1The control of sound propagation and reflection has always been the goal of engineers involved in the design of acoustic systems. A recent design approach based on coordinate transformations, which is applicable to many physical systems [1][2][3][4][5][6][7][8][9][10][11][12][13]15 , together with the explosive development of a new class of engineered materials called metamaterials, has opened the road to the unconstrained control of sound. However, the ideal material parameters prescribed by this methodology are complex and challenging to obtain experimentally, even using metamaterial design approaches. Not surprisingly, experimental demonstration of devices obtained using transformation acoustics is difficult, and has been implemented only in two-dimensional configurations 10,16 . Here, we demonstrate the design and experimental characterization of an almost perfect threedimensional, broadband, and, most importantly, omnidirectional acoustic device that renders a region of space three wavelengths in diameter invisible to sound.It is well understood that, given an arbitrary geometric transformation of a sound field, the effective mass density and the bulk modulus required to implement that transformation is determined as 5,17 : ρ r = det(A)(A −1 ) T ρ v A −1 and B r = det(A)B v , where ρ is the mass density tensor, B is the bulk modulus, A is the Jacobian matrix of the transformation and r and v denotes the real and virtual space, respectively. One application of the coordinate transformation method that received significant attention, and that we focus on here, is the so called "ground cloak". The ground cloak is a material shell that when placed over arbitrary objects sitting on reflecting surfaces, i.e. ground, makes the object undetectable using sound radiation. The concept has been introduced in the context of electromagnetics 18-20 , but has rapidly been extended to other physical systems, including acoustics 10 .The coordinate transformation technique enabling these cloaking devices is especially suitable for acoustics. Developed by noticing the similarity between the acoustic wave equation and the conduction equation 5 , the method requires a wide range of anisotropic and inhomogeneous material parameters. Unlike electromagnetics, however, these are easier to realize in acoustics in a broadband manner using metamaterial methods because conventional materials have a broad range of acoustic material parameters spanning multiple orders of magnitude.There have been attempts to avoid the difficulties associated with the coordinate transformation approach by using more conventional techniques. However, these entail lowering 2 design requirements, such as replacing omnidirectionality with unidirectionality, and have been proven very challenging as well when applied experimentally 14,26 . Here we show that omnidirectional three-dimensional ground cloaks obtained using coordinate transformation methods are feasible in practice.There are several options for geometric transformations that will map the volume occu...

We present the design, fabrication, and performance analysis for a class of two-dimensional acoustic cloaking coatings in air. Our approach takes advantage of transformation acoustics and linear coordinate transformations that result in shells which are homogeneous, broadband, and compact. The required material parameters are highly anisotropic; however, we show that they are easily achievable in practice in metamaterials made of perforated plastic plates. The good performance of the fabricated design is assessed from measurements of the sound field produced around the cloak by a broadband source. The remarkably low complexity of the device made of perforated plastic plates shows that sound in air can be fully and effectively manipulated using realizable transformation acoustics devices.

We report the experimental demonstration of broadband negative refractive index obtained in a labyrinthine acoustic metamaterial structure. Two different approaches were employed to prove the metamaterial negative index nature: one-dimensional extractions of effective parameters from reflection and transmission measurements, and two-dimensional prism-based measurements that convincingly show the transmission angle corresponding to negative refraction. The transmission angles observed in the latter case also agree very well with the refractive index obtained in the one-dimensional measurements and numerical simulations. We expect this labyrinthine metamaterial to become the unit cell of choice for practical acoustic metamaterial devices that require broadband and significantly negative indexes of refraction.

[1] The temporal and spatial development of sprite-producing lightning flashes is examined with coordinated observations over an asymmetric mesoscale convective system (MCS) on 29 June 2011 near the Oklahoma Lightning Mapping Array (LMA). Sprites produced by a total of 26 lightning flashes were observed simultaneously on video from Bennett, Colorado and Hawley, Texas, enabling a triangulation of sprites in comparison with temporal development of parent lightning (in particular, negatively charged stepped leaders) in three-dimensional space. In general, prompt sprites produced within 20 ms after the causative stroke are less horizontally displaced (typically <30 km) from the ground stroke than delayed sprites, which usually occur over 40 ms after the stroke with significant lateral offsets (>30 km). However, both prompt and delayed sprites are usually centered within 30 km of the geometric center of relevant LMA sources (with affinity to negative stepped leaders) during the prior 100 ms interval. Multiple sprites appearing as dancing/jumping events associated with a single lightning flash could be produced either by distinct strokes of the flash, by a single stroke through a series of current surges superposed on an intense continuing current, or by both. Our observations imply that sprites elongated in one direction are sometimes linked to in-cloud leader structure with the same elongation, and sprites that were more symmetric were produced above the progression of multiple negative leaders. This suggests that the large-scale structure of sprites could be affected by the in-cloud geometry of positive charge removal. Based on an expanded dataset of 39 sprite-parent flashes by including more sprites recorded by one single camera over the same MCS, the altitude (above mean sea level, MSL) of positively charged cloud region tapped by sprite-producing strokes declined gradually from~10 km MSL (À35 C) to around 6 km MSL (À10 C) as the MCS evolved through the mature stage. On average, the positive charge removal by causative strokes of sprites observed on 29 June is centered at 3.6 km above the freezing level or at 7.9 km above ground level.

[1] Sprites are structured high altitude optical emissions produced by lightning-driven electric fields. Both strong positive and negative cloud to ground flashes (CGs) are capable of initiating sprites. However, reported sprites are almost exclusively produced by +CGs. The very limited number of negative polarity sprites makes it difficult to reveal their morphologies and mechanisms. Since 2008, we have operated low light cameras at 5 locations in the United States to detect lightning-driven transient luminous events (TLEs). At Duke University, two pairs of magnetic sensors simultaneously record lightning-radiated magnetic fields. During 4 years of observations, the low light cameras collectively captured 1651 sprite events. Among them, 6 were produced by ÀCG lightning, which was confirmed by both the National Lightning Detection Network (NLDN) and magnetic field measurements. All of these negative sprites show similar features in their morphology, lightning source current, and lightning-driven ambient electric fields. They all initiate within a few ms from their parent lightning discharges and always are accompanied by sprite halos. Compared to positive sprites, the downward streamers in negative sprites terminate at higher altitudes, about 55-60 km. The extracted source current of their parent lightning discharges is very impulsive and produces at least 450 C km charge moment change in 0.5 ms or less. Unlike most +CG strokes, essentially no continuing current follows these ÀCGs. Thus the uniformity of negative sprite morphology appears to reflect the uniformity of the characteristics of high charge transfer negative strokes. Numerical simulation shows these impulsive source currents produce very high (>2 E k , where E k is the local air breakdown field) but short-lived electric fields at halo altitudes between 70 km and 90 km. At streamer termination altitudes, the inferred background electric field is 0.2-0.3 E k , which is close to but below the critical field (0.4 E k ) for negative streamer propagation. The simulations also show that the timescale of the lightning source current has a significant impact on the high altitude electric fields and thus the sprite initiation and morphology. With the same amount of charge transfer, a more impulsive current source produces a higher electric field of shorter duration at halo and sprite altitudes. The short timescales may explain why a larger threshold of total charge moment change is required to initiate negative sprites than short-delayed positive sprites, whose parent lightning source current is usually less impulsive.Citation: Li, J., S. Cummer, G. Lu, and L. Zigoneanu (2012), Charge moment change and lightning-driven electric fields associated with negative sprites and halos,