| 000 | 02485cam a2200361Mi 4500 | ||
|---|---|---|---|
| 001 | on1296693065 | ||
| 003 | OCoLC | ||
| 005 | 20240726105305.0 | ||
| 008 | 220203p20212022xx o u00| u eng d | ||
| 040 |
_aUKKNU _beng _erda _cUKKNU _dOCLCO _dOCLCF _dUAB _dUKKNU _dOCLCQ _dNT |
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| 020 | _a3832553789 | ||
| 020 |
_a9783832553784 _q((electronic)l(electronic)ctronic) |
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| 050 | 0 | 4 |
_aQA41 _b.O584 2021 |
| 049 | _aMAIN | ||
| 100 | 1 |
_aSteinbach, Martin, _e1 |
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| 245 | 1 | 0 | _aOn the Stability of Objective Structures /Martin Steinbach. |
| 300 | _a1 online resource (174 pages). | ||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_adata file _2rda |
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| 490 | 1 |
_aAugsburger Schriften zur Mathematik, Physik und Informatik ; _vband 38 |
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| 504 | _a2 | ||
| 520 | 0 | _aThe main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative of the configurational energy (at the corresponding point) and the coerciveness of the second derivative of the configurational energy with respect to an appropriate semi-norm. Atomistic stability of a lattice is well understood, see, e.,g., 40.. The aim of this thesis is to generalize the theory to objective structures. In particular, we first investigate discrete subgroups of the Euclidean group, then define an appropriate seminorm and the atomistic stability for a given objective structure, and finally provide an efficient algorithm to check its atomistic stability. The algorithm particularly checks the validity of the Cauchy-Born rule for objective structures. To illustrate our results, we prove numerically the stability of a carbon nanotube by applying the algorithm. | |
| 530 |
_a2 _ub |
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| 650 | 0 | _aMathematics. | |
| 655 | 1 | _aElectronic Books. | |
| 758 |
_iIs found in: _aKnowledge Unlatched _1https://torl.biblioboard.com/module/2774bc74-146a-484f-a7ba-ab1d6a09bbfb |
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| 856 | 4 | 0 |
_uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=3541227&site=eds-live&custid=s3260518 _zClick to access digital title | log in using your CIU ID number and my.ciu.edu password |
| 942 |
_cOB _D _eEB _hQA. _m2021 _QOL _R _x _8NFIC _2LOC |
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| 994 |
_a92 _bNT |
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| 999 |
_c95391 _d95391 |
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| 902 |
_a1 _bCynthia Snell _c1 _dCynthia Snell |
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