Natural discretizations for the divergence, gradient, and curl on logically rectangular grids

AbstractThis is the first in series of papers creating a discrete analog of vector analysis on logically rectangular, nonorthogonal, nonsmooth grids. We introduce notations for 2-D logically rectangular grids, describe both cell-valued and nodal discretizations for scalar functions, and construct the natural discretizations of vector fields, using the vector components normal and tangential to the cell boundaries. We then define natural discrete analogs of the divergence, gradient, and curl operators based on coordinate invariant definitions and interpret these formulas in terms of curvilinear coordinates, such as length of elements of coordinate lines, areas of elements of coordinate surfaces, and elementary volumes.We introduce the discrete volume integral of scalar functions, the discrete surface integral, and a discrete analog of the line integral and prove discrete versions of the main theorems relating these objects. These theorems include the following: the discrete analog of relationship div A→ = 0 if and only if A→ = curl B→; curl A→ = 0 if and only if A→ = grad ϕ; if A→ = grad ϕ, then the line integral does not depend on path; and if the line integral of a vector function is equal to zero for any closed path, then this vector is the gradient of a scalar function.Last, we define the discrete operators DIV, GRAD, and CURL in terms of primitive differencing operators (based on forward and backward differences) and primitive metric operators (related to multiplications of discrete functions by length of edges, areas of surfaces, and volumes of 3-D cells). These formulations elucidate the structure of the discrete operators and are useful when investigating the relationships between operators and their adjoints

Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation

There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices

The convergence of mimetic discretization for rough grids

AbstractWe prove that the mimetic finite-difference discretizations of Laplace's equation converges on rough logically-rectangular grids with convex cells. Mimetic discretizations for the invariant operators' divergence, gradient, and curl satisfy exact discrete analogs of many of the important theorems of vector calculus. The mimetic discretization of the Laplacian is given by the composition of the discrete divergence and gradient. We first construct a mimetic discretization on a single cell by geometrically constructing inner products for discrete scalar and vector fields, then constructing a finite-volume discrete divergence, and then constructing a discrete gradient that is consistent with the discrete divergence theorem. This construction is then extended to the global grid. We demonstrate the convergence for the two-dimensional Laplace equation with Dirichlet boundary conditions on grids with a lower bound on the angles in the cell corners and an upper bound on the cell aspect ratios. The best convergence rate to be expected is first order, which is what we prove. The techniques developed apply to far more general initial boundary-value problems

Numerical studies of the two- and three-dimensional gauge glass at low temperature

We present results from Monte Carlo simulations of the two- and three-dimensional gauge glass at low temperature using the parallel tempering Monte Carlo method. Our results in two dimensions strongly support the transition being at T_c=0. A finite-size scaling analysis, which works well only for the larger sizes and lower temperatures, gives the stiffness exponent theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01, compatible with recent results from domain wall renormalization group studies.Comment: 7 pages, 10 figures, submitted to PR

On the existence of a finite-temperature transition in the two-dimensional gauge glass

Results from Monte Carlo simulations of the two-dimensional gauge glass supporting a zero-temperature transition are presented. A finite-size scaling analysis of the correlation length shows that the system does not exhibit spin-glass order at finite temperatures. These results are compared to earlier claims of a finite-temperature transition.Comment: 4 pages, 2 figure

Biharmonic pattern selection

A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements $u$. The model is based on the biharmonic equation $\nabla^{4}u =0$ in two-dimensional isotropic defect-free media as follows from the Kuramoto-Sivashinsky equation for pattern formation -or, alternatively, from the theory of elasticity. As a difference with Laplacian and Poisson growth models, in the new model the Laplacian of $u$ is neither zero nor proportional to $u$. Its discretization allows to reproduce a transition from dense to multibranched growth at a point in which the growth velocity exhibits a minimum similarly to what occurs within Poisson growth in planar geometry. Furthermore, in circular geometry the transition point is estimated for the simplest case from the relation $r_{\ell}\approx L/e^{1/2}$ such that the trajectories become stable at the growing surfaces in a continuous limit. Hence, within the biharmonic growth model, this transition depends only on the system size $L$ and occurs approximately at a distance $60 \%$ far from a central seed particle. The influence of biharmonic patterns on the growth probability for each lattice site is also analysed.Comment: To appear in Phys. Rev. E. Copies upon request to [email protected]

Chandra Smells a RRAT: X-ray Detection of a Rotating Radio Transient

"Rotating RAdio Transients" (RRATs) are a newly discovered astronomical phenomenon, characterised by occasional brief radio bursts, with average intervals between bursts ranging from minutes to hours. The burst spacings allow identification of periodicities, which fall in the range 0.4 to 7 seconds. The RRATs thus seem to be rotating neutron stars, albeit with properties very different from the rest of the population. We here present the serendipitous detection with the Chandra X-ray Observatory of a bright point-like X-ray source coincident with one of the RRATs. We discuss the temporal and spectral properties of this X-ray emission, consider counterparts in other wavebands, and interpret these results in the context of possible explanations for the RRAT population.Comment: 5 pages, 2 b/w figures, 1 color figure. To appear in the proceedings of "Isolated Neutron Stars", Astrophysics & Space Science, in pres

Frustrated two-dimensional Josephson junction array near incommensurability

To study the properties of frustrated two-dimensional Josephson junction arrays near incommensurability, we examine the current-voltage characteristics of a square proximity-coupled Josephson junction array at a sequence of frustrations f=3/8, 8/21, 0.382 $(\approx (3-\sqrt{5})/2)$, 2/5, and 5/12. Detailed scaling analyses of the current-voltage characteristics reveal approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The approximately universal scaling behaviors and high superconducting transition temperatures indicate that both the nature of the superconducting transition and the vortex configuration near the transition at the high-order rational frustrations f=3/8, 8/21, and 0.382 are similar to those at the nearby simple frustration f=2/5. This finding suggests that the behaviors of Josephson junction arrays in the wide range of frustrations might be understood from those of a few simple rational frustrations.Comment: RevTex4, 4 pages, 4 eps figures, to appear in Phys. Rev.

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Crop Ontology: Vocabulary For Crop-related Concepts

Abstract. A recurrent issue for data integration is the lack of a common and structured vocabulary used by different parties to describe their data sets. The Crop Ontology (www.cropontology.org) project aims to provide a central place where the crop community can gather to generate such standardized vocabularies and structure them into ontologies. Having standardized ontologies opens the world of the Semantic Web to data integration between different data providers. Crop Ontology is a community-based project, providing a central place for the creation of crop-related ontologies, but it can also be integrated into third-party tools through its Application Programming Interface, providing retrieval of specific terms or a more generic search functionality for all terms. The ontologies are available in RDF format, described using the OWL and RDFS standards, allowing them to be consumed by popular semantic reasoners. We believe that Crop Ontology will lead to better description of crop-related data, improving collaboration between partners and should serve as an example for other scientific fields