The primary source of nonlinearity in graphene membranes is motion-induced tension modulation. Similar to mode coupling in other mechanical systems 4,20,21 , one vibrational mode (here assumed to be the fundamental mode at frequency 1 ) can be parametrically manipulated through its interaction with a second mode, which is deemed the phonon 3 cavity (at ). Exciting the coupled system at the cavity's red sideband ( − 1 ) results in energy flow from the fundamental to the cavity, whereas pumping the blue sideband ( + 1 ) generates amplification of both the fundamental and cavity modes; these processes are depicted in Figure 1c. The efficiency of this inter-modal energy exchange is dictated by the coupling rate, = / 1 , where 1 is the amplitude of motion at 1 .This coupling rate is reminiscent of cavity opto-mechanics, and an identical formalism can be used to derive the resulting equations of motion (supplementary material, section S1).The advantages of graphene over other membrane materials (e.g. SiN) in generating this effect are two-fold: 1) For the coupling mechanism under consideration, increases linearly with the static membrane deflection, 0 . In graphene this value can be tuned electrostatically with a dc bias voltage. Moreover, because of its atomic thinness (ℎ ∼ 0.3nm), graphene can withstand large out-of plane stretching. This is the result of an extremely low in-plane stiffness, = ℎ/(1 − 2 ) , where and are the elastic modulus (1.0TPa for exfoliated 22 and 160GPa for CVD 23 graphene) and Poisson ratio, respectively. Previous studies of graphene have shown 0 can exceed 3% of the suspended length without rupturing 24 . 2) Because the tension in graphene is highly tunable, the frequency spectrum can be adjusted to obtain 3-mode alignment,Here signifies the resonance of a third mode, which overlaps the cavity sideband and enhances pumping by a factor of ; this arrangement is also depicted in Fig. 1c. Under these conditions, it is thus possible to generate large phonon cavity effects in the room temperature graphene system. 4It should be noted that there are alternative inter-modal coupling mechanisms available for tensioned membranes -most notably, mutual coupling to a resonance of the surrounding substrate 21 . Such systems enable parametric membrane control in a manner qualitatively similar to the coupling studied here, but also necessitate the 3-mode alignment described above, which can be a challenge if the spectrum is not experimentally tunable. Moreover, a unique feature of the graphene system is the tunability of the coupling rate itself, ∝ 0 , which is present neither in the substratecoupled case nor in standard optomechanics experiments.We have fabricated circular graphene drums with diameters ranging from 5 to 20 μm;we report measurements of two drums -"Device 1" ( = 8 and detected optically through laser interferometry 11 . Unlike previous generations of graphene resonators, our structures feature two independent back-gates, which enable efficient actuation of several mechanical modes. The gate-...

This review paper provides a recent overview of current international research that is being conducted into the functional properties of cellulose as a nanomaterial. A particular emphasis is placed on fundamental and applied research that is being undertaken to generate applications, which are now becoming a real prospect given the developments in the field over the last 20 years. A short introduction covers the context of the work, and definitions of the different forms of cellulose nanomaterials (CNMs) that are most widely studied. We also address the terminology used for CNMs, suggesting a standard way to classify these materials. The reviews are separated out into theme areas, namely healthcare, water purification, biocomposites, and energy. Each section contains a short review of the field within the theme and summarizes recent work being undertaken by the groups represented. Topics that are covered include cellulose nanocrystals for directed growth of tissues, bacterial cellulose in healthcare, nanocellulose for drug delivery, nanocellulose for water purification, nanocellulose for thermoplastic composites, nanocellulose for structurally colored materials, transparent wood biocomposites, supercapacitors and batteries.

The influence of confinement on the phases of superfluid helium-3 is studied using the torsional pendulum method. We focus on the transition between the A and B phases, where the A phase is stabilized by confinement and a spatially modulated stripe phase is predicted at the A–B phase boundary. Here we discuss results from superfluid helium-3 contained in a single 1.08-μm-thick nanofluidic cavity incorporated into a high-precision torsion pendulum, and map the phase diagram between 0.1 and 5.6 bar. We observe only small supercooling of the A phase, in comparison to bulk or when confined in aerogel, with evidence for a non-monotonic pressure dependence. This suggests that an intrinsic B-phase nucleation mechanism operates under confinement. Both the phase diagram and the relative superfluid fraction of the A and B phases, show that strong coupling is present at all pressures, with implications for the stability of the stripe phase.

In bulk superfluid 3He at zero magnetic field, two phases emerge with the B-phase stable everywhere except at high pressures and temperatures, where the A-phase is favoured. Aerogels with nanostructure smaller than the superfluid coherence length are the only means to introduce disorder into the superfluid. Here we use a torsion pendulum to study 3He confined in an extremely anisotropic, nematically ordered aerogel consisting of ∼10 nm-thick alumina strands, spaced by ∼100 nm, and aligned parallel to the pendulum axis. Kinks in the development of the superfluid fraction (at various pressures) as the temperature is varied correspond to phase transitions. Two such transitions are seen in the superfluid state, and we identify the superfluid phase closest to Tc at low pressure as the polar state, a phase that is not seen in bulk 3He.

Tensioned graphene membranes are of interest both for fundamental physics and for applications ranging from water filtration to nanomechanical resonators. It is generally assumed that these membranes have a stretching modulus of about 340 N/m and a negative, temperature-independent thermal expansion coefficient due to transverse phonon modes. In this paper, we study the Young's modulus and thermal expansion of graphene as functions of temperature using laser interferometry to detect the static displacement of the membrane in a cryostat. Surprisingly, we find the modulus decreases strongly with increasing temperature, which leads to a positive temperature-dependent thermal expansion coefficient. We show that the thermally-rippled membrane theory is not consistent with our data, while the effects of surface contaminants typically present 1 on these membranes may explain the observed behavior. Our experiments undermine long-standing assumptions about tensioned 2D membranes, but are consistent with puzzling behaviors observed in previous experiments on graphene resonators.