Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.Comment: 36 pages, 18 figure

Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Cytokine profiles in patients with lower limb ischaemia

postprin

Reconstruction Mechanism of FCC Transition-Metal (001) Surfaces

The reconstruction mechanism of (001) fcc transition metal surfaces is investigated using a full-potential all-electron electronic structure method within density-functional theory. Total-energy supercell calculations confirm the experimental finding that a close-packed quasi-hexagonal overlayer reconstruction is possible for the late 5$d$-metals Ir, Pt, and Au, while it is disfavoured in the isovalent 4$d$ metals (Rh, Pd, Ag). The reconstructive behaviour is driven by the tensile surface stress of the unreconstructed surfaces; the stress is significantly larger in the 5$d$ metals than in 4$d$ ones, and only in the former case it overcomes the substrate resistance to the required geometric rearrangement. It is shown that the surface stress for these systems is due to $d$ charge depletion from the surface layer, and that the cause of the 4th-to-5th row stress difference is the importance of relativistic effects in the 5$d$ series.Comment: RevTeX 3.0, 12 pages, 1 PostScript figure available upon request] 23 May 199

A review of challenges and framework development for corrosion fatigue life assessment of monopile-supported horizontal-axis offshore wind turbines

Digital tools such as machine learning and the digital twins are emerging in asset management of offshore wind structures to address their structural integrity and cost challenges due to manual inspections and remote sites of offshore wind farms. The corrosive offshore environments and salt-water effects further increase the risk of fatigue failures in offshore wind turbines. This paper presents a review of corrosion fatigue research in horizontal-axis offshore wind turbines (HAOWT) support structures, including the current trends in using digital tools that address the current state of asset integrity monitoring. Based on the conducted review, it has been found that digital twins incorporating finite element analysis, material characterisation and modelling, machine learning using artificial neural networks, data analytics, and internet of things (IoT) using smart sensor technologies, can be enablers for tackling the challenges in corrosion fatigue (CF) assessment of offshore wind turbines in shallow and deep waters

Relaxation and reconstruction on (111) surfaces of Au, Pt, and Cu

We have theoretically studied the stability and reconstruction of (111) surfaces of Au, Pt, and Cu. We have calculated the surface energy, surface stress, interatomic force constants, and other relevant quantities by ab initio electronic structure calculations using the density functional theory (DFT), in a slab geometry with periodic boundary conditions. We have estimated the stability towards a quasi-one-dimensional reconstruction by using the calculated quantities as parameters in a one-dimensional Frenkel-Kontorova model. On all surfaces we have found an intrinsic tensile stress. This stress is large enough on Au and Pt surfaces to lead to a reconstruction in which a denser surface layer is formed, in agreement with experiment. The experimentally observed differences between the dense reconstruction pattern on Au(111) and a sparse structure of stripes on Pt(111) are attributed to the details of the interaction potential between the first layer of atoms and the substrate.Comment: 8 pages, 3 figures, submitted to Physical Review

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure

Influence of a knot on the strength of a polymer strand

Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or `overhand' knot is likely to be present with high probability in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use {\it ab initio} computational methods to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot.Comment: 3 pages, 4 figure

The role of social capital in participatory arts for wellbeing: findings from a qualitative systematic review

BACKGROUND:Social capital is often cited as shaping impacts of participatory arts, although the concept has not been systematically mapped in arts, health and wellbeing contexts. In wider health inequalities research, complex, differential, and sometimes negative impacts of social capital have been recognised. METHODS:This paper maps of social capital concepts in qualitative research as part of the UK What Works for Wellbeing evidence review programme on culture, sport and wellbeing. RESULTS:Studies often cite positive impacts of bonding and, to a lesser extent, bridging social capital. However, reported challenges suggest the need for a critical approach. Forms of linking social capital, such as reframing and political engagement to address social divisions, are less often cited but may be important in participatory arts and wellbeing. CONCLUSIONS:Future research should further specify dimensions of social capital as well as their nuanced effects in arts, and wellbeing contexts