R 2 a bounded and simply connected C 1 domain, with either Dirichlet boundary conditions (1.3) uε = g on ∂Ω, where g ∈ C 1 (∂Ω, S 1), or Neumann boundary conditions

Automated Selection of the Optimal On-board Systems Architecture within MDO Collaborative Environment

The on-board systems are having even more importance in aircraft design since the continuous research for a competitive, more optimized and less costly aircraft. In addition, the introduction of new technologies related to the More Electric Aircraft and All Electric Aircraft concepts have raised the interest on on-board systems discipline giving the option of analyzing different architectures. The present paper would enhance the selection of the best on-board systems architecture introducing a new workflow, which is able to identify the best architecture in terms of procurement and operating cost. Since the importance of fuel required providing the secondary power, the effect of each specific architecture on engine performance is particularly considered including a detailed engine module. The workflow is implemented in Optimus framework within a collaborative and multidisciplinary environment and it is open to be integrated with additional modules increasing the fidelity of the analysis. To explore the capability of the defined workflow, the H2020 AGILE regional jet is identified as test case