Lagrangian Based Methods for Coherent Structure Detection

There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic

Throughput analysis for cognitive radio networks with multiple primary users and imperfect spectrum sensing

In cognitive radio networks, the licensed frequency bands of the primary users (PUs) are available to the secondary user (SU) provided that they do not cause significant interference to the PUs. In this study, the authors analysed the normalised throughput of the SU with multiple PUs coexisting under any frequency division multiple access communication protocol. The authors consider a cognitive radio transmission where the frame structure consists of sensing and data transmission slots. In order to achieve the maximum normalised throughput of the SU and control the interference level to the legal PUs, the optimal frame length of the SU is found via simulation. In this context, a new analytical formula has been expressed for the achievable normalised throughput of SU with multiple PUs under prefect and imperfect spectrum sensing scenarios. Moreover, the impact of imperfect sensing, variable frame length of SU and the variable PU traffic loads, on the normalised throughput has been critically investigated. It has been shown that the analytical and simulation results are in perfect agreement. The authors analytical results are much useful to determine how to select the frame duration length subject to the parameters of cognitive radio network, such as network traffic load, achievable sensing accuracy and number of coexisting PUs

Phase glass and zero-temperature phase transition in a randomly frustrated two-dimensional quantum rotor model

The ground state of the quantum rotor model in two dimensions with random phase frustration is investigated. Extensive Monte Carlo simulations are performed on the corresponding (2+1)-dimensional classical model under the entropic sampling scheme. For weak quantum fluctuation, the system is found to be in a phase glass phase characterized by a finite compressibility and a finite value for the Edwards-Anderson order parameter, signifying long-ranged phase rigidity in both spatial and imaginary time directions. Scaling properties of the model near the transition to the gapped, Mott insulator state with vanishing compressibility are analyzed. At the quantum critical point, the dynamic exponent $z_{\rm dyn}\simeq 1.17$ is greater than one. Correlation length exponents in the spatial and imaginary time directions are given by $\nu\simeq 0.73$ and $\nu_z\simeq 0.85$, respectively, both assume values greater than 0.6723 of the pure case. We speculate that the phase glass phase is superconducting rather than metallic in the zero current limit.Comment: 14 pages, 4 figures, to appear in JSTA

Multi-Modes Phonon Softening in Two-Dimensional Electron-Lattice System

Phonon dispersion in a two-dimensional electron-lattice system described by a two-dimensional square-lattice version of Su-Schrieffer-Heeger's model and having the half-filled electronic band is studied theoretically at temperatures higher than the mean field critical temperature of the Peierls transition. When the temperature is lowered from the higher region down to the critical one, softening of multi phonon modes which have wave vectors equal to the nesting vector \vv{Q}=(\pi/a,\pi/a) with $a$ the lattice constant or parallel to \vv{Q} is observed. Although both of the transverse and longitudinal modes are softened at the critical temperature in the case of the wave vector equal to \vv{Q}, only the transverse modes are softened for other wave vectors parallel to \vv{Q}. This behavior is consistent with the Peierls distortions at lower temperatures.Comment: 10 pages, 5 Figure

Optical band edge shift of anatase cobalt-doped titanium dioxide

We report on the optical properties of magnetic cobalt-doped anatase phase titanium dioxide Ti_{1-x}Co_{x}O_{2-d} films for low doping concentrations, 0 <= x <= 0.02, in the spectral range 0.2 to 5 eV. For well oxygenated films (d << 1) the optical conductivity is characterized by an absence of optical absorption below an onset of interband transitions at 3.6 eV and a blue shift of the optical band edge with increasing Co concentration. The absence of below band gap absorption is inconsistent with theoretical models which contain midgap magnetic impurity bands and suggests that strong on-site Coulomb interactions shift the O-band to Co-level optical transitions to energies above the gap.Comment: 5 pages, 4 figures, 1 table; Version 2 - major content revisio

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

Antiferromagnetic Exchange Interaction between Electrons on Degenerate LUMOs in Benzene Dianion

We discuss the ground state of Benzene dianion (Bz$^{2-}$) on the basis of the numerical diagonalization method of an effective model of $\pi$ orbitals. It is found that the ground state can be the spin singlet state, and the exchange coupling between LUMOs can be antiferromagnetic.Comment: Accepted for publication in J. Phys. Soc. Jpn., 2 pages, 3 figure