Transient luminous events in the atmosphere, such as lighting-induced sprites and upwardly discharging blue jets, were discovered recently in the region between thunderclouds and the ionosphere. In the conventional picture, the main components of Earth's global electric circuit include thunderstorms, the conducting ionosphere, the downward fair-weather currents and the conducting Earth. Thunderstorms serve as one of the generators that drive current upward from cloud tops to the ionosphere, where the electric potential is hundreds of kilovolts higher than Earth's surface. It has not been clear, however, whether all the important components of the global circuit have even been identified. Here we report observations of five gigantic jets that establish a direct link between a thundercloud (altitude approximately 16 km) and the ionosphere at 90 km elevation. Extremely-low-frequency radio waves in four events were detected, while no cloud-to-ground lightning was observed to trigger these events. Our result indicates that the extremely-low-frequency waves were generated by negative cloud-to-ionosphere discharges, which would reduce the electrical potential between ionosphere and ground. Therefore, the conventional picture of the global electric circuit needs to be modified to include the contributions of gigantic jets and possibly sprites.

When a force deforms an elastic object, practical experience suggests that the resulting displacement will be in the same direction as the force. This property is known as positive stiffness. Less familiar is the concept of negative stiffness, where the deforming force and the resulting displacement are in opposite directions. (Negative stiffness is distinct from negative Poisson's ratio, which refers to the occurrence of lateral expansion upon stretching an object.) Negative stiffness can occur, for example, when the deforming object has stored (or is supplied with) energy. This property is usually unstable, but it has been shown theoretically that inclusions of negative stiffness can be stabilized within a positive-stiffness matrix. Here we describe the experimental realization of this composite approach by embedding negative-stiffness inclusions of ferroelastic vanadium dioxide in a pure tin matrix. The resulting composites exhibit extreme mechanical damping and large anomalies in stiffness, as a consequence of the high local strains that result from the inclusions deforming more than the composite as a whole. Moreover, for certain temperature ranges, the negative-stiffness inclusions are more effective than diamond inclusions for increasing the overall composite stiffness. We expect that such composites could be useful as high damping materials, as stiff structural elements or for actuator-type applications.

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Analytical investigations on the contact problems between two homogeneous and isotropic soft bodies were performed to simulate the contact of human buttocks and seat cushions. The cushion materials' Poisson's ratio were allowed to be negative. The human buttocks were modeled as an ideal sphere with radius 15 cm, and assumed to have a low Young's modulus and a Poisson's ratio close to 0.5. These parameters were held constant during our analysis. Peak contact pressure was reduced by adjusting the contour curvature of cushions according to Hertz theory, as expected. Moreover, analysis by both the Hertz model and a finite thickness 3D elasticity model showed that using negative Poisson's ratio cushions could further reduce the pressure. Negative Poisson's ratio cushions may be beneficial in the prevention of pressure sores or ulcers in the sick and in reduction of pressure-induced discomfort in seated people.

The effect of a negative bulk modulus phase in elastic composites is studied. Negative bulk modulus K<0 is shown to be possible in selected unit cells. In isotropic solids, K<0 can be attained when negative Poisson's ratio is sufficiently small, below the stability limit (for stress control) ¼ À1. Such materials, if used as inclusions, are predicted to be stable with respect to the band formation, even if they are large. Composites with spherical inclusions of negative bulk moduli are shown to exhibit negative Poisson's ratio and anomalies in composite bulk modulus and Young's modulus (and in the corresponding mechanical damping) but not in the shear modulus.

When an elastic object is pressed, we expect it to resist by exerting a restoring force. A reversal of this force corresponds to negative stiffness. If we combine elements with positive and negative stiffness in a composite, it is possible to achieve stiffness greater than ͑or less than͒ that of any of the constituents. This behavior violates established bounds that tacitly assume that each phase has positive stiffness. Extreme composite behavior has been experimentally demonstrated in a lumped system using a buckled tube to achieve negative stiffness and in a composite material in the vicinity of a phase transformation of one of the constituents. In the context of a composite system, extreme refers to a physical property greater than either constituent. We consider a simple spring model with pre-load to achieve negative stiffness. When suitably tuned to balance positive and negative stiffness, the system shows a critical equilibrium point giving rise to extreme overall stiffness. A stability analysis of a viscous damped system containing negative stiffness springs reveals that the system is stable when tuned for high compliance, but metastable when tuned for high stiffness. The metastability of the extreme system is analogous to that of diamond. The frequency response of the viscous damped system shows that the overall stiffness increases with frequency and goes to infinity when one constituent has a suitable negative stiffness.

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Several foams of different cell-size, including Scott Industrial polyurethane foam with large cells (20 pores per inch, ppi, or 1.2 mm per pore, black), medium cells (65 ppi, or 0.4 mm per pore, green), and near-microcellular (100 ppi, 0.25 mm per pore, white), were processed over various time and temperature regimes to ascertain the role of cell size in transformation to negative Poisson's ratio materials. These foams were transformed successfully, and exhibited negative Poisson's ratio behavior. Poisson's ratio was measured using a new laser based setup. For all as-received (unprocessed) foams with different cell sizes, Poisson's ratio decreased with compressive axial strain and increased with tensile strain up to a maximum. The maximum Poisson's ratio in tension decreased as cell size increases. The strain at which maximum Poisson's ratio occurs, increased with cell size. In negative Poisson's ratio foams, minimum Poisson's ratios of −0.8, −0.5, and −0.4 for 20 ppi, 65 ppi, and 100 ppi foams, respectively were observed. Furthermore, the cell size effects on transformation parameters were also found.