An in-house FORTRAN code was developed to analyze the hybrid powders migration within a porous domain which was in appearance of Lorentz force. The permeable 2D enclosure was full of nanomaterial, ...and properties were selected via empirical formulas. Results indicate that positive impact on Nu
ave
can be obtained with rise of permeability which is related to greater temperature gradient. Also, similar impact exists for buoyancy force which shows the greater convective flow with rise of Ra. Reduction in temperature gradient with rise of Ha makes the convective flow to reduce.
We present an implementation of an interface between the full-potential linearized augmented plane wave package Wien2k and the wannier90 code for the construction of maximally localized Wannier ...functions. The FORTRAN code and a documentation is made available and results are discussed for SrVO
3, Sr
2IrO
4 (including spin–orbit coupling), LaFeAsO, and FeSb
2.
In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and ...partial differential equations (PDE), the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR), DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1) to demonstrate the potential of using R for dynamic modeling, (2) to highlight typical uses of the different methods implemented and (3) to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in the future; it is free software and distributed under the GNU General Public License, as part of the R software project.
SHTools: Tools for Working with Spherical Harmonics Wieczorek, Mark A.; Meschede, Matthias
Geochemistry, geophysics, geosystems,
August 2018, 2018-08-00, 20180801, 2018-08, 2018-08-01, Letnik:
19, Številka:
8
Journal Article
Recenzirano
Odprti dostop
Geophysical analyses are often performed in spherical geometry and require the use of spherical harmonic functions to express observables or physical quantities. When expanded to high degree, the ...accuracy and speed of the spherical harmonic transforms and reconstructions are of paramount importance. SHTools is a time and user‐tested open‐source archive of both Fortran 95 and Python routines for performing spherical harmonic analyses. The routines support all spherical‐harmonic normalization conventions used in the geosciences, including 4π‐normalized, Schmidt seminormalized, orthonormalized, and unnormalized harmonics, along with the option of employing the Condon‐Shortley phase factor of
(−1)m. Data on the sphere can be sampled on a variety of grid formats, including equally spaced cylindrical grids and grids appropriate for integration by Gauss‐Legendre quadrature. The spherical‐harmonic transforms are proven to be fast and accurate for spherical harmonic degrees up to 2800. Several tools are provided for the geoscientist, including routines for performing localized spectral analyses and basic operations related to global gravity and magnetic fields. In the Python environment, operations are very simple to perform as a result of three class structures that encompass all operations on grids, spherical harmonic coefficients, and spatiospectral localization windows. SHTools is released under the unrestrictive BSD 3‐clause license.
Key Points
SHTools is an archive of Fortran 95 and Python software for spherical harmonic analyses
The routines are fast, accurate, and support all normalization conventions used in the geosciences
SHTools is open source, versioned by git, and is released with an unrestrictive license
Harald Siebert studierte Philosophie in Augsburg, München und an der Sorbonne. In Paris und Berlin promovierte er in Wissenschaftsgeschichte. Er wurde 2007 mit dem Nachwuchspreis der International ...Academy of the History of Science ausgezeichnet.
The stability of rock engineering is generally dominated by existing seepage, particularly the seepage evolution due to the rock masses damage. However, the current research generally overlooks the ...seepage-damage coupling when studying the hydraulic-mechanical coupling effect in rock masses. This study aims to propose a dual-medium model, including equivalent continuous and discrete fracture media to study the coupled seepage-damage effect in fractured rock masses. The dual-medium seepage model considers the substantial water storage of the fracture network and the high conductivity of major large-scale fractures. Also, the seepage evolution is constructed to be a function of stress, seepage pressure and length of crack propagation in the rock mass. To illustrate the new model's application, a case of high-pressure water injection in a coal seam has been investigated to reveal the damage evolution in the coal seam. The results indicate that during the initial stage of the water injection, the seepage pressure in the discrete fracture medium increases faster than that in the equivalent continuous medium. Moreover, the seepage pressure difference between the two media gradually decreases with the increase of the seepage time, eventually forming a stable seepage field in the coal seam. Notably, the high-pressure water injection in the coal seam significantly affects the distribution of the coal seam's stress field, resulting in the effective minimum principle stress changing from compression to tension states. Also, during coal seam water injection, the damage zone and major fracture apertures in the coal seam gradually increase with increasing injection time.
Languages and libraries based on Partitioned Global Address Space (PGAS) programming models are convenient for exploiting scalable parallelism on large applications across different domains with ...irregular memory access patterns. OpenSHMEM is a PGAS-based library interface specification. As a result of using legacy non-standard Fortran features, support for Fortran language bindings is deprecated in OpenSHMEM specification version 1.4. In this work, we propose a new OpenSHMEM interface using the Fortran-C interoperability bind(C) feature introduced in Fortran 2003 language standard. This new interface is implemented over the existing C-language bindings in the OpenSHMEM specification. Through this work, we intend to showcase the expressiveness of the new proposed interface, along with its productivity and performance benefits that can be extracted in applications with irregular memory access patterns.
Realistic 3D finite strain analysis and crack propagation with tetrahedral meshes require mesh refinement/division. In this work, we use edges to drive the division process. Mesh refinement and mesh ...cutting are edge-based. This approach circumvents the variable mapping procedure adopted with classical mesh adaptation algorithms. The present algorithm makes use of specific problem data (either level sets, damage variables or edge deformation) to perform the division. It is shown that global node numbers can be used to avoid the Schönhardt prisms. We therefore introduce a nodal numbering that maximizes the trapezoid quality created by each mid-edge node. As a by-product, the requirement of determination of the crack path using a crack path criterion is not required. To assess the robustness and accuracy of this algorithm, we propose 4 benchmarks. In the knee-lever example, crack slanting occurs as part of the solution. The corresponding Fortran 2003 source code is provided.
•Unique tetrahedral partition by edges without Steiner points.•Node pre-ordering to optimize mesh quality.•Screened-Poisson equation to regularize the constitutive problem.•3D fracture without explicit crack path criterion.•Prediction of slanting in plane stress.
In the second article of the series, we present the Gibbs2 code, a Fortran90 reimplementation of the original Gibbs program Comput. Phys. Commun. 158 (2004) 57 for the calculation of ...pressure–temperature dependent thermodynamic properties of solids under the quasiharmonic approximation. We have taken advantage of the detailed analysis carried out in the first paper to implement robust fitting techniques. In addition, new models to introduce temperature effects have been incorporated, from the simple Debye model contained in the original article to a full quasiharmonic model that requires the phonon density of states at each calculated volume. Other interesting novel features include the empirical energy corrections, that rectify systematic errors in the calculation of equilibrium volumes caused by the choice of the exchange-correlation functional, the electronic contributions to the free energy and the automatic computation of phase diagrams. Full documentation in the form of a userʼs guide and a complete set of tests and sample data are provided along with the source code.
Program title:Gibbs2
Catalogue identifier: AEJI_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJI_v1_0.html
Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland
Licensing provisions: GNU General Public License, v3
No. of lines in distributed program, including test data, etc.: 936 087
No. of bytes in distributed program, including test data, etc.: 8 596 671
Distribution format: tar.gz
Programming language: Fortran90
Computer: Any running Unix/Linux
Operating system: Unix, GNU/Linux
Classification: 7.8
External routines: Part of the minpack, pppack and slatec libraries (downloaded from www.netlib.org) are distributed along with the program.
Nature of problem: Given the static E(V) curve, and possibly vibrational information such as the phonon density of states, calculate the equilibrium volume and thermodynamic properties of a solid at arbitrary temperatures and pressures in the framework of the quasiharmonic approximation.
Additional comments: A detailed analysis concerning the fitting of equations of state has been carried out in the first part of this article, and implemented in the code presented here.
Running time: The tests provided only take a few seconds to run.
► Calculation of thermodynamic properties from first principles data. ► Robust fitting of energy versus volume curves using averages of strain polynomials. ► Models for introducing ab initio temperature effects under the quasiharmonic approximation. ► A Fortran90 program implementing the techniques: Gibbs2.
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