Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

The well-posedness of the boundary value problems for second gradient elasticity has been studied under the assumption of strong ellipticity of the dependence on the second placement gradients (see, e.g., Chambon and Moullet in Comput. Methods Appl. Mech. Eng. 193:2771–2796, 2004 and Mareno and Healey in SIAM J. Math. Anal. 38:103–115, 2006). The study of the equilibrium of planar pantographic lattices has been approached in two different ways: in dell’Isola et al. (Proc. R. Soc. Lond. Ser. A 472:20150, 2016) a discrete model was introduced involving extensional and rotational springs which is also valid in large deformations regimes while in Boutin et al. (Math. Mech. Complex Syst. 5:127–162, 2017) the lattice has been modelled as a set of beam elements interconnected by internal pivots, but the analysis was restricted to the linear case. In both papers a homogenized second gradient deformation energy, quadratic in the neighbourhood of non deformed configuration, is obtained via perturbative methods and the predictions obtained with the obtained continuum model are successfully compared with experiments. This energy is not strongly elliptic in its dependence on second gradients. We consider in this paper also the important particular case of pantographic lattices whose first gradient energy does not depend on shear deformation: this could be considered either a pathological case or an important exceptional case (see Stillwell et al. in Am. Math. Mon. 105:850–858, 1998 and Turro in Angew. Chem., Int. Ed. Engl. 39:2255–2259, 2000). In both cases we believe that such a particular case deserves some attention because of what we can understand by studying it (see Dyson in Science 200:677–678, 1978). This circumstance motivates the present paper, where we address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E; (iii) we prove that the set of placements for which the strain energy is vanishing (the so-called floppy modes) must strictly include rigid motions; (iv) we determine the restrictions on displacement boundary conditions which assure existence and uniqueness of linear static problems. The presented results represent one of the first mechanical applications of the concept of Anisotropic Sobolev space, initially introduced only on the basis of purely abstract mathematical considerations

Resonance fluorescence from an artificial atom in squeezed vacuum

We present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our results are in excellent agreement with predictions for spectra produced by a two-level atom in squeezed vacuum [Phys. Rev. Lett. \textbf{58}, 2539-2542 (1987)], demonstrating that resonance fluorescence offers a resource-efficient means to characterize squeezing in cryogenic environments

Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise

We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extract an equivalent flux noise spectral density at f ~ 1 GHz and find agreement with values extrapolated from a $1/f^\alpha$ fit to the measured flux noise spectral density below 1 Hz.Comment: 5 pages, 4 figures. Final journal versio

Annual and monthly range fidelity of female boreal woodland caribou in respons to petroleum development

Petroleum-sector development in northern Alberta, Canada has been implicated as one factor influencing the decline of boreal woodland caribou (Rangifer tarandus caribou). Previous research showed that caribou are farther from petroleum-sector disturbances within their home range than expected. As petroleum development increases, the distance caribou can selectively place themselves relative to industrial disturbance must decrease, because distances between disturbances decrease. Conceptually, the number of local disturbances becomes so large that caribou either abandon their local avoidance behaviour or leave their traditional home range. We evaluated whether an intense petroleum- development event in northern Alberta was sufficient to result in home range abandonment by female woodland caribou. Using well locations as an index of petroleum development, we found that caribou studied from 1992 to 2000 did not change their annual or monthly range fidelity as a function of development intensity. Caribou remained in peatland complexes containing a large number of petroleum-sector disturbances rather than move to new areas, presumably because the risks of dispersing across upland habitat to reach other suitable habitat are high. Such range fidelity may have fitness consequences for woodland caribou if they suffer greater predation in areas where petroleum development is occurring

Increase of dissolved inorganic carbon and decrease in pH in near-surface waters in the Mediterranean Sea during the past two decades

Two 3-year time series of hourly measurements of the fugacity of CO2 (fCO2) in the upper 10 m of the surface layer of the northwestern Mediterranean Sea have been recorded by CARIOCA sensors almost two decades apart, in 1995–1997 and 2013–2015. By combining them with the alkalinity derived from measured temperature and salinity, we calculate changes in pH and dissolved inorganic carbon (DIC). DIC increased in surface seawater by ∼25 µmol kg−1 and fCO2 by 40 µatm, whereas seawater pH decreased by ∼0.04 (0.0022 yr−1). The DIC increase is about 15 % larger than expected from the equilibrium with atmospheric CO2. This could result from natural variability, e.g. the increase between the two periods in the frequency and intensity of winter convection events. Likewise, it could be the signature of the contribution of the Atlantic Ocean as a source of anthropogenic carbon to the Mediterranean Sea through the Strait of Gibraltar. We then estimate that the part of DIC accumulated over the last 18 years represents ∼30 % of the total inventory of anthropogenic carbon in the Mediterranean Sea

PROTOCOL: Digital interventions to reduce social isolation and loneliness in older adults: An evidence and gap map

This is the protocol for a Campbell systematic review. The objectives are as follows: the aim is to map available evidence on the effects of digital interventions to mitigate social isolation and/or loneliness in older adults in all settings except hospital settings

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl