Elastic Moduli and Vibrational Modes in Jammed Particulate Packings

When we elastically impose a homogeneous, affine deformation on amorphous solids, they also undergo an inhomogeneous, non-affine deformation, which can have a crucial impact on the overall elastic response. To correctly understand the elastic modulus $M$, it is therefore necessary to take into account not only the affine modulus $M_A$, but also the non-affine modulus $M_N$ that arises from the non-affine deformation. In the present work, we study the bulk ($M=K$) and shear ($M=G$) moduli in static jammed particulate packings over a range of packing fractions $\varphi$. One novelty of this work is to elucidate the contribution of each vibrational mode to the non-affine $M_N$ through a modal decomposition of the displacement and force fields. In the vicinity of the (un)jamming transition, $\varphi_{c}$, the vibrational density of states, $g(\omega)$, shows a plateau in the intermediate frequency regime above a characteristic frequency $\omega^\ast$. We illustrate that this unusual feature apparent in $g(\omega)$ is reflected in the behavior of $M_N$: As $\varphi \rightarrow \varphi_c$, where $\omega^\ast \rightarrow 0$, those modes for $\omega < \omega^\ast$ contribute less and less, while contributions from those for $\omega > \omega^\ast$ approach a constant value which results in $M_N$ to approach a critical value $M_{Nc}$, as $M_N-M_{Nc} \sim \omega^\ast$. At $\varphi_c$ itself, the bulk modulus attains a finite value $K_c=K_{Ac}-K_{Nc} > 0$, such that $K_{Nc}$ has a value that remains below $K_{Ac}$. In contrast, for the critical shear modulus $G_c$, $G_{Nc}$ and $G_{Ac}$ approach the same value so that the total value becomes exactly zero, $G_c = G_{Ac}-G_{Nc} =0$. We explore what features of the configurational and vibrational properties cause such the distinction between $K$ and $G$, allowing us to validate analytical expressions for their critical values.Comment: 23 pages, 13 figure

Three-Dimensional Relativistic Magnetohydrodynamic Simulations of Current-Driven Instability with A Sub-Alfvenic Jet: Temporal Properties

We have investigated the influence of a velocity shear surface on the linear and non-linear development of the CD kink instability of force-free helical magnetic equilibria in 3D. In this study we follow the temporal development within a periodic computational box and concentrate on flows that are sub-Alfvenic on the cylindrical jet's axis. Displacement of the initial force-free helical magnetic field leads to the growth of CD kink instability. We find that helically distorted density structure propagates along the jet with speed and flow structure dependent on the radius of the velocity shear surface relative to the characteristic radius of the helically twisted force-free magnetic field. At small velocity shear surface radius the plasma flows through the kink with minimal kink propagation speed. The kink propagation speed increases as the velocity shear radius increases and the kink becomes more embedded in the plasma flow. A decreasing magnetic pitch profile and faster flow enhance the influence of velocity shear. Simulations show continuous transverse growth in the nonlinear phase of the instability. The growth rate of the CD kink instability and the nonlinear behavior also depend on the velocity shear surface radius and flow speed, and the magnetic pitch radial profile. Larger velocity shear radius leads to slower linear growth, makes a later transition to the nonlinear stage, and with larger maximum amplitude than occur for a static plasma column. However, when the velocity shear radius is much greater than the characteristic radius of the helical magnetic field, linear and non-linear development can be similar to the development of a static plasma column.Comment: 38 pages, 18 figures, accepted for publication in Ap

Experimental demonstration of entanglement assisted coding using a two-mode squeezed vacuum state

We have experimentally realized the scheme initially proposed as quantum dense coding with continuous variables [Ban, J. Opt. B \textbf{1}, L9 (1999), and Braunstein and Kimble, \pra\textbf{61}, 042302 (2000)]. In our experiment, a pair of EPR (Einstein-Podolski-Rosen) beams is generated from two independent squeezed vacua. After adding two-quadrature signal to one of the EPR beams, two squeezed beams that contain the signal were recovered. Although our squeezing level is not sufficient to demonstrate the channel capacity gain over the Holevo limit of a single-mode channel without entanglement, our channel is superior to conventional channels such as coherent and squeezing channels. In addition, optical addition and subtraction processes demonstrated are elementary operations of universal quantum information processing on continuous variables.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

A statistical analysis of product prices in online markets

We empirically investigate fluctuations in product prices in online markets by using a tick-by-tick price data collected from a Japanese price comparison site, and find some similarities and differences between product and asset prices. The average price of a product across e-retailers behaves almost like a random walk, although the probability of price increase/decrease is higher conditional on the multiple events of price increase/decrease. This is quite similar to the property reported by previous studies about asset prices. However, we fail to find a long memory property in the volatility of product price changes. Also, we find that the price change distribution for product prices is close to an exponential distribution, rather than a power law distribution. These two findings are in a sharp contrast with the previous results regarding asset prices. We propose an interpretation that these differences may stem from the absence of speculative activities in product markets; namely, e-retailers seldom repeat buy and sell of a product, unlike traders in asset markets.Comment: 5 pages, 5 figures, 1 table, proceedings of APFA

Cut-off nonlinearities in the low-temperature vibrations of glasses and crystals

We present a computer simulation study of glassy and crystalline states using the standard Lennard-Jones interaction potential that is truncated at a finite cut-off distance, as is typical of many computer simulations. We demonstrate that the discontinuity at the cut-off distance in the first derivative of the potential (corresponding to the interparticle force) leads to the appearance of cut-off nonlinearities. These cut-off nonlinearities persist into the very-low-temperature regime thereby affecting low-temperature thermal vibrations, which leads to a breakdown of the harmonic approximation for many eigen modes, particularly for low-frequency vibrational modes. Furthermore, while expansion nonlinearities which are due to higher order terms in the Taylor expansion of the interaction potential are usually ignored at low temperatures and show up as the temperature increases, cut-off nonlinearities can become most significant at the lowest temperatures. Anharmonic effects readily show up in the elastic moduli which not only depend on the eigen frequencies, but are crucially sensitive to the eigen vectors of the normal modes. Whereas, those observables that rely mainly on static structural information or just the eigen frequencies, such as the vibrational density of states, total potential energy, and specific heat, show negligible dependence on the presence of the cut-off. Similar aspects of nonlinear behavior have recently been reported in model granular materials, where the constituent particles interact through finite-range, purely-repulsive potentials. These nonlinearities have been ascribed to the nature of the sudden cut-off at contact in the force-law, thus we demonstrate that cut-off nonlinearities emerge as a general feature of ordered and disordered solid state systems interacting through truncated potentials.Comment: 20 pages, 16 figures, 2 table

Anatomy of helical relativistic jets: The case of S5 0836+710

Helical structures are common in extragalactic jets. They are usually attributed in the literature to periodical phenomena in the source (e.g., precession). In this work, we use VLBI data of the radio-jet in the quasar S5 0836+710 and hypothesize that the ridge-line of helical jets like this corresponds to a pressure maximum in the jet and assume that the helically twisted pressure maximum is the result of a helical wave pattern. For our study, we use observations of the jet in S5 0836+710 at different frequencies and epochs. The results show that the structures observed are physical and not generated artificially by the observing arrays. Our hypothesis that the observed intensity ridge-line can correspond to a helically twisted pressure maximum is confirmed by our observational tests. This interpretation allows us to explain jet misalignment between parsec and kiloparsec scales when the viewing angle is small, and also brings us to the conclusion that high-frequency observations may show only a small region of the jet flow concentrated around the maximum pressure ridge-line observed at low frequencies. Our work provides a potential explanation for the apparent transversal superluminal speeds observed in several extragalactic jets by means of transversal shift of an apparent core position with time.Comment: Accepted for publication in the Astrophysical Journa

UVES spectra of young brown dwarfs in Cha I: radial and rotational velocities

Based on high-resolution UVES spectra we found that the radial velocity (RV) dispersion of nine of twelve known young bona fide and candidate brown dwarfs in the Cha I dark cloud is 2.0 km/s, i.e. significantly smaller than the RV dispersion of T Tauri stars in Cha I (3.6 km/s) and only slightly larger than the dispersion of the surrounding molecular gas (1.2 km/s) (Mizuno et al. 1999). This result indicates that the majority of these brown dwarfs are not ejected with high velocity out of a dense region as proposed by some formation scenarios for brown dwarfs. The mean RV values are consistent with the objects being kinematic members of Cha I. The RV dispersion of the T Tauri stars confined to the Cha I region is based on a compilation of T Tauri stars with known RVs from the literature plus three T Tauri stars observed with UVES and unpublished RVs for nine T Tauri stars. Time-resolved spectroscopy revealed RV variations for five out of nine of the bona fide and candidate brown dwarfs in Cha I, which could be due to orbiting planets or surface features. Furthermore we derived rotational velocities vsin(i) and the Lithium 6708 \AA equivalent width.Comment: A&A Letter, in pres

New Insights into the Charge-Transfer-to-Solvent Spectrum of Aqueous Iodide: Surface versus Bulk.

Liquid phase charge-transfer-to-solvent (CTTS) transitions are important, as they serve as photochemical routes to solvated electrons. In this work, broadband deep-ultraviolet electronic sum frequency generation (DUV-ESFG) and two-photon absorption (2PA) spectroscopic techniques were used to assign and compare the nature of the aqueous iodide CTTS excitations at the air/water interface and in bulk solution. In the one-photon absorption (1PA) spectrum, excitation to the 6s Rydberg-like orbital (5p → 6s) gives rise to a pair of spin-orbit split iodine states, 2P3/2 and 2P1/2. In the 2PA spectra, the lower-energy 2P3/2 peak is absent and the observed 2PA peak, which is ∼0.14 eV blue-shifted relative to the upper 2P1/2 CTTS peak seen in 1PA, arises from 5p → 6p electronic promotion. The band observed in the ESFG spectrum is attributed to mixing of excited states involving 5p → 6p and 5p → 6s promotions caused by both vibronic coupling and the external electric field generated by asymmetric interfacial solvation