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The phase of complex number is: 3.89793 Converting from polar to rectangular form and vice versa Conversion to polar is done using polar, which returns a pair(r,ph) denoting the modulus r and phase angle ph. Modulus can be displayed using abs and phase using phase. Check the fixed point 0, 0 The real part of the first eigenvalue is -1.0 The real part of the second eigenvalue is 2.0 The fixed point in 0, 0 is unstable - Check.
Computational thermodynamics is the use of computers to simulate thermodynamic problems specific to materials science, particularly used in the construction of phase diagrams.[1] Several open and commercial programs exist to perform these operations. The concept of the technique is minimization of Gibbs free energy of the system; the success of this method is due not only to properly measuring thermodynamic properties, such as those in the list of thermodynamic properties, but also due to the extrapolation of the properties of metastable allotropes of the chemical elements.
History[edit]
The computational modeling of metal-based phase diagrams, which dates back to the beginning of the previous century mainly by Johannes van Laar and to the modeling of regular solutions, has evolved in more recent years to the CALPHAD (CALculation of PHAse Diagrams).[2] This has been pioneered by American metallurgist Larry Kaufman since the 1970s.[3][4][5]
Current state[edit]
Computational thermodynamics may be considered a part of materials informatics and is a cornerstone of the concepts behind the materials genome project. While crystallographic databases are used mainly as a reference source, thermodynamic databases represent one of the earliest examples of informatics, as these databases were integrated into thermochemical computations to map phase stability in binary and ternary alloys.[6] Many concepts and software used in computational thermodynamics are credited to the SGTE Group, a consortium devoted to the development of thermodynamic databases; the open elements database is freely available[7] based on the paper by Dinsdale.[8] This so-called 'unary' system proves to be a common basis for the development of binary and multiple systems and is used by both commercial and open software in this field.
However, as stated in recent[when?] CALPHAD papers and meetings, such a Dinsdale/SGTE database will likely need to be corrected over time despite the utility in keeping a common base. In this case, most published assessments will likely have to be revised, similarly to rebuilding a house due to a severely broken foundation. This concept has also been depicted as an 'inverted pyramid.'[9] Merely extending the current approach (limited to temperatures above room temperature) is a complex task.[10] PyCalpahd, a Python library, was designed to facilitate simple computational thermodynamics calculation using open source code.[11] In complex systems, computational methods such as CALPHAD are employed to model thermodynamic properties for each phase and simulate multicomponent phase behavior.[12] The application of CALPHAD to high pressures in some important applications, which are not restricted to one side of materials science like the Fe-C system,[13] confirms experimental results by using computational thermodynamic calculations of phase relations in the Fe–C system at high pressures. Other scientists even considered viscosity and other physical parameters, which are beyond the domain of thermodynamics.[14]
Future developments[edit]
There is still a gap between ab initio methods[15] and operative computational thermodynamics databases. In the past, a simplified approach introduced by the early works of Larry Kaufman, based on Miedema's Model, was employed to check the correctness of even the simplest binary systems. However, relating the two communities to Solid State Physics and Materials Science remains a challenge,[16] as it has been for many years.[17] Promising results from ab initio quantum mechanics molecular simulation packages like VASP - Vienna Ab-initio Simulation Package are readily integrated in thermodynamic databases with approaches like Zentool.[18]A relatively easy way to collect data for intermetallic compounds is now possible by using Open Quantum Materials Database.
See also[edit]
References[edit]
- ^Liu, Zi-Kui; Wang, Yi (2016-06-30). Computational Thermodynamics of Materials. Cambridge University Press. ISBN9780521198967.
- ^Fabrichnaya, Olga; Saxena, Surendra K.; Richet, Pascal; Westrum, Edgar F. (2013-03-14). Thermodynamic Data, Models, and Phase Diagrams in Multicomponent Oxide Systems: An Assessment for Materials and Planetary Scientists Based on Calorimetric, Volumetric and Phase Equilibrium Data. Springer Science & Business Media. ISBN9783662105047.
- ^L Kaufman and H Bernstein, Computer Calculation of Phase Diagrams, Academic Press N Y (1970) ISBN0-12-402050-X[page needed]
- ^N Saunders and P Miodownik, Calphad, Pergamon Materials Series, Vol 1 Ed. R W Cahn (1998) ISBN0-08-042129-6[page needed]
- ^H L Lukas, S G Fries and B Sundman, Computational Thermodynamics, the Calphad Method, Cambridge University Press (2007) ISBN0-521-86811-4[page needed]
- ^K., Saxena, Surendra (1993). Thermodynamic Data on Oxides and Silicates : an Assessed Data Set Based on Thermochemistry and High Pressure Phase Equilibrium. Chatterjee, Nilanjan., Fei, Yingwei., Shen, Guoyin. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN9783642783326. OCLC840299125.
- ^http://www.crct.polymtl.ca/sgte/unary50.tdb[full citation needed]
- ^Dinsdale, A.T. (1991). 'SGTE data for pure elements'. Calphad. 15 (4): 317–425. doi:10.1016/0364-5916(91)90030-N.
- ^http://web.micress.de/ICMEg1/presentations_pdfs/Hallstedt.pdf[full citation needed]
- ^http://thermocalc.micress.de/proceedings/proceedings2015/tc2015_tumminello_public.pdf[full citation needed]
- ^Otis, Richard; Liu, Zi-Kui (2017). 'Pycalphad: CALPHAD-based Computational Thermodynamics in Python'. Journal of Open Research Software. 5. doi:10.5334/jors.140.
- ^L., Lukas, H. (2007). Computational thermodynamics : the CALPHAD method. Fries, Suzana G., Sundman, Bo. Cambridge: Cambridge University Press. ISBN978-0521868112. OCLC663969016.
- ^Fei, Yingwei; Brosh, Eli (2014). 'Experimental study and thermodynamic calculations of phase relations in the Fe–C system at high pressure'. Earth and Planetary Science Letters. 408: 155–62. Bibcode:2014E&PSL.408..155F. doi:10.1016/j.epsl.2014.09.044.
- ^Zhang, Fan; Du, Yong; Liu, Shuhong; Jie, Wanqi (2015). 'Modeling of the viscosity in the AL–Cu–Mg–Si system: Database construction'. Calphad. 49: 79–86. doi:10.1016/j.calphad.2015.04.001.
- ^P. Turchi AB INITIO AND CALPHAD THERMODYNAMICS OF MATERIALS https://e-reports-ext.llnl.gov/pdf/306920.pdf
- ^J. A. Alonso and N. H. March Electrons in Metals and Alloys http://www.sciencedirect.com/science/book/9780120536207[page needed]
- ^https://www.elsevier.com/books/proceedings-of-the-international-symposium-on-thermodynamics-of-alloys/miedema/978-1-4832-2782-5[full citation needed][page needed]
- ^http://zengen.cnrs.fr/manual.pdf[full citation needed]
External links[edit]
- Gaye, Henri; Lupis, C.H.P (1970). 'Computer calculations of multicomponent phase diagrams'. Scripta Metallurgica. 4 (9): 685–91. doi:10.1016/0036-9748(70)90207-3.
- Cool, Thomas; Bartol, Alexander; Kasenga, Matthew; Modi, Kunal; García, R. Edwin (2010). 'Gibbs: Phase equilibria and symbolic computation of thermodynamic properties'. Calphad. 34 (4): 393–404. doi:10.1016/j.calphad.2010.07.005.
- Miodownik, Peter (2012). 'Working with Larry Kaufman: Some thoughts on his 80th birthday'. Calphad. 36: iii–iv. doi:10.1016/j.calphad.2011.08.008.
- Kaufman, Larry; Ågren, John (2014). 'CALPHAD, first and second generation – Birth of the materials genome'. Scripta Materialia. 70: 3–6. doi:10.1016/j.scriptamat.2012.12.003.
- [The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies https://www.nature.com/articles/npjcompumats201510]
- [Open Quantum Mechanics http://oqmd.org]
University Courses on Computational Thermodynamics[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Computational_thermodynamics&oldid=877897702'
Codes for electromagnetic scattering by spheres - this article list codes for electromagnetic scattering by a homogeneous sphere, layered sphere, and cluster of spheres.
- 2Classification
Solution techniques[edit]
Majority of existing codes for calculation of electromagnetic scattering by a single sphere is based on Mie theory which is an analytical solution of Maxwell's equations in terms of infinite series. Other approximations to scattering by a single sphere include: Debye series, ray tracing (geometrical optics), ray tracing including the effects of interference between rays, Airy theory, Rayleigh scattering, diffraction approximation. There are many phenomena related to light scattering by spherical particles such as resonances, surface waves, plasmons, near-field scattering. Even though Mie theory offers convenient and fast way of solving light scattering problem by homogeneous spherical particles, there are other techniques, such as discrete dipole approximation, FDTD, T-matrix, which can also be used for such tasks.[1]
Classification[edit]
The compilation contains information about the electromagnetic scattering by spherical particles, relevant links, and applications.[2]
Codes for electromagnetic scattering by a single homogeneous sphere[edit]
Year | Name | Authors | References | Language | Short Description |
---|---|---|---|---|---|
1983 | BHMIE [3] | Craig F. Bohren and Donald R. Huffman | [1] | 'Mie solutions' (infinite series) to scattering, absorption and phase function of electromagnetic waves by a homogeneous sphere. | |
2002 | MiePlot [4] | Philip Laven | [5] | Visual Basic | MiePlot offers the following mathematical models for the scattering of light by a sphere: Mie solutions, Debye series, ray tracing (based on geometrical optics), ray tracing including the effects of interference between rays, Airy theory, Rayleigh scattering, diffraction, surface waves. In addition to single-wavelength calculations, MiePlot can also perform calculations for some wavelengths, thus approximating a continuous spectrum (such as sunlight) to produce simulations of atmospheric optical effects such as rainbows, coronas and glories. |
2003 | Mie_Single etc. | Gareth Thomas and Don Grainger | [6] | IDL | The Sub-Department of Atmospheric Oceanic and Planetary Physics in the University of Oxford maintains an archive of Mie scattering routines for both single spheres and populations of particles in which sizes follow a log-normal distribution. The code is also available for calculating the analytical derivatives of Mie scattering (i.e. the derivative of the extinction and scattering coefficients, and the intensity functions with respect to size parameter and complex refractive index). The routines are written in IDL, but a Fortran-based DLM version (which substantially reduces runtime) of the single-sphere code is also available. |
Codes for electromagnetic scattering by a layered sphere[edit]
Algorithmic literature includes several contributions[7][8][9][10]
Year | Name | Authors | Ref | Language | License | Short Description |
---|---|---|---|---|---|---|
1981 | DMILAY | Owen B. Toon and T. P. Ackerman | [9] | Fortran | No license specified but open source (public domain) | Scattering by a stratified sphere (a particle with a spherical core surrounded by a spherical shell). Code dates from 1968 available here:[11] |
1983 | BHCOAT | Craig F. Bohren and Donald R. Huffman | [1] | Fortran | No specified but open source (public domain via [1]) | 'Mie solutions' (infinite series) to scattering, absorption and phase function of electromagnetic waves by a homogeneous concentring shells. |
1997 | BART [12] | A. Quirantes | [13] | Fortran | Open source (own license) | Based on the Aden–Kerker theory to calculate light-scattering properties for coated spherical particles |
2004 | MjcLscCoatSph[14] | M. Jonasz | GUI/Windows | Proprietary / closed source | This program calculates the scattering, absorption, and attenuation parameters, as well as the angular scattering patterns of a single coated sphere according to Aden-Kerker theory. | |
2007 | L. Liu, H. Wang, B. Yu, Y. Xu, J. Shen | [15] | C | Unknown | Light scattering by a coated sphere (extinction efficiency, scattering efficiency, light scattering intensity) | |
2009-2016 | scattnlay[16] v2.0[17] | O. Pena, U. Pal, K. Ladutenko | [18] | C++ and Python | GPLv3 | Light scattering from a multilayered sphere based on the algorithm by W Yang.[19] Very robust and stable, slower than Toon and Ackerman. Evaluate integral parameters and angular patterns, near-field and power flow streamlines plotting. Has a compilation option to use Boost.Multiprecision for higher accuracy. |
Codes for electromagnetic scattering by cluster of spheres[edit]
Year | Name | Authors | References | Language | Short Description |
---|---|---|---|---|---|
1998-2003 | GMM | Yu-lin Xu and Bo A. S. Gustafson | [20] | Fortran | Codes which calculate exactly electromagnetic scattering by an aggregate of spheres in a single orientation or at an average over individual orientations. |
2013 | MSTM | D. W. Mackowski | [21] | Fortran | Codes which calculate exactly electromagnetic scattering by an aggregate of spheres and spheres within spheres for complex materials. Works in parallel as well. |
2015 | py_gmm | G. Pellegrini | [22] | Python + Fortran | A Python + Fortran 90 implementation of the Generalized Multiparticle Mie method, especially suited for plasmonics and near field computation. |
2017 | CELES | A. Egel, L. Pattelli and G. Mazzamuto | [23] | MATLAB + CUDA | Running on NVIDIA GPUs, with high performance for many spheres. |
Relevant scattering codes[edit]
External links[edit]
![Calculation Calculation](/uploads/1/2/5/8/125844325/824228461.jpg)
See also[edit]
References[edit]
- ^ abcdBohren, Craig F. and Donald R. Huffman, Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., ISBN0-471-29340-7, ISBN978-0-471-29340-8 (second edition)
- ^Wriedt, T. (2009). 'Light scattering theories and computer codes'. Journal of Quantitative Spectroscopy and Radiative Transfer. 110 (11): 833–843. Bibcode:2009JQSRT.110..833W. doi:10.1016/j.jqsrt.2009.02.023.
- ^This code is maintained as part of scatterlib, and can be downloaded from http://scatterlib.wikidot.com/mie
- ^The MiePlot program can be downloaded from http://www.philiplaven.com/mieplot.htm
- ^Philip Laven, 'Simulation of Rainbows, Coronas, and Glories by use of Mie Theory', Applied Optics Vol. 42, 3, 436-444 (January 2003) plus various other published papers (all available at http://www.philiplaven.com/Publications.html).
- ^Grainger, R.G.; Lucas, J.; Thomas, G.E.; Ewan, G. (2004). 'The Calculation of Mie Derivatives'. Appl. Opt. 43 (28): 5386–5393. Bibcode:2004ApOpt..43.5386G. doi:10.1364/AO.43.005386.
- ^Mackowski, D.W.; Altenkirch, R. A.; Menguc, M. P. (1990). 'Internal absorption cross sections in a stratified sphere'. Applied Optics. 29 (10): 1551–1559. Bibcode:1990ApOpt..29.1551M. doi:10.1364/ao.29.001551. PMID20563039.
- ^Yang, W (2003). 'Improved recursive algorithm for light scattering by a multilayered sphere'. Applied Optics. 42 (9): 1710–1720. Bibcode:2003ApOpt..42.1710Y. doi:10.1364/ao.42.001710.
- ^ abToon, O. B.; Ackerman, T. P. (1981). 'Algorithms for the calculation of scattering by stratified spheres'. Applied Optics. 20 (20): 3657–3660. Bibcode:1981ApOpt..20.3657T. doi:10.1364/ao.20.003657. PMID20372235.
- ^Liu, L.; Wang, H.; Yu, B.; Xua, Y.; Shen, J. (2007). 'Improved algorithm of light scattering by a coated sphere'. China Particuology. 5 (3): 230–236. doi:10.1016/j.cpart.2007.03.003.
- ^http://www.atmos.washington.edu/~ackerman/Mie_code/rtpmie.ackerman.dmiess.f
- ^/http://www.ugr.es/~aquiran/ciencia/codigos/bart.f
- ^A Quirantes and A V Delgado, The scattering of light by a suspension of coated sphericalparticles: effects of polydispersity on cross sections, J. Phys. D: Appl. Phys. 30 (1997) 2123–2131.
- ^'||'.
- ^Liu, L.; Wang, H.; Yu, B.; Xu, Y.; Shen, J. (2007). 'Improved algorithm of light scattering by a coated sphere'. China Particuology. 5 (3): 230–236. doi:10.1016/j.cpart.2007.03.003.
- ^http://cpc.cs.qub.ac.uk/cpc/cgi-bin/showversions.pl/?catid=AEEY&usertype=toolbar&deliverytype=view
- ^'Near- and far-field Mie scattering by a multilayered sphere: Ovidiopr/scattnlay'. 2019-02-15.
- ^O Pena and U Pal, Scattering of EM radiation by a multilayer sphere, Computer Physics Communications, 180, 2348-2354, 2009
- ^W Yang, Improved recursive algorithm for light scattering by a multilayered sphere, Applied Optics, Vol. 42, No. 9, 2003
- ^Yu-lin Xu , Bo A.S. Gustafson, A generalized multiparticle Mie-solution: further experimental verification, Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 395–419
- ^'Scatcodes'.
- ^'A Generalized Multiparticle Mie code, especially suited for plasmonics: Gevero/py_gmm'. 2019-02-11.
- ^'CELES: CUDA-accelerated electromagnetic scattering by large ensembles of spheres: Disordered-photonics/celes'. 2019-02-14.
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Codes_for_electromagnetic_scattering_by_spheres&oldid=935957657'
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