Transition from rotating waves to modulated rotating waves on the sphere

We study non-resonant and resonant Hopf bifurcation of a rotating wave in SO(3)-equivariant reaction-diffusion systems on a sphere. We obtained reduced differential equations on so(3), the characterization of modulated rotating waves obtained by Hopf bifurcation of a rotating wave, as well as results regarding the resonant case. Our main tools are the equivariant center manifold reduction and the theory of Lie groups and Lie algebras, especially for the group SO(3) of all rigid rotations on a sphere

Risk of miscarriage following amniocentesis or chorionic villus sampling: systematic review of literature and updated meta-analysis

Objectives: To estimate the procedure-related risks of miscarriage after amniocentesis and trans-abdominal chorionic villus sampling (CVS) based on a systematic review of the literature and an updated meta-analysis. Methods: A search of MEDLINE, EMBASE, and The Cochrane Library was carried out to identify studies reporting complications following CVS or amniocentesis. The inclusion criteria for the systematic review were studies reporting results from large controlled studies and those reporting data for pregnancy loss prior to 24 weeks’ gestation. Study authors were contacted when required to identify additional necessary data. Data for cases that had invasive procedure and controls groups were inputted in contingency tables and risk of miscarriage was estimated for each study. Summary statistics based on a fixed and random effects model were calculated after taking into account the weighting for each study included in the systematic review. Procedure-related risk of miscarriage was estimated as a weighted risk difference from the summary statistics for cases and controls. A subgroup analyses according to the similarity risk levels in the invasive testing and control groups was performed. Heterogeneity was assessed using Cochrane’s Q and I2 statistic. Egger Bias was estimated to assess reporting bias in published studies. Summary statistics for procedure-related risk of miscarriage were graphically represented in Forest plots. Results: The electronic search from the databases yielded 2,943 potential citations, from which, we selected 20 controlled studies for inclusion in the systematic review to estimate the procedure-related risk of miscarriage from invasive procedures. There were a total of 580 miscarriages from 63,273 amniocentesis procedures with a weighted risk of pregnancy loss of 0.91% (95%CI: 0.73 to 1.09). In the control group, there were 1,726 miscarriages in 330,469 pregnancies with a loss rate of 0.58% (95CI%: 0.47 to 0.70). The weighted procedure-related risk of miscarriage was 0.30% (95%CI: 0.11 to 0.49, I2=70.1%). There were a total of 163 miscarriages from 13,011 CVS procedures with a risk of pregnancy loss of 1.39% (95%CI: 0.76 to 2.02). In the control group, there were 1,946 miscarriages in 232,680 pregnancies with a loss rate of 1.23% (95CI%: 0.86 to 1.59). The weighted procedure-related risk of miscarriage following CVS was 0.20% (95%CI: -0.12 to 0.52, I2=51.9%). However, when only studies with similar risk profiles between the intervention and control groups were considered, the procedure related risk for amniocentesis became 0.03% (95%CI -0.08 to 0.14, I2=0%) and for CVS -0.38 (95% CI -1.12 to 0.36, I2=0%). Conclusion: The procedure-related risks of miscarriage following amniocentesis and CVS are lower than currently quoted to women. The risk appears to be negligible when these interventions are compared to control groups of the same risk profile

Forced Symmetry Breaking from SO(3) to SO(2) for Rotating Waves on the Sphere

We consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating wave on the sphere that persists to a normally hyperbolic SO(2)-invariant manifold $M(\epsilon)$. We investigate the effects of this forced symmetry breaking by studying the perturbed dynamics induced on $M(\epsilon)$ by the above reaction-diffusion system. We prove that depending on the frequency vectors of the rotating waves that form the relative equilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotating waves or SO(2)-orbits of modulated rotating waves (if some transversality conditions hold). The orbital stability of these solutions is established as well. Our main tools are the orbit space reduction, Poincare map and implicit function theorem

Monte Carlo study of the evaporation/condensation transition on different Ising lattices

In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous magnetisation). By identifying a dimensionless parameter \Delta (\delta M) and a universal constant \Delta_c, they showed in the limit of large system sizes that for \Delta < \Delta_c the excess is absorbed in the background (``evaporated'' system), while for \Delta > \Delta_c a droplet of the dense phase occurs (``condensed'' system). To check the applicability of the analytical results to much smaller, practically accessible system sizes, we performed several Monte Carlo simulations for the 2D Ising model with nearest-neighbour couplings on a square lattice at fixed magnetisation M. Thereby, we measured the largest minority droplet, corresponding to the condensed phase, at various system sizes (L=40, >..., 640). With analytic values for for the spontaneous magnetisation m_0, the susceptibility \chi and the Wulff interfacial free energy density \tau_W for the infinite system, we were able to determine \lambda numerically in very good agreement with the theoretical prediction. Furthermore, we did simulations for the spin-1/2 Ising model on a triangular lattice and with next-nearest-neighbour couplings on a square lattice. Again, finding a very good agreement with the analytic formula, we demonstrate the universal aspects of the theory with respect to the underlying lattice. For the case of the next-nearest-neighbour model, where \tau_W is unknown analytically, we present different methods to obtain it numerically by fitting to the distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl

Research on a superconducting niobium-thorium eutectic alloy and superconducting composites

Superconducting niobium-thorium eutectic alloy and composite

Quantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem

Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful classical algorithms, the CVRP is challenging to solve classically. Quantum computing may offer a way to improve the time to solution, although the question remains open as to whether Noisy Intermediate-Scale Quantum (NISQ) devices can achieve a practical advantage compared to classical heuristics. The most prominent algorithms proposed to solve combinatorial optimization problems in the NISQ era are the Quantum Approximate Optimization Algorithm (QAOA) and the more general Variational Quantum Eigensolver (VQE). However, implementing them in a way that reliably provides high-quality solutions is challenging, even for toy examples. In this work, we discuss decomposition and formulation aspects of the CVRP and propose an application-driven way to measure solution quality. Considering current hardware constraints, we reduce the CVRP to a clustering phase and a set of TSPs. For the TSP, we extensively test both QAOA and VQE and investigate the influence of various hyperparameters, such as the classical optimizer choice and strength of constraint penalization. Results of QAOA are generally of limited quality because the algorithm does not reach the energy threshold for feasible TSP solutions, even when considering various extensions such as recursive, warm-start and constraint-preserving mixer QAOA. On the other hand, the VQE reaches the energy threshold and shows a better performance. Our work outlines the obstacles to quantum-assisted solutions for real-world optimization problems and proposes perspectives on how to overcome them.Comment: Submitted to the IEEE for possible publicatio

Spontaneous Breakdown of Superhydrophobicity

In some cases water droplets can completely wet micro-structured superhydrophobic surfaces. The {\it dynamics} of this rapid process is analyzed by ultra-high-speed imaging. Depending on the scales of the micro-structure, the wetting fronts propagate smoothly and circularly or -- more interestingly -- in a {\it stepwise} manner, leading to a growing {\it square-shaped} wetted area: entering a new row perpendicular to the direction of front propagation takes milliseconds, whereas once this has happened, the row itself fills in microseconds ({\it ``zipping''})Comment: Accepted for publication in Physical Review Letter