On Robust Stability of Limit Cycles for Hybrid Systems with Multiple Jumps

In this paper, we address stability and robustness properties of hybrid limit cycles for a class of hybrid systems with multiple jumps in one period. The main results entail equivalent characterizations of stability of hybrid limit cycles for hybrid systems. The hybrid limit cycles may have multiple jumps in one period and the jumps are allowed to occur on sets. Conditions guaranteeing robustness of hybrid limit cycles are also presented

Statistical switching kinetics in ferroelectrics

By assuming a more realistic nucleation and polarization reversal scenario we build a new statistical switching model for ferroelectrics, which is different from either the Kolmogorov-Avrami-Ishibashi (KAI) model or the Nucleation-Limited-Switching (NLS) model. After incorporating a time-dependent depolarization field this model gives a good description about the retardation behavior in polycrystalline thin films at medium or low fields, which can not be described by the traditional KAI model. This model predicts correctly n=1 for polycrystalline thin films at high Eappl or ceramic bulks in the ideal case

Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure

Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

Distribution of Spectral Lags in Gamma Ray Bursts

Using the data acquired in the Time To Spill (TTS) mode for long gamma-ray bursts (GRBs) collected by the Burst and Transient Source Experiment on board the Compton Gamma Ray Observatory (BATSE/CGRO), we have carefully measured spectral lags in time between the low (25-55 keV) and high (110-320 keV) energy bands of individual pulses contained in 64 multi-peak GRBs. We find that the temporal lead by higher-energy gamma-ray photons (i.e., positive lags) is the norm in this selected sample set of long GRBs. While relatively few in number, some pulses of several long GRBs do show negative lags. This distribution of spectral lags in long GRBs is in contrast to that in short GRBs. This apparent difference poses challenges and constraints on the physical mechanism(s) of producing long and short GRBs. The relation between the pulse peak count rates and the spectral lags is also examined. Observationally, there seems to be no clear evidence for systematic spectral lag-luminosity connection for pulses within a given long GRB.Comment: 20 pages, 4 figure

Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a simple direct method which is thus utilized to find \em exact analytical \rm vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1)-dimensional EE can be obtained for \em arbitrary spectral parameter \rm from the general symmetry group theorem. \rm Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.Comment: 25 pages, 9 figure

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided

Global structures in a composite system of two scale-free discs with a coplanar magnetic field

We investigate a theoretical MHD disc problem involving a composite disc system of gravitationally coupled stellar and gaseous discs with a coplanar magnetic field in the presence of an axisymmetric dark matter halo. The two discs are expediently approximated as razor-thin, a ring-like magnetic field, and a power-law rotation curve in radius . By imposing the scale-free condition, we construct analytically stationary global MHD perturbation configurations for both aligned and logarithmic spiral patterns. MHD perturbation configurations in a composite system of partial discs in the presence of an axisymmetric dark matter halo are also considered. We derive analytically the stationary MHD dispersion relations for both aligned and unaligned perturbation structures and analyze the corresponding phase relationships between surface mass densities and the magnetic field. Compared with earlier results, we obtain three solution branches corresponding to super fast MHD density waves, fast MHD density waves and slow MHD density waves, respectively. By evaluating the unaligned $m=0$ case, we determine the marginal stability curves where the two unstable regimes corresponding to Jeans collapse instability and ring fragmentation instability are identified. We find that the aligned $m=0$ case is simply the limit of the unaligned $m=0$ case with the radial wavenumber $\xi\to0$. We further show that a composite system of partial discs behaves much differently from a composite system of full discs in certain aspects. Our formalism provides a useful theoretical framework in the study of stationary global perturbation configurations for MHD disc galaxies with bars, spirals and barred spirals.Comment: 35 pages, 24 figures, Accepted for publication in MNRA

Phase Separation of Bismuth Ferrite into Magnetite under Voltage Stressing

Micro-Raman studies show that under ~700 kV/cm of d.c. voltage stressing for a few seconds, thin-film bismuth ferrite BiFeO3 phase separates into magnetite Fe3O4. No evidence is found spectroscopically of hemite alpha-Fe2O3, maghemite gamma-Fe2O3, or of Bi2O3. This relates to the controversy regarding the magnitude of magnetization in BiFeO3.Comment: 9 pages and 2 figure