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We combine data sets from the CGM2 and CASBaH surveys to model a transition point, R cross, between circumgalactic and intergalactic media (CGM and IGM, respectively). In total, our data consist of 7244 galaxies at z < 0.5 with precisely measured spectroscopic redshifts, all having impact parameters of 0.01–20 comoving Mpc from 28 QSO sightlines with high-resolution UV spectra that cover H i Ly α. Our best-fitting model is a two-component model that combines a 3D absorber–galaxy cross-correlation function with a simple Gaussian profile at inner radii to represent the CGM. By design, this model gives rise to a determination of R cross as a function of galaxy stellar mass, which can be interpreted as the boundary between the CGM and IGM. For galaxies with 108 ≤ M ⋆/ M ⊙ ≤ 1010.5, we find that R cross(M ⋆) ≈ 2.0 ± 0.6 R vir. Additionally, we find excellent agreement between R cross(M ⋆) and the theoretically determined splashback radius for galaxies in this mass range. Overall, our results favor models of galaxy evolution at z < 0.5 that distribute T ≈ 104K gas to distances beyond the virial radius. [ABSTRACT FROM AUTHOR]

We propose a p-adaptive quadrature-free discontinuous Galerkin method for the shallow water equations based on a computationally efficient adaptivity indicator which works without any problem-dependent parameters. The error and smoothness of the solution are detected using the information collected for slope limiting and, for piecewise constant discretizations, by carrying out a reconstruction procedure. The accuracy and robustness of the new scheme are evaluated using several benchmarks and compared to other adaptivity indicators. Our results indicate that the proposed indicator finds a good balance between solution quality and computational overhead. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method using an adaptive functional basis for reduced order models based on proper orthogonal decomposition (POD). The method is intended to be applied, in particular, to hydrocarbon reservoir simulations, where a range of varying boundary conditions must be explored. The proposed method allows updating the POD functional basis constructed for a specific problem setting to match varying boundary conditions, such as modified well locations and geometry, without the necessity to recalculate each time the entire set of basis functions. This adaptive technique leads to a significant reduction in the number of snapshots required to calculate the new basis, and hence reduces the computational cost of the simulations. The proposed method was applied to a two-dimensional immiscible displacement model; the simulations were performed using a high-resolution model, a classical POD reduced model, and a reduced model whose POD basis was adapted to varying well locations and geometry. Numerical simulations show that the proposed approach leads to a reduction of the required number of model snapshots by a few orders of magnitude compared to the classical POD scheme, without noticeable loss of accuracy of calculated fluid production rates. The adaptive POD scheme can therefore provide a significant gain in computational efficiency for problems where multiple or iterative simulations with varying boundary conditions are required, such as optimization of well design or production optimization. [ABSTRACT FROM AUTHOR]

In this work, we develop an improved shock-capturing and high-resolution Lagrangian–Eulerian method for hyperbolic systems and balance laws. This is a new method to deal with discontinuous flux and complicated source terms having concentrations for a wide range of applications science and engineering, namely, 1D shallow-water equations, sedimentation processes, Geophysical flows in 2D, N-Wave models, and Riccati-type problems with forcing terms. We also include numerical simulations of a 1D two-phase flow model in porous media, with gravity and a nontrivial singular δ -source term representing an injection point. Moreover, we present approximate solutions for 2D nonlinear systems (Compressible Euler Flows and Shallow-Water Equations) for distinct benchmark configurations available in the literature aiming to present convincing and robust numerical results. In addition, for the linear advection model in 1D and for a smooth solution of the nonlinear Burgers’ problem, second order approximations were obtained. We also present a high-resolution approximation of the nonlinear non-convex Buckley–Leverett problem. Based on the work of A. Harten, we derive a convergent Lagrangian–Eulerian scheme that is total variation diminishing and second-order accurate, away from local extrema and discontinuous data. Additionally, using a suitable Kružkov’s entropy definition, introduced by K. H. Karlsen and J. D. Towers, we can verify that our improved Lagrangian–Eulerian scheme converges to the unique entropy solution for conservation laws with a discontinuous space-time dependent flux. A key hallmark of our method is the dynamic tracking forward of the no-flow curves, which are locally conservative and preserve the natural setting of weak entropic solutions related to hyperbolic problems that are not reversible systems in general. In the end, we have a general procedure to construct a class of Lagrangian–Eulerian schemes to deal with hyperbolic problems with or without forcing terms. The proposed scheme is free of Riemann problem solutions and no adaptive space-time discretizations are needed. The numerical experiments verify the efficiency and accuracy of our new Lagrangian–Eulerian method. [ABSTRACT FROM AUTHOR]

The problem of vibrations generated in a homogeneous and isotropic elastic half-space by spatially concentrated forces, known in Seismology as (part of) the Lamb problem, is formulated here in terms of Helmholtz potentials of the elastic displacement. The method is based on time Fourier transforms, spatial Fourier transforms with respect to the coordinates parallel to the surface (in-plane Fourier transforms) and generalized wave equations, which include the surface values of the functions and their derivatives. This formulation provides a formal general solution to the problem of forced elastic vibrations in the homogeneous and isotropic half-space. Explicit results are given for forces derived from a gradient, localized at an inner point in the half-space, which correspond to a scalar seismic moment of the seismic sources. Similarly, explicit results are given for a surface force perpendicular to the surface and localized at a point on the surface. Both harmonic time dependence and time δ -pulses are considered (where δ stands for the Dirac delta function). It is shown that a δ -like time dependence of the forces generates transient perturbations which are vanishing in time, such that they cannot be viewed properly as vibrations. The particularities of the generation and the propagation of the seismic waves and the effects of the inclusion of the boundary conditions are discussed, as well as the role played by the eigenmodes of the homogeneous and isotropic elastic half-space. Similarly, the distinction is highlighted between the transient regime of wave propagation prior to the establishment of the elastic vibrations and the stationary-wave regime. [ABSTRACT FROM AUTHOR]

With the rapid development in Earth observation technology, a variety of satellite sensors have provided large and open sets of remote sensing data. However, traditional methods of analysis are no longer available for time-serial remote sensing data analysis that typically handles multidimensional spatio-temporal data models. Moreover, researchers have found it trivial and tedious to obtain ready-to-analyze data for Earth science models from regular Earth observation data. For an easy and efficient time-serial remote sensing data analysis, a spatial-featured data cube analysis tool based on multidimensional data model is proposed for time-serial remote sensing data processing and analysis. For the performance consideration, a distributed execution engine was also used for efficient implementation of large-scale tasks in parallel. Finally, through experiments on both normalized difference vegetation index product and water detection within a 20-year period, we confirmed that our approach is efficient and scalable for a long time-series analysis. [ABSTRACT FROM AUTHOR]

This work presents an enriched Galerkin (EG) discretization for the two-dimensional shallow-water equations. The EG finite element spaces are obtained by extending the approximation spaces of the classical finite elements by discontinuous functions supported on elements. The simplest EG space is constructed by enriching the piecewise linear continuous Galerkin space with discontinuous, element-wise constant functions. Similar to discontinuous Galerkin (DG) discretizations, the EG scheme is locally conservative, while, in multiple space dimensions, the EG space is significantly smaller than that of the DG method. This implies a lower number of degrees of freedom compared to the DG method. The EG discretization presented for the shallow-water equations is well-balanced, in the sense that it preserves lake-at-rest configurations. We evaluate the method’s robustness and accuracy using various analytical and realistic problems and compare the results to those obtained using the DG method. Finally, we briefly discuss implementation aspects of the EG method within our MATLAB / GNU Octave framework FESTUNG. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of the asymptotic stability of the three-dimensional viscous primitive equations for large-scale moist atmosphere in the pressure coordinate system. An asymptotic stability criterion for the solutions of such model with time-dependent forcing terms is obtained. In particular, under the assumptions that the associated forces are both time-periodic and small (in a suitable sense), we obtain the existence of the time-periodic solution for the primitive equations of large-scale moist atmosphere. Moreover, this time-periodic solution is asymptotically stable insense. [ABSTRACT FROM PUBLISHER]

Approximate solutions for Bayesian estimation in large scale models is a topic under investigation in many scientific communities. We define an iterative method based on the adaptive Gaussian mixture filter with batch updates as a robust alternative to adaptive importance sampling. We prove asymptotic optimality under certain conditions, contrary to other methods discussed where the sample distribution depends on the nonlinearity and scaling of the model. The finite sample implementation of the method is compared to an ensemble smoother with multiple data assimilation and an ensemble-based randomized maximum likelihood approach on a synthetic 1D reservoir model. [ABSTRACT FROM AUTHOR]

A new linear model for the sea breeze circulation that includes Coriolis effect, crucial for the tropical region, and a non-zero background wind speed is derived from the mesoscale equations. Earlier studies of Rotunno (J Atmos Sci 40(8):1999-2009, ) and Qian et al. (J Atmos Sci 66(6):1749, ) considered these effects separately. These two models can be obtained as special cases from the proposed model. The basic set of equations are first non-dimensionalised and the solutions to this new system are obtained using Fourier transform followed by a judicious application of the Sommerfeld radiation condition. Unlike in earlier studies on this topic, solution for the wind velocity along the coast line is also obtained and is shown to vanish in the absence of the Coriolis effect. These solutions are then changed to their respective dimensional form to obtain the solutions for the proposed model. Boundedness of these solutions are established theoretically, something not pursued so far in the literature of sea breeze equations. These solutions are then studied quantitatively as functions of three physical parameters, viz. latitude, coastal width and the background wind speed. [ABSTRACT FROM AUTHOR]

The ensemble technique has been widely used in numerical weather prediction and extended-range forecasting. Current approaches to evaluate the predictability using the ensemble technique can be divided into two major groups. One is dynamical, including generating Lyapunov vectors, bred vectors, and singular vectors, sampling the fastest error-growing directions of the phase space, and examining the dependence of prediction efficiency on ensemble size. The other is statistical, including distributional analysis and quantifying prediction utility by the Shannon entropy and the relative entropy. Currently, with simple models, one could choose as many ensembles as possible, with each ensemble containing a large number of members. When the forecast models become increasingly complicated, however, one would only be able to afford a small number of ensembles, each with limited number of members, thus sacrificing estimation accuracy of the forecast errors. To uncover connections between different information theoretic approaches and between dynamical and statistical approaches, we propose an ( ɛ, τ)-entropy and scale-dependent Lyapunov exponent—based general theoretical framework to quantify information loss in ensemble forecasting. More importantly, to tremendously expedite computations, reduce data storage, and improve forecasting accuracy, we propose a technique for constructing a large number of “pseudo” ensembles from one single solution or scalar dataset. This pseudo-ensemble technique appears to be applicable under rather general conditions, one important situation being that observational data are available but the exact dynamical model is unknown. [ABSTRACT FROM AUTHOR]

The recently developed short-time linear response algorithm, which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation, yields high precision of the response prediction. However, the computation of the short-time linear response formula with the full rank tangent map can be expensive. Here, a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed. The conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established, and two practical situations are examined, where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties. [ABSTRACT FROM AUTHOR]

Higher-order boundary element methods (BEM) for transient convective diffusion phenomena presented in Parts I and II of the paper are implemented numerically to examine their performance for a series of model problems. In order to highlight the importance of proper resolution in time and space for the transient problems, we consider both the one- and two-dimensional formulations in this paper. We utilize an implicit time-recurring formulation to advance in the time domain. The use of higher-order time interpolation functions facilitates extremely high resolution with respect to time step sizes, and thus necessitates similar levels of spatial resolution. In this paper, linear, quadratic and quartic boundary elements as well as bi-linear, bi-quadratic and bi-quartic volume cells are implemented to ensure a desired high level of accuracy both in time and in space.In order to investigate the performance of the BEM formulations, we introduce five problems of unsteady convection–diffusion that possess exact solutions. For all five numerical examples considered in this paper, the higher-order BEM demonstrate an extremely high level of accuracy even for predominantly convective flows. It is shown that the use of the convective kernels provide an analytical upwinding for any Peclet number and any mesh orientation with respect to the flow direction. The introduction of the kernel influence domains facilitates a very efficient and robust algorithm for integration over boundary elements and volume cells. Due to the nature of the convective kernels, the resulting global matrix is sparse with the non-zero elements localized around the main diagonal. The preconditioned bi-conjugate gradient method utilized in the paper allows very efficient factorization of the global sparse matrix. Moreover, the efficiency of the BEM formulations increases dramatically with the increase of the Peclet number of the flow. [Copyright &y& Elsevier]

In this paper we report on a differential absorption technique using a CO waveguide laser. The method is based on the measurement of the differential absorption between two different frequencies of the same selected CO laser line. The sensitivity of the technique depends strongly on the total pressure and has been estimated to be about a few tens of ppb or better over a 1 km path length in CH diluted with air to a total pressure of a few tens of torrs. Its relative simplicity and high sensitivity at low total pressure enable this technique to be applied to gas detection either at high altitude or to local monitoring of a low pressure sample. [ABSTRACT FROM AUTHOR]