8,612 research outputs found
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
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
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
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