Understanding and mapping water resources by multidimensional statistics and fuzzy logic: Missouri River basin case

Time series from 46 gauging station with drainage areas from 113 to 398 sq mi in the Upper Missouri River basin with mutual period of observation from 1963 to 1991 were used for analysis. Factor analysis of average annual flow revealed five patterns of river runoff within four distinct subregions of the territory (east, two carbonate karsts areas, uplands). This factor model reflected 62% variance of initial matrix. Each of four groups of watersheds obtained as a factor was presented by one gauging station with time series of annual and monthly discharges (I- 06218500, II- 06478690, III- 06412500, and IV- 06323000). Streams represented by patterns I, II and IV have increase of values and those represented by III have a decrease. The positive trend for pattern II is statistically significant. For four typical flow records, monthly average values were obtained from three to four seasons composed of different ensembles of months. The trends for seasonal components were analyzed for four typical watersheds and a significant increase was obtained for fall-winter season for type IV. Stream runoff is the most appropriate regional indicator for hydroclimatological processes. With multidimensional statistics this process can be considered as spatiotemporal structure of different scale of landscape properties and dynamics. Uncertainties of process originating stream runoff based on dynamic of regional meteorological system and diversity of local landscapes. Boundaries for domains with different annul and seasonal regimes of stream runoff were defined with factor loadings and fuzzy logic rules. With case of Missouri River basin presented that more complete decryption of real events in nature requires use probability and fuzzy logic together

Spontaneous symmetry breaking of fundamental states, vortices, and dipoles in two- and one-dimensional linearly coupled traps with cubic self-attraction

We introduce two- and one-dimensional (2D and 1D) systems of two linearly-coupled Gross-Pitaevskii equations (GPEs) with the cubic self-attraction and harmonic-oscillator (HO) trapping potential in each GPE. The system models a Bose-Einstein condensate with a negative scattering length, loaded in a double-pancake trap, combined with the in-plane HO potential. In addition to that, the 1D version applies to the light transmission in a dual-core waveguide with the Kerr nonlinearity and in-core confinement represented by the HO potential. The subject of the analysis is spontaneous symmetry breaking in 2D and 1D ground-state (GS, alias fundamental) modes, as well as in 2D vortices and 1D dipole modes (the latter ones do not exist without the HO potential). By means of the variational approximation and numerical analysis, it is found that both the 2D and 1D systems give rise to a symmetry-breaking bifurcation (SBB) of the supercrtical type. Stability of symmetric states and asymmetric ones, produced by the SBB, is analyzed through the computation of eigenvalues for perturbation modes, and verified by direct simulations. The asymmetric GSs are always stable, while the stability region for vortices shrinks and eventually disappears with the increase of the linear-coupling constant, $\kappa$. The SBB in the 2D system does not occur if $\kappa$ is too large (at $\kappa >\kappa_{\max }$); in that case, the two-component system behaves, essentially, as its single-component counterpart. In the 1D system, both asymmetric and symmetric dipole modes feature an additional oscillatory instability, unrelated to the symmetry breaking. This instability occurs in several regions, which expand with the increase of $\kappa$.Comment: 22 pages, 19 figures, Phys. Rev. A, in pres