Strange attractors in periodically-kicked degenerate Hopf bifurcations

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.Comment: 16 page

DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognition

Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by modelling the nonlinearity in the local descriptor set. Nevertheless, neither the descriptors nor the kernel matrix is deeply learned. Worse, they are considered separately, hindering the pursuit of an optimal SPD representation. This work proposes a deep network that jointly learns local descriptors, kernel-matrix-based SPD representation, and the classifier via an end-to-end training process. We derive the derivatives for the mapping from a local descriptor set to the SPD representation to carry out backpropagation. Also, we exploit the Daleckii-Krein formula in operator theory to give a concise and unified result on differentiating SPD matrix functions, including the matrix logarithm to handle the Riemannian geometry of kernel matrix. Experiments not only show the superiority of kernel-matrix-based SPD representation with deep local descriptors, but also verify the advantage of the proposed deep network in pursuing better SPD representations for fine-grained image recognition tasks

Noisy Monte Carlo revisited

We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. Our algorithm, simplified from that of L. Lin et al. hep-lat/9905033, avoids the computation of almost all non-leading terms. We illustrate its use by simulating SU(2) lattice gauge theory with a 5-loop action, and discuss further applications to full QCD.Comment: latex, 8 page

Noisy Monte Carlo Algorithm

We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by simulating SU(2) lattice gauge theory with a 5-loop improved action. A new approach for dynamical fermion simulations is proposed.Comment: Lattice 2000 (Algorithms), latex, espcrc2.sty, 4 page

Magnetic order in the pseudogap phase of high-TCT_C superconductors

One of the leading issues in high-$T_C$ superconductors is the origin of the pseudogap phase in underdoped cuprates. Using polarized elastic neutron diffraction, we identify a novel magnetic order in the YBa$_2$Cu$_3$O$_{6+x}$ system. The observed magnetic order preserves translational symmetry as proposed for orbital moments in the circulating current theory of the pseudogap state. To date, it is the first direct evidence of an hidden order parameter characterizing the pseudogap phase in high-$T_C$ cuprates.Comment: 3 figure

Electronic structure, magnetic and dielectric properties of the edge-sharing copper-oxide chain compound NaCu2_{2}O2_{2}

We report an experimental study of \nco, a Mott insulator containing chains of edge-sharing CuO$_4$ plaquettes, by polarized x-ray absorption spectroscopy (XAS), resonant magnetic x-ray scattering (RMXS), magnetic susceptibility, and pyroelectric current measurements. The XAS data show that the valence holes reside exclusively on the Cu$^{2+}$ sites within the copper-oxide spin chains and populate a $d$-orbital polarized within the CuO$_4$ plaquettes. The RMXS measurements confirm the presence of incommensurate magnetic order below a N\'eel temperature of $T_N = 11.5$ K, which was previously inferred from neutron powder diffraction and nuclear magnetic resonance data. In conjunction with the magnetic susceptibility and XAS data, they also demonstrate a new "orbital" selection rule for RMXS that is of general relevance for magnetic structure determinations by this technique. Dielectric property measurements reveal the absence of significant ferroelectric polarization below $T_N$, which is in striking contrast to corresponding observations on the isostructural compound \lco. The results are discussed in the context of current theories of multiferroicity.Comment: 7 pages, 7 figure

Nucleon Electromagnetic Form Factors from Lattice QCD using 2+1 Flavor Domain Wall Fermions on Fine Lattices and Chiral Perturbation Theory

We present a high-statistics calculation of nucleon electromagnetic form factors in $N_f=2+1$ lattice QCD using domain wall quarks on fine lattices, to attain a new level of precision in systematic and statistical errors. Our calculations use $32^3 \times 64$ lattices with lattice spacing a=0.084 fm for pion masses of 297, 355, and 403 MeV, and we perform an overdetermined analysis using on the order of 3600 to 7000 measurements to calculate nucleon electric and magnetic form factors up to $Q^2 \approx$ 1.05 GeV$^2$. Results are shown to be consistent with those obtained using valence domain wall quarks with improved staggered sea quarks, and using coarse domain wall lattices. We determine the isovector Dirac radius $r_1^v$, Pauli radius $r_2^v$ and anomalous magnetic moment $\kappa_v$. We also determine connected contributions to the corresponding isoscalar observables. We extrapolate these observables to the physical pion mass using two different formulations of two-flavor chiral effective field theory at one loop: the heavy baryon Small Scale Expansion (SSE) and covariant baryon chiral perturbation theory. The isovector results and the connected contributions to the isoscalar results are compared with experiment, and the need for calculations at smaller pion masses is discussed.Comment: 44 pages, 40 figure

Innovative sponge-based moving bed-osmotic membrane bioreactor hybrid system using a new class of draw solution for municipal wastewater treatment

© 2016 Elsevier Ltd. For the first time, an innovative concept of combining sponge-based moving bed (SMB) and an osmotic membrane bioreactor (OsMBR), known as the SMB-OsMBR hybrid system, were investigated using Triton X-114 surfactant coupled with MgCl2 salt as the draw solution. Compared to traditional activated sludge OsMBR, the SMB-OsMBR system was able to remove more nutrients due to the thick-biofilm layer on sponge carriers. Subsequently less membrane fouling was observed during the wastewater treatment process. A water flux of 11.38 L/(m2 h) and a negligible reverse salt flux were documented when deionized water served as the feed solution and a mixture of 1.5 M MgCl2 and 1.5 mM Triton X-114 was used as the draw solution. The SMB-OsMBR hybrid system indicated that a stable water flux of 10.5 L/(m2 h) and low salt accumulation were achieved in a 90-day operation. Moreover, the nutrient removal efficiency of the proposed system was close to 100%, confirming the effectiveness of simultaneous nitrification and denitrification in the biofilm layer on sponge carriers. The overall performance of the SMB-OsMBR hybrid system using MgCl2 coupled with Triton X-114 as the draw solution demonstrates its potential application in wastewater treatment

Simultaneous Observations of GRS 1758-258 in 1997 by VLA, IRAM, SEST, RXTE and OSSE: Spectroscopy and Timing

We report the results of our multi-wavelength observations of GRS 1758-258 made in August 1997. The energy bands include radio, millimeter, X-ray, and gamma-ray. The observations enable us to obtain a complete spectrum of the source over an energy range of 2 - 500 keV. The spectrum shows that GRS 1758-258 was in its hard state. It is well fitted by the Sunyaev-Titarchuk (ST) Compton scattering model. The spectrum is also fit by a power law with an exponential cutoff (PLE) plus a soft black-body component. The temperature of the soft component is about 1.2 keV, and the energy flux is less than 1.5% of the total X- and gamma-ray flux. The deduced hydrogen column density is in the range of (0.93 - 2.0) 10^{22} cm^{-2}. No significant iron lines are detected. The radio emission has a flat energy spectrum. The daily radio, X-ray and gamma-ray light curves show that GRS 1758-258 was stable during the observation period, but was highly variable on smaller time scales in X- and gamma-rays. The power density spectra are typical for the low-state, but we find the photon flux for the 5 to 10 keV band to be more variable than that in the other two energy bands (2 - 5 keV and 10 - 40 keV). Harmonically spaced quasi-periodic oscillations (QPOs) are observed in the power spectra. The phase lags between the hard photons and the soft photons have a flat distribution over a wide range of frequencies. A high coherence of about 1.0 (0.01 - 1 Hz) between the hard photons and the soft photons is also obtained in our observations. We compare these results with two variation models. Our millimeter observations did not reveal any conclusive signatures of an interaction between the jet from GRS 1758-258 and the molecular cloud that lies in the direction of GRS 1758-258.Comment: 32 pages, 13 figures, to appear in ApJ, 2000, V.533, no. 1, Apr. 10. For better figure resolution, please directly download the paper from http://spacsun.rice.edu/~lin/publication.htm