Statistical Gaussian Model of Image Regions in Stochastic Watershed Segmentation

International audienceStochastic watershed is an image segmentation technique based on mathematical morphology which produces a probability density function of image contours. Estimated probabilities depend mainly on local distances between pixels. This paper introduces a variant of stochastic watershed where the probabilities of contours are computed from a Gaussian model of image regions. In this framework, the basic ingredient is the distance between pairs of regions, hence a distance between normal distributions. Hence several alternatives of statistical distances for normal distributions are compared, namely Bhattacharyya distance, Hellinger metric distance and Wasserstein metric distance

Signature of nonlinear damping in geometric structure of a nonequilibrium process

We investigate the effect of nonlinear interaction on the geometric structure of a nonequilibrium process. Specifically, by considering a driven-dissipative system where a stochastic variable x is damped either linearly (∝x) or nonlinearly (∝x3) while driven by a white noise, we compute the time-dependent probability density functions (PDFs) during the relaxation towards equilibrium from an initial nonequilibrium state. From these PDFs, we quantify the information change by the information length L, which is the total number of statistically distinguishable states which the system passes through from the initial state to the final state. By exploiting different initial PDFs and the strength D of the white-noise forcing, we show that for a linear system, L increases essentially linearly with an initial mean value y0 of x as L ∝ y0, demonstrating the preservation of a linear geometry. In comparison, in the case of a cubic damping, L has a power-law scaling as L ∝ ym 0 , with the exponent m depending on D and the width of the initial PDF. The rate at which information changes also exhibits a robust power-law scaling with time for the cubic damping

Magnetization plateaus in weakly coupled dimer spin system

I study a spin system consisting of strongly coupled dimers which are in turn weakly coupled in a plane by zigzag interactions. The model can be viewed as the strong-coupling limit of a two-dimensional zigzag chain structure typical, e.g., for the $(ac)$-planes of KCuCl_3. It is shown that the magnetization curve in this model has plateaus at 1/3 and 2/3 of the saturation magnetization, and an additional plateau at 1/2 can appear in a certain range of the model parameters; the critical fields are calculated perturbatively. It is argued that for the three-dimensional lattice structure of the KCuCl_3 family the plateaus at 1/4 and 3/4 of the saturation can be favored in a similar way, which might be relevant to the recent experiments on NH_4CuCl_3 by Shiramura et al., J. Phys. Soc. Jpn. {\bf 67}, 1548 (1998).Comment: serious changes in Sect. II,III, final version to appear in PR

Fermi surface of PtCoO2 from quantum oscillations and electronic structure calculations

The authors would like to acknowledge the financial support from the Max-Planck Society. E.H. and M.N. acknowledge support from Deutsche Forschungsgemeinschaft (DFG) through the Project No. 107745057 (TRR80: From Electronic Correlations to Functionality). This work is also supported by JSPS KAKENHI (No. 18K04715). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreements No. DMR-1157490 and No. DMR-1644779 and the State of Florida.The delafossite series of layered oxides includes some of the highest conductivity metals ever discovered. Of these, PtCoO2, with a room-temperature resistivity of 1.8 μΩcm for in-plane transport, is the most conducting of all. The high conduction takes place in triangular lattice Pt layers, separated by layers of Co-O octahedra, and the electronic structure is determined by the interplay of the two types of layers. We present a detailed study of quantum oscillations in PtCoO2, at temperatures down to 35 mK and magnetic fields up to 30 T. As for PdCoO2 and PdRhO2, the Fermi surface consists of a single cylinder with mainly Pt character and an effective mass close to the free-electron value. Due to Fermi-surface warping, two close-lying high frequencies are observed. Additionally, a pronounced difference frequency appears. By analyzing the detailed angular dependence of the quantum-oscillation frequencies, we establish the warping parameters of the Fermi surface. We compare these results to the predictions of first-principles electronic-structure calculations including spin-orbit coupling on Pt and Co and on-site correlation U on Co, and hence demonstrate that electronic correlations in the Co-O layers play an important role in determining characteristic features of the electronic structure of PtCoO2.Publisher PDFPeer reviewe

Specific heat of an S=1/2 Heisenberg ladder compound Cu2_2(C5_5H12_{12}N2_2)2_2Cl4_4 under magnetic fields

Specific heat measurements down to 0.5 K have been performed on a single crystal sample of a spin-ladder like compound Cu$_{2}$(C$_{5}$H$_{12}$N$_{2}$)$_{2}$Cl$_{4}$ under magnetic fields up to 12 T. The temperature dependence of the observed data in a magnetic field below 6 T is well reproduced by numerical results calculated for the S=1/2 two-leg ladder with $J_{\rm{rung}}$/$J_{\rm{leg}}$=5. In the gapless region above 7 T ($H_{\rm{c1}}$), the agreement between experiment and calculation is good above about 2 K and a sharp and a round peak were observed below 2 K in a magnetic field around 10 T, but the numerical data show only a round peak, the magnitude of which is smaller than that of the observed one. The origin of the sharp peak and the difference between the experimental and numerical round peak are discussed.Comment: 14 pages, 11 figures, Submitted to PR

Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number

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Field- and pressure-induced magnetic quantum phase transitions in TlCuCl_3

Thallium copper chloride is a quantum spin liquid of S = 1/2 Cu^2+ dimers. Interdimer superexchange interactions give a three-dimensional magnon dispersion and a spin gap significantly smaller than the dimer coupling. This gap is closed by an applied hydrostatic pressure of approximately 2kbar or by a magnetic field of 5.6T, offering a unique opportunity to explore the both types of quantum phase transition and their associated critical phenomena. We use a bond-operator formulation to obtain a continuous description of all disordered and ordered phases, and thus of the transitions separating these. Both pressure- and field-induced transitions may be considered as the Bose-Einstein condensation of triplet magnon excitations, and the respective phases of staggered magnetic order as linear combinations of dimer singlet and triplet modes. We focus on the evolution with applied pressure and field of the magnetic excitations in each phase, and in particular on the gapless (Goldstone) modes in the ordered regimes which correspond to phase fluctuations of the ordered moment. The bond-operator description yields a good account of the magnetization curves and of magnon dispersion relations observed by inelastic neutron scattering under applied fields, and a variety of experimental predictions for pressure-dependent measurements.Comment: 20 pages, 17 figure