A k-space method for nonlinear wave propagation

A k-space method for nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme [Mast et al., IEEE Tran. Ultrason. Ferroelectr. Freq. Control 48, 341-354 (2001)]. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to the finite element method. It is found that, in order to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as small as 0.4. As a result, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient than the conventional finite element method or finite-difference time-domain method for the conditions studied here. However, although the present method is highly accurate for weakly inhomogeneous media, it is found to be less accurate for strongly inhomogeneous media. A possible remedy to this limitation is discussed

The study of B→J/Ψη(′)B\to J/\Psi \eta^{(\prime)} decays and determination of η−η′\eta-\eta^{\prime} mixing angle

We study $B\to J/\Psi \eta^{(\prime)}$ decays and suggest two methods to determine the $\eta-\eta^{\prime}$ mixing angle. We calculate not only the factorizable contribution in QCD facorization scheme but also the nonfactorizable hard spectator corrections in pQCD approach. We get the branching ratio of $B\to J/\Psi \eta$ which is consistent with recent experimental data and predict the branching ratio of $B\to J/\Psi \eta^{\prime}$ to be $7.59\times 10^{-6}$. Two methods for determining $\eta-\eta^{\prime}$ mixing angle are suggested in this paper. For the first method, we get the $\eta-\eta^{\prime}$ mixing angle to be about $-13.1^{\circ}$, which is in consistency with others in the literature. The second method depends on less parameters so can be used to determine the $\eta-\eta^{\prime}$ mixing angle with better accuracy but needs, as an input, the branching ratio for $B\to J/\Psi \eta^{\prime}$which should be measured in the near future.Comment: 16pages,4figure

Spatial optimization for land use allocation: accounting for sustainability concerns

Land-use allocation has long been an important area of research in regional science. Land-use patterns are fundamental to the functions of the biosphere, creating interactions that have substantial impacts on the environment. The spatial arrangement of land uses therefore has implications for activity and travel within a region. Balancing development, economic growth, social interaction, and the protection of the natural environment is at the heart of long-term sustainability. Since land-use patterns are spatially explicit in nature, planning and management necessarily must integrate geographical information system and spatial optimization in meaningful ways if efficiency goals and objectives are to be achieved. This article reviews spatial optimization approaches that have been relied upon to support land-use planning. Characteristics of sustainable land use, particularly compactness, contiguity, and compatibility, are discussed and how spatial optimization techniques have addressed these characteristics are detailed. In particular, objectives and constraints in spatial optimization approaches are examined

Nonlinear force-free field modeling of a solar active region using SDO/HMI and SOLIS/VSM data

We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces to dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compares to each other.Comment: 9 pages, 5 figure

Statistical study of free magnetic energy and flare productivity of solar active regions

Photospheric vector magnetograms from Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory are utilized as the boundary conditions to extrapolate both non-linear force-free and potential magnetic fields in solar corona. Based on the extrapolations, we are able to determine the free magnetic energy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We compare FME with ARs' flare index (FI) and find that there is a weak correlation ($<60\%$) between FME and FI. FME shows slightly improved flare predictability relative to total unsigned magnetic flux of ARs in the following two aspects: (1) the flare productivity predicted by FME is higher than that predicted by magnetic flux and (2) the correlation between FI and FME is higher than that between FI and magnetic flux. However, this improvement is not significant enough to make a substantial difference in time-accumulated FI, rather than individual flare, predictions.Comment: The paper was submitted to ApJ and it is accepted no

Synthesis of Gaussian Trees with Correlation Sign Ambiguity: An Information Theoretic Approach

In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we resort to information theoretical approaches to achieve two fundamental goals: First, we quantify the amount of information loss due to unrecoverable sign information. Second, we show the importance of such information in determining the maximum achievable rate region, in which the observed output vector can be synthesized, given its probability density function. In particular, we model the graphical model as a communication channel and propose a new layered encoding framework to synthesize observed data using upper layer Gaussian inputs and independent Bernoulli correlation sign inputs from each layer. We find the achievable rate region for the rate tuples of multi-layer latent Gaussian messages to synthesize the desired observables.Comment: 14 pages, 9 figures, part of this work is submitted to Allerton 2016 conference, UIUC, IL, US