A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite:
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2005
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 107 S. Ill., graph. Darst. 30 cm |
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Record in the Search Index
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| adam_text | SUB GOTTINGEN 7 219 734 78X DISS 2006 B 1845 A QUALITATIVE AND
QUANTITATIVE MATHEMATICAL ANALYSIS OF CHALCOPYRITE DISEASE WITHIN
SPHALERITE DER FAKULTAT FIIR MATHEMATIK UND INFORMATIK DER UNIVERSITAT
LEIPZIG EINGEREICHTE HABILITATIONSSCHRIFT ZUR ERLANGUNG DES AKADEMISCHEN
GRADES DOCTOR RERUM NATURALIUM HABILITATUS DR. RER. NAT. HABIL.
VORGELEGT .. VON DR. THOMAS BLESGEN GEBOREN AM 15.12.1966 IN BONN DIE
ANNAHME DER HABILITATIONSSCHRIFT HABEN EMPFOHLEN: 1. PROF. DR. S.
LUCKHAUS (FAKULTAT FIIR MATHEMATIK U. INFORMATIK, UNIVERSITAT LEIPZIG)
2. PROF. DR. M. RUMPF (MATHEMATISCHES INSTITUT, UNIVERSITAT
DUISBURG-ESSEN) 3. PROF. DR. E. SALJE (DEPARTMENT OF EARTH-SCIENCES,
UNIVERSITY OF CAMBRIDGE(UK)) BESCHLUB IIBER DIE VERLEIHUNG DES
AKADEMISCHEN GRADES VOM 14.02.2005. /^H^.. CONTENTS 1 INTRODUCTION 1 2
DERIVATION OF THE MODEL 5 2.1 THE GENERAL MATHEMATICAL APPROACH 5 2.2 A
PURELY REACTIVE SYSTEM 8 2.3 THE MODEL FOR CHALCOPYRITE DISEASE 9 2.4
TWO FURTHER MODELS FOR SIMULATIONS RELYING ON DATA BASES OF THE FREE
ENERGY 14 2.5 DIMENSIONALITY ANALYSIS 16 2.6 FREE ENERGY INEQUALITY FOR
THE ISOTHERMAL SYSTEM 18 2.7 THE NON-ISOTHERMAL CASE 21 2.8 MORE GENERAL
FORMS OF THE SURFACE ENERGY 23 3 EXISTENCE AND UNIQUENESS RESULTS FOR
THE DERIVED MODELS 25 3.1 PRELIMINARIES 26 3.2 THE WEAK FORMULATION OF
THE PROBLEM 27 3.3 A SEMI-IMPLICIT TIME DISCRETISATION 28 3.4 STRUCTURAL
ASSUMPTIONS . ; 28 3.5 EXISTENCE OF SOLUTIONS TO THE TIME DISCRETE
SCHEME 29 3.6 UNIFORM ESTIMATES 32 3.7 GLOBAL EXISTENCE OF SOLUTIONS FOR
POLYNOMIAL FREE ENERGY 35 3.8 UNIQUENESS OF THE SOLUTION 36 3.9
LOGARITHMIC FREE ENERGY 39 3.10 UNIFORM ESTIMATES 42 3.11 HIGHER
INTEGRABILITY FOR THE LOGARITHMIC FREE ENERGY 43 3.12 GLOBAL EXISTENCE
OF SOLUTIONS FOR LOGARITHMIC FREE ENERGIES ... .. 45 3.13 THE LIMIT
EQUATIONS 47 3.14 PROOF OF EXISTENCE OF SOLUTIONS TO MODEL III 49 I 4
COMPUTATIONAL METHODS 53 4.1 GENERAL NUMERICAL SOLUTION TECHNIQUE 54 4.2
A TABLE LOOKUP PRINCIPLE FOR THE FREE ENERGY 56 4.3 THE HARMONIC FREE
ENERGY APPROXIMATION 57 4.4 FREE ENERGY COMPUTATION WITH GULP 60 4.5
MOLECULAR DYNAMICS COMPUTATIONS OF THE FREE ENERGY 68 4.6 QUANTUM
MECHANICAL COMPUTATIONS 69 5 NUMERICAL SIMULATIONS 79 5.1 VERIFICATION
OF THE ALGORITHMS 79 5.1.1 TWO SIMPLE ANALYTIC TESTS FOR MODEL I 79
5.1.2 ANALYSIS OF THE DIFFERENT PARTS OF THE ENTROPY 81 5.2 THE
DEPENDENCE OF GULP DATA ON ATOMISTIC LATTICE CONFIGURATIONS 82 5.3
NUMERICAL RESULTS FOR MODEL I 84 5.4 EXTENSION OF MODEL I TO LINEAR
ELASTICITY 86 5.5 FINITE ELEMENT COMPUTATIONS WITH THE TABULATED FREE
ENERGY . . . . 91 5.6 FREE ENERGY MINIMISATION FOR MODEL III 94 6
DISCUSSION OF THE RESULTS AND OUTLOOK 95 A NOTATIONS 99 B MATHEMATICAL
SYMBOLS 102 B.I FUNCTION SPACES 102 B.2 VECTOR- AND TENSOR NOTATIONS 103
REFERENCES 104
|
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| author | Blesgen, Thomas 1966- |
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| discipline | Physik |
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| indexdate | 2024-07-09T20:08:12Z |
| institution | BVB |
| language | English |
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| physical | IV, 107 S. Ill., graph. Darst. 30 cm |
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| spelling | Blesgen, Thomas 1966- Verfasser (DE-588)120003848 aut A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite vorgelegt von Thomas Blesgen 2005 IV, 107 S. Ill., graph. Darst. 30 cm txt rdacontent n rdamedia nc rdacarrier Leipzig, Univ., Habil.-Schr., 2005 Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Kupferkies (DE-588)4166125-4 gnd rswk-swf Zinkblende (DE-588)4190844-2 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kupferkies (DE-588)4166125-4 s Zinkblende (DE-588)4190844-2 s Phasenumwandlung (DE-588)4132140-6 s Mathematisches Modell (DE-588)4114528-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013202088&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blesgen, Thomas 1966- A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite Mathematisches Modell (DE-588)4114528-8 gnd Kupferkies (DE-588)4166125-4 gnd Zinkblende (DE-588)4190844-2 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4166125-4 (DE-588)4190844-2 (DE-588)4132140-6 (DE-588)4113937-9 |
| title | A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite |
| title_auth | A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite |
| title_exact_search | A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite |
| title_full | A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite vorgelegt von Thomas Blesgen |
| title_fullStr | A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite vorgelegt von Thomas Blesgen |
| title_full_unstemmed | A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite vorgelegt von Thomas Blesgen |
| title_short | A qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite |
| title_sort | a qualitative and quantitative mathematical analysis of chalcopyrite disease within sphalerite |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Kupferkies (DE-588)4166125-4 gnd Zinkblende (DE-588)4190844-2 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| topic_facet | Mathematisches Modell Kupferkies Zinkblende Phasenumwandlung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013202088&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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