Tail asymptotics of the Brownian signature

The signature of a path \gamma is a sequence whose n-th term is the order-n iterated integrals of \gamma. It arises from solving multidimensional linear differential equations driven by \gamma. We are interested in relating the path properties of \gamma with its signature. If \gamma is C1, then an elegant formula of Hambly and Lyons relates the length of \gamma to the tail asymptotics of the signature. We show an analogous formula for the multidimensional Brownian motion,with the quadratic variation playing a similar role to the length. In the proof, we study the hyperbolic development of Brownian motion and also obtain a new subadditive estimate for the asymptotic of signature, which may be of independent interest. As a corollary, we strengthen the existing uniqueness results for the signatures of Brownian motion

Compact Circularly Polarized Patch Antenna Using a Composite Right/Left-Handed Transmission Line Unit-Cell

A compact circularly polarized (CP) patch antenna using a composite right/left-handed (CRLH) transmission line (TL) unit-cell is proposed. The CRLH TL unit-cell includes a complementary split ring resonator (CSRR) for shunt inductance and a gap loaded with a circular-shaped slot for series capacitance. The CSRR can decrease the TM10 mode resonance frequency, thus reducing the electrical size of the proposed antenna. In addition, the asymmetry of the CSRR brings about the TM01 mode, which can be combined with the TM10 mode by changing the slot radius. The combination of these two orthogonal modes with 90° phase shift makes the proposed antenna provide a CP property. The experimental results show that the proposed antenna has a wider axial ratio bandwidth and a smaller electrical size than the reported CP antennas. Moreover, the proposed antenna is designed without impedance transformer, 90° phase shift, dual feed and ground via

High-pressure behavior of dense hydrogen up to 3.5 TPa from density functional theory calculations

Structural behavior and equation of state of atomic and molecular crystal phases of dense hydrogen at pressures up to 3.5 TPa are systematically investigated with density functional theory. The results indicate that the Vinet EOS model that fitted to low-pressure experimental data overestimates the compressibility of dense hydrogen drastically when beyond 500 GPa. Metastable multi-atomic molecular phases with weak covalent bonds are observed. When compressed beyond about 2.8 TPa, these exotic low-coordinated phases become competitive with the groundstate and other high-symmetry atomic phases. Using nudged elastic band method, the transition path and the associated energy barrier between these high-pressure phases are evaluated. In particular for the case of dissociation of diatomic molecular phase into the atomic metallic Cs-IV phase, the existent barrier might raise the transition pressure about 200 GPa at low temperatures. Plenty of flat and broad basins on the energy surface of dense hydrogen have been discovered, which should take a major responsibility for the highly anharmonic zero point vibrations of the lattice, as well as the quantum structure fluctuations in some extreme cases. At zero pressure, our analysis demonstrates that all of these atomic phases of dense hydrogen known so far are unquenchable. NOTE: In the previous version of this paper (1010.3392v1) we made a mistake when evaluating the enthalpy of Cs-IV phase, which misled us to a conclusion that taking the multi-atomic molecular phases as the ground-state. After corrected this error, however, the atomic phase of Cs-IV becomes the static structure with the lowest enthalpy. Current version not only includes a substantial improvement of the previous one, but also contains many NEW interesting topics that were not touched before.Comment: 33 pages, 15 figures, published at J. Appl. Phys. 111, 063510 (2012

Anomalies in non-stoichiometric uranium dioxide induced by pseudo-phase transition of point defects

A uniform distribution of point defects in an otherwise perfect crystallographic structure usually describes a unique pseudo phase of that state of a non-stoichiometric material. With off-stoichiometric uranium dioxide as a prototype, we show that analogous to a conventional phase transition, these pseudo phases also will transform from one state into another via changing the predominant defect species when external conditions of pressure, temperature, or chemical composition are varied. This exotic transition is numerically observed along shock Hugoniots and isothermal compression curves in UO2 with first-principles calculations. At low temperatures, it leads to anomalies (or quasi-discontinuities) in thermodynamic properties and electronic structures. In particular, the anomaly is pronounced in both shock temperature and the specific heat at constant pressure. With increasing of the temperature, however, it transforms gradually to a smooth cross-over, and becomes less discernible. The underlying physical mechanism and characteristics of this type of transition are encoded in the Gibbs free energy, and are elucidated clearly by analyzing the correlation with the variation of defect populations as a function of pressure and temperature. The opportunities and challenges for a possible experimental observation of this phase change are also discussed.Comment: 11 pages, 5 figure

Mgb2 Nonlinear Properties Investigated under Localized High RF Magnetic Field Excitation

In order to increase the accelerating gradient of Superconducting Radio Frequency (SRF) cavities, Magnesium Diboride (MgB2) opens up hope because of its high transition temperature and potential for low surface resistance in the high RF field regime. However, due to the presence of the small superconducting gap in the {\pi} band, the nonlinear response of MgB2 is potentially quite large compared to a single gap s-wave superconductor (SC) such as Nb. Understanding the mechanisms of nonlinearity coming from the two-band structure of MgB2, as well as extrinsic sources, is an urgent requirement. A localized and strong RF magnetic field, created by a magnetic write head, is integrated into our nonlinear-Meissner-effect scanning microwave microscope [1]. MgB2 films with thickness 50 nm, fabricated by a hybrid physical-chemical vapor deposition technique on dielectric substrates, are measured at a fixed location and show a strongly temperature-dependent third harmonic response. We propose that at least two mechanisms are responsible for this nonlinear response, one of which involves vortex nucleation and penetration into the film. [1] T. M. Tai, X. X. Xi, C. G. Zhuang, D. I. Mircea, S. M. Anlage, "Nonlinear Near-Field Microwave Microscope for RF Defect Localization in Superconductors", IEEE Trans. Appl. Supercond. 21, 2615 (2011).Comment: 6 pages, 6 figure

Signature of a spin-up magnetar from multi-band afterglow rebrightening of GRB 100814A

In recent years, more and more gamma-ray bursts with late rebrightenings in multi-band afterglows unveil the late-time activities of the central engines. GRB 100814A is a special one among the well-sampled events, with complex temporal and spectral evolution. The single power-law shallow decay index of the optical light curve observed by GROND between 640 s and 10 ks is $\alpha_{\rm opt} = 0.57 \pm 0.02$, which apparently conflicts with the simple external shock model expectation. Especially, there is a remarkable rebrightening in the optical to near infrared bands at late time, challenging the external shock model with synchrotron emission coming from the interaction of the blast wave with the surrounding interstellar medium. In this paper, we invoke a magnetar with spin evolution to explain the complex multi-band afterglow emission of GRB 100814A. The initial shallow decay phase in optical bands and the plateau in X-ray can be explained as due to energy injection from a spin-down magnetar. At late time, with the falling of materials from the fall-back disk onto the central object of the burster, angular momentum of the accreted materials is transferred to the magnetar, which leads to a spin-up process. As a result, the magnetic dipole radiation luminosity will increase, resulting in the significant rebrightening of the optical afterglow. It is shown that the observed multi-band afterglow emission can be well reproduced by the model.Comment: 14 pages, 2 figures, accepted by The Astrophysical Journa

CP Violation in Fermion Pair Decays of Neutral Boson Particles

We study CP violation in fermion pair decays of neutral boson particles with spin 0 or 1. We study a new asymmetry to measure CP violation in $\eta, K_L \rightarrow \mu^+\mu^-$ decays and discuss the possibility of measuring it experimentally. For the spin-1 particles case, we study CP violation in the decays of $J/\psi$ to $SU(3)$ octet baryon pairs. We show that these decays can be used to put stringent constraints on the electric dipole moments of $\Lambda$, $\Sigma$ and $\Xi$.Comment: 14p, OZ-93/22, UM-93/89, OITS 51