We investigate the electromagnetic response of asymmetric broadside coupled split ring resonators (ABC-SRRs) as a function of the relative in-plane displacement between the two component SRRs. The asymmetry is defined as the difference in the capacitive gap widths (\Delta g) between the two resonators comprising a coupled unit. We characterize the response of ABC-SRRs both numerically and experimentally via terahertz time-domain spectroscopy. As with symmetric BC-SRRs (\Delta g=0 \mu m), a large redshift in the LC resonance is observed with increasing displacement, resulting from changes in the capacitive and inductive coupling. However, for ABC-SRRs, in-plane shifting between the two resonators by more than 0.375Lo (Lo=SRR sidelength) results in a transition to a response with two resonant modes, associated with decoupling in the ABC-SRRs. For increasing \Delta g, the decoupling transition begins at the same relative shift (0.375Lo), though with an increase in the oscillator strength of the new mode. This strongly contrasts with symmetric BC-SRRs which present only one resonance for shifts up to 0.75Lo. Since all BC-SRRs are effectively asymmetric when placed on a substrate, an understanding of ABC-SRR behavior is essential for a complete understanding of BC-SRR based metamaterials.

George R. Keiser Andrew C. Strikwerda Kebin Fan Valerie Young Xin Zhang Richard D. Averitt

We explore air invasion in an initially water-filled dead-end compliant microchannel containing a constriction. The phenomenon is driven by the pervaporation of the liquid present in the channel through the surrounding medium. The penetration is intermittent, jerky, and characterised by a stop-and-go dynamics as the bubble escapes the constriction. We demonstrate that this sequence of arrest and jump of the bubble is due to an elastocapillary coupling between the air-liquid interface and the elastic medium. When the interface enters the constriction, its curvature strongly increases, leading to a depression within the liquid-filled channel which drives a compression of the channel. As the interface is forced to leave the constriction at a given threshold, due to the ongoing loss of liquid content by pervaporation, the pressure is suddenly released, which gives rise to a rapid propagation of the air bubbles away from the constriction and a restoration of the rest shape of the channel. Combining macroscopic observations and confocal imaging, we present a comprehensive experimental study of this phenomenon. In particular, the effect of the channel geometry on the time of arrest in the constriction and the jump length is investigated. Our novel microfluidic design succeeds in mimicking the role of inter-vessel pits in plants, which transiently stop the propagation of air embolism during long and severe droughts. It is expected to serve as a building block for further biomimetic studies in more complex leaf-like architectures, in order to recover this universal phenomena of intermittent propagation reported in real leaves.

Ludovic Keiser Philippe Marmottant Benjamin Dollet

Rosetta/OSIRIS took optical measurements of the intensity of scattered light from the coma of 67P/Churyumov-Gerasimenko over a wide range of phase angles. These data have been used to measure the phase angle dependent radiance profile of the dust coma. We want to provide information about the column area densities of the dust coma as seen from Rosetta. This information in combination with the measured OSIRIS phase function can then be used to determine the scattering phase function of the dust particles. We use a simple numerical model to calculate the dust density in the coma. For this we neglect all forces but solar gravitation and radiation pressure. As this cannot describe particles close to the surface of the comet, we assume starting conditions at a sufficient distance. We evaluate the column area density as observed from Rosetta/OSIRIS and compare the results for different spacecraft positions, dust sizes and surface activity distributions. We find the phase angle dependence of the column area density to be largely independent of particle size and spacecraft positions. The determining factor is the activity distribution across the surface, especially the activity on the night side. For models with no night side activity, we find the column area density at high phase angles to be roughly two orders of magnitude larger than at low phase angles. The radiance profile measured from inside a cometary coma results from the combined effects of a phase angle dependent column area density and the scattering phase function. The radiance profile is therefore strongly dependent on the surface activity distribution, and - unless the dust emission is isotropic - any attempt to infer particle properties (as expressed through the scattering phase function) from such data must take into account and de-bias for this spatial variation of the dust column area density.

Felix Keiser Johannes Markannen Jessica Agarwal

The geometrical and quantum mechanical basis for Davies' and Unruh's acceleration temperature is traced to a type of quantum mechanical (``achronal'') spin. Its existence and definition are based on pairs of causally disjoint accelerated frames. For bosons the expected spin vector of monochromatic particles is given by the ``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. Under spacetime translation the spin direction precesses around that ``Planckian'' vector. By exhibiting the conserved achronal spin four-current, we extend the identification of achronal spin from single quanta to multiparticle systems. Total achronal spin conservation is also shown to hold, even in the presence of quadratic interactions.

Ulrich H. Gerlach

Arguments are made in favor of broadening the scope of the various approaches to splitting spacetime into a single common framework in which measured quantities, derivative operations, and adapted coordinate systems are clearly understood in terms of associated test observer families. This ``relativity of splitting formalisms" for fully nonlinear gravitational theory has been tagged with the name "gravitoelectromagnetism" because of the well known analogy between its linearization and electromagnetism, and it allows relationships between the various approaches to be better understood and makes it easier to extrapolate familiarity with one approach to the others. This is important since particular problems or particular features of those problems in gravitational theory are better suited to different approaches, and the present barriers between the proponents of each individual approach sometimes prevent the best match from occurring.

Robert T. Jantzen Paolo Carini Donato Bini

The benefits of portfolio diversification is a central tenet implicit to modern financial theory and practice. Linked to diversification is the notion of breadth. Breadth is correctly thought of as the number of in- dependent bets available to an investor. Conventionally applications us- ing breadth frequently assume only the number of separate bets. There may be a large discrepancy between these two interpretations. We uti- lize a simple singular-value decomposition (SVD) and the Keiser-Gutman stopping criterion to select the integer-valued effective dimensionality of the correlation matrix of returns. In an emerging market such as South African we document an estimated breadth that is considerably lower than anticipated. This lack of diversification may be because of market concentration, exposure to the global commodity cycle and local currency volatility. We discuss some practical extensions to a more statistically correct interpretation of market breadth, and its theoretical implications for both global and domestic investors.

Daniel Polakow Tim Gebbie

The short-lived radioisotope $^{60}$Fe requires production in a core collapse supernova or AGB star immediately before its incorporation into the earliest solar system solids. Shock waves from a somewhat distant supernova, or a relatively nearby AGB star, have the right speeds to simultaneously trigger the collapse of a dense molecular cloud core and to inject shock wave material into the resulting protostar. A new set of FLASH2.5 adaptive mesh refinement hydrodynamical models shows that the injection efficiency depends sensitively on the assumed shock thickness and density. Supernova shock waves appear to be thin enough to inject the amount of shock wave material necessary to match the short-lived radioisotope abundances measured for primitive meteorites. Planetary nebula shock waves from AGB stars, however, appear to be too thick to achieve the required injection efficiencies. These models imply that a supernova pulled the trigger that led to the formation of our solar system.

Alan P. Boss Sandra A. Keiser

Gravity Probe B, launched 20 April 2004, is a space experiment testing two fundamental predictions of Einstein's theory of General Relativity (GR), the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection started 28 August 2004 and ended 14 August 2005. Analysis of the data from all four gyroscopes results in a geodetic drift rate of -6,601.8+/- 18.3 mas/yr and a frame-dragging drift rate of -37.2 +/- 7.2 mas/yr, to be compared with the GR predictions of -6,606.1 mas/yr and -39.2 mas/yr, respectively (`mas' is milliarc-second; 1mas = 4.848 x 10-9 rad).

C. W. F. Everitt D. B. DeBra B. W. Parkinson J. P. Turneaure J. W. Conklin M. I. Heifetz G. M. Keiser A. S. Silbergleit T. Holmes J. Kolodziejczak M. Al-Meshari J. C. Mester B. Muhlfelder V. Solomonik K. Stahl P. Worden W. Bencze S. Buchman B. Clarke A. Al-Jadaan H. Al-Jibreen J. Li J. A. Lipa J. M. Lockhart B. Al-Suwaidan M. Taber S. Wang

We investigated the low-frequency Raman spectra of freestanding few-layer graphene (FLG) at varying temperatures (400 - 900 K) controlled by laser heating. At high temperature, we observed the fundamental Raman mode for the lowest-frequency branch of rigid-plane layer-breathing mode (LBM) vibration. The mode frequency redshifts dramatically from 81 cm-1 for bilayer to 23 cm-1 for 8-layer. The thickness dependence is well described by a simple model of coupled oscillators. Notably, the LBM Raman response is unobservable at room temperature, and it is turned on at higher temperature (>600 K) with a steep increase of Raman intensity. The observation suggests that the LBM vibration is strongly suppressed by molecules adsorbed on the graphene surface, but is activated as desorption occurs at high temperature.

Chun Hung Lui Zhipeng Ye Courtney Keiser Xun Xiao Rui He

We observed distinct interlayer shear mode Raman spectra for trilayer graphene with ABA and ABC stacking order. There are two rigid-plane shear-mode phonon branches in trilayer graphene. We found that ABA trilayers exhibit pronounced Raman response from the high-frequency shear branch, without any noticeable response from the low-frequency branch. In contrast, ABC trilayers exhibit no response from the high-frequency shear branch, but significant Raman response from the low-frequency branch. Such complementary behaviors of Raman shear modes can be explained by the distinct symmetry of the two trilayer allotropes. The strong stacking-order dependence was not found in the layer-breathing modes, and thus represents a unique characteristic of the shear modes.

Chun Hung Lui Zhipeng Ye Courtney Keiser Eduardo B. Barros Rui He