Caustics, catastrophes and wave fields:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Edition: | 2. ed. |
| Series: | Springer series on wave phenomena
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 202 - 213. - Bildet Forts. zu: Kravcov, Jurij A.: Geometrical optics of inhomogeneous media |
| Physical Description: | XII, 216 S. Ill., graph. Darst. |
| ISBN: | 3540642277 |
Staff View
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| 245 | 1 | 0 | |a Caustics, catastrophes and wave fields |c Yu. A. Kravtsov ; Yu. I. Orlov |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XII, 216 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Catastrophes (Mathematics) | |
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Record in the Search Index
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| adam_text | CONTENTS 1 INTRODUCTION . 1 1.1 CAUSTIC FIELDS IN PHYSICAL PROBLEMS 1
1.2 THE GEOMETRICAL ASPECT OF THE CAUSTIC PROBLEM 4 1.3 THE WAVE ASPECT
OF THE CAUSTIC PROBLEM 5 2 RAYS AND CAUSTICS 8 2.1 EQUATIONS OF
GEOMETRICAL OPTICS 8 2.1.1 THE SCALAR PROBLEM 8 2.1.2 ELECTROMAGNETIC
WAVES IN AN ISOTROPIC MEDIUM 11 2.1.3 ELECTROMAGNETIC WAVES IN AN
ANISOTROPIC MEDIUM ... 12 2.2 THE ROLE OF RAYS IN THE METHOD OF
GEOMETRICAL OPTICS .... 13 2.2.1 THE LOCALITY PRINCIPLE . 13 2.2.2 RAYS
AS ENERGY AND PHASE TRAJECTORIES 13 2.2.3 FRESNEL VOLUME OF A RAY: THE
PHYSICAL CONTENT OF THE RAY CONCEPT 14 2.2.4 HEURISTIC CRITERIA OF
APPLICABILITY FOR RAY THEORY .... 16 2.2.5 DISTINGUISHABILITY OF RAYS 17
2.3 PHYSICAL CHARACTERISTICS OF CAUSTICS 17 2.3.1 CAUSTICS AS ENVELOPES
OF RAY FAMILIES 17 2.3.2 CAUSTIC PHASE SHIFT 18 2.3.3 CAUSTIC ZONE AND
CAUSTIC VOLUME . 19 2.3.4 RAY ESTIMATES OF FIELDS AT CAUSTICS AND IN
FOCAL SPOTS 23 2.3.5 INDISTINGUISHABILITY OF RAYS IN A CAUSTIC ZONE 24
2.3.6 REALITY OF CAUSTICS 25 2.3.7 A REMARK ON MULTIPATH PROPAGATION 26
2.4 COMPLEX RAYS 27 2.4.1 MAIN PROPERTIES OF COMPLEX RAYS 27 2.4.2
REFLECTION OF A PLANE WAVE FROM A LINEAR SLAB 29 2.4.3 NONLOCAL NATURE
OF COMPLEX RAYS 30 2.4.4 DOMAIN OF LOCALIZATION OF COMPLEX RAYS 32 3
CAUSTICS AS CATASTROPHES 34 3.1 MAPPINGS INDUCED BY RAYS 34 3.1.1 THE
RAY SURFACE AND LAGRANGE S MANIFOLD 34 3.1.2 CLASSIFICATION OF
STRUCTURALLY STABLE CAUSTICS 36 3.2 CLASSIFICATION OF TYPICAL CAUSTICS
39 3.2.1 GENERATING FUNCTION: CODIMENSION AND CORANK 39 3.2.2 CAUSTIC
SURFACES OF LOW CODIMENSION 40 3.2.3 CAUSTICS OF HIGH CODIMENSION 44
3.2.4 SUBORDINANCE RELATIONS 47 4 TYPICAL INTEGRALS OF CATASTROPHE
THEORY 48 4.1 STANDARD CAUSTIC INTEGRALS 48 4.1.1 USE OF GENERATING
FUNCTIONS AS PHASE FUNCTIONS .... 48 4.1.2 REDUCING INTEGRALS TO NORMAL
FORM 51 4.1.3 MULTIPLICITY OF STANDARD INTEGRALS 53 4.2 THE AIRY
INTEGRAL 54 4.2.1 BASIC PROPERTIES 54 4.2.2 THE AIRY DIFFERENTIAL
EQUATION 57 4.2.3 AN EXAMPLE OF AIRY-INTEGRAL SOLUTION TO THE WAVE
PROBLEM 57 4.2.4 THE AIRY INTEGRAL AS A STANDARD FUNCTION FOR THE
ONE-DIMENSIONAL WAVE EQUATION 58 4.2.5 APPLICABILITY CONDITIONS OF THE
UNIFORM AIRY ASYMPTOTIC IN ONE-DIMENSIONAL PROBLEMS 59 4.3. THE PEARCEY
INTEGRAL 60 4.3.1 PROPERTIES 60 4.3.2 FOCUSING IN THE PRESENCE OF
CYLINDRICAL ABERRATION ... 61 4.3.3 CAUSTIC INDICES AND FIELD STRUCTURE
63 4.4 OTHER TYPICAL INTEGRALS 64 4.4.1 GENERALIZED AIRY FUNCTIONS 64
4.4.2 FRESNEL CRITERIA FOR TRANSITION TO SUBASYMPTOTICS .... 66 4.4.3
FIELD STRUCTURE IN DIFFERENT AREAS OF THE EXTERNAL VARIABLE DOMAIN 67
4.4.4 INTEGRALS OF THE D M+1 SERIES 68 4.4.5 CAUSTICS WITH A LARGE
NUMBER OF RAYS 69 4.4.6 CALCULATION OF STANDARD INTEGRALS 71 5 UNIFORM
CAUSTIC ASYMPTOTICS DERIVED WITH STANDARD INTEGRALS .... 73 5.1 UNIFORM
AIRY ASYMPTOTIC OF A SCALAR FIELD 73 5.1.1 HEURISTIC FOUNDATION OF THE
METHOD OF STANDARD INTEGRALS 73 5.1.2 GUESSING AT A FORM OF SOLUTION 74
5.1.3 EQUATIONS FOR UNKNOWN FUNCTIONS 75 5.1.4 RELATION OF THE AIRY
ASYMPTOTIC TO THE RAY FIELDS ... 77 5.1.5 FIELD IN THE CAUSTIC SHADOW 79
5.1.6 LOCAL FIELD ASYMPTOTIC NEAR A CAUSTIC 80 5.1.7 INTERPOLATION
FORMULA FOR A CAUSTIC FIELD 85 5.1.8 ESTIMATING THE COEFFICIENT OF THE
AIRY FUNCTION DERIVATIVE 85 5.1.9 THE GEOMETRIC BACKBONE AND WAVE
FLESH 86 5.1.10 UNIFORM AIRY ASYMPTOTIC OF AN EM FIELD 87 5.1.11 LOCAL
ASYMPTOTIC OF AN EM FIELD 89 5.1.12 ONE-DIMENSIONAL PROBLEM 90 5.1.13
APPLICABILITY CONDITIONS FOR THE AIRY ASYMPTOTIC .... 91 5.2 UNIFORM
CAUSTIC ASYMPTOTICS BASED ON GENERAL STANDARD INTEGRALS 92 5.2.1
STRUCTURE OF A SOLUTION 92 5.2.2 EQUATIONS FOR PHASE AND AMPLITUDE
FUNCTIONS 93 5.2.3 RELATION TO GEOMETRICAL OPTICS 94 5.2.4 GENERAL
SCHEME TO COMPUTE CAUSTIC FIELDS 97 5.2.5 UNIFORM CAUSTIC ASYMPTOTIC OF
AN EM FIELD 98 5.2.6 THE RAY SKELETON AND UNIFORM CAUSTIC ASYMPTOTICS .
99 5.2.7 SOME SPECIFIC SITUATIONS 99 5.2.8 LOCAL ASYMPTOTICS 101 5.3
ILLUSTRATIVE EXAMPLES 103 5.3.1 THE CIRCULAR CAUSTIC 103 5.3.2 POINT
SOURCE IN A LINEAR SLAB 106 5.3.3 SWALLOWTAIL CAUSTICS IN A LINEAR LAYER
BORDERING UPON A HOMOGENEOUS HALFSPACE 108 5.3.4 BUTTERFLY IN A
PARABOLIC PLASMA LAYER ILL 5.3.5 ELLIPTIC UMBILIC FORMED BY AN ANTENNA
IN A PLASMA LAYER ILL 5.3.6 ELLIPTIC UMBILICS IN UNDERWATER ACOUSTICS
112 5.3.7 HOW FAR CAN WE ADVANCE IN CONSTRUCTING CAUSTIC ASYMPTOTICS?
113 5.3.8 DO SWALLOWTAILS EXIST IN TWO DIMENSIONS? 114 6 MASLOV S METHOD
OF THE CANONICAL OPERATOR 116 6.1 PRINCIPAL RELATIONSHIPS . 116 6.1.1
THE WAVE EQUATION IN THE COORDINATE-MOMENTUM REPRESENTATION 116 6.1.2
ASYMPTOTIC SOLUTION OF THE WAVE EQUATION 117 6.1.3 ELIMINATION OF FIELD
DIVERGENCE AT CAUSTICS 119 6.1.4 THE CANONICAL OPERATOR 120 6.1.5
REMARKS ON APPLICABILITY CONDITIONS 121 6.2 SPECIFIC PROBLEMS 122 6.2.1
PLANE WAVE IN A LINEAR LAYER 122 6.2.2 DIFFRACTION ON A PHASE SCREEN 124
6.2.3 ASYMPTOTIC SOLUTION OF THE PARABOLIC EQUATION 126 6.2.4
MISCELLANEOUS PROBLEMS 127 6.3. GENERALIZATION BY USING FRACTIONAL
TRANSFORMATIONS 128 6.3.1 FRACTIONAL FOURIER TRANSFORMATION 128 6.3.2
FRACTIONAL REPRESENTATION FOR TWO-DIMENSIONAL PROPAGATION 129 6.3.3
CONSTRUCTION OF THE OVERALL FIELD 131 6.3.4 ADVANTAGES OF THE
ALONSO-FORBES REPRESENTATION 134 METHOD OF INTERFERENCE INTEGRALS 135
7.1 RAY TYPE INTEGRALS 135 7.1.1 WIDE AND NARROW SENSE INTERPRETATIONS
135 7.1.2 EICONALS AND AMPLITUDES OF PARTIAL WAVES 136 7.1.3 VIRTUAL
RAYS 140 7.1.4 SPECIFIC PROBLEMS 141 7.2 CAUSTIC INTEGRALS 143 7.2.1
AIRY FUNCTION BASED INTEGRALS 143 7.2.2 USE OF MISCELLANEOUS SPECIAL
FUNCTIONS 144 7.2.3 SPECIFIC PROBLEMS 144 7.3 ADDITIONAL TOPICS AND
GENERALIZATIONS 146 7.3.1 COMPARISON WITH MASLOV S METHOD 146 7.3.2
IMPLEMENTATION OF INTERFERENCE-INTEGRAL ALGORITHMS . . . 146 7.3.3
APPLICABILITY LIMITS 147 7.3.4 SOME GENERALIZATIONS 147 PENUMBRA
CAUSTICS 148 8.1 BROKEN PENUMBRA CAUSTICS 148 8.1.1 BROKEN CAUSTICS IN
DIFFRACTION AT SCREENS 148 8.1.2 A UNIFORM ASYMPTOTIC 150 8.1.3
PARTICULAR CASES 151 8.1.4 A UNIFORM ASYMPTOTIC FOR AN EM FIELD 152
8.1.5 BROKEN CAUSTICS OF HIGHER DIMENSION 152 8.1.6 BROKEN CAUSTICS AT
DISCONTINUITIES OF PHASE-FRONT CURVATURE AND JUMPS OF REFRACTIVE INDEX
153 8.2 PENUMBRA CAUSTICS OF DIFFRACTION RAYS 154 8.2.1 GENERATION OF
CAUSTICS 154 8.2.2 ASYMPTOTIC SOLUTION 156 8.2.3 PROPERTIES OF THE
ASYMPTOTIC SOLUTION 156 8.2.4 SOME GENERALIZATIONS 157 8.3 PENUMBRA
CAUSTICS AND EDGE CATASTROPHES 157 8.3.1 SIMPLE EDGE CATASTROPHES 157
8.3.2 TYPICAL INTEGRALS OF EDGE CATASTROPHE THEORY 158 8.3.3. CORNER
CATASTROPHES 159 MODIFICATIONS AND GENERALIZATIONS OF STANDARD INTEGRALS
AND FUNCTIONS 160 9.1 NONPOLYNOMIAL PHASE STANDARD INTEGRALS 160 9.1.1
STANDARD INTEGRALS WITH ARBITRARY PHASE FUNCTIONS ... 160 9.1.2 UNIFORM
ASYMPTOTICS BASED ON STANDARD INTEGRALS WITH ARBITRARY PHASE FUNCTIONS
160 9.1.3 BESSEL FUNCTION BASED UNIFORM ASYMPTOTICS NEAR SIMPLE CAUSTICS
161 9.1.4 CONTOUR STANDARD INTEGRALS 163 9.2 STRUCTURALLY UNSTABLE
CAUSTICS 163 9.2.1 STRUCTURALLY STABLE AND UNSTABLE OBJECTS 163 9.2.2
UNIFORM ASYMPTOTICS FOR AXIALLY SYMMETRIC CAUSTICS . 164 9.2.3 A UNIFORM
ASYMPTOTIC FOR AN AXIAL CAUSTIC 166 9.2.4 APPLICABILITY OF AXIAL CAUSTIC
ASYMPTOTICS IN THE PRESENCE OF ABERRATIONS 167 9.3 STANDARD INTEGRALS
WITH AMPLITUDE CORRECTION 168 9.3.1 INTEGRALS OF WEIGHTED RAPIDLY
OSCILLATING FUNCTIONS . . 168 9.3.2 UNIFORM PENUMBRAL ASYMPTOTICS NEAR A
FUZZY LIGHT-SHADOW BOUNDARY 168 9.3.3 BROKEN CAUSTICS NEAR DIFFUSED
SHADOW 170 9.4 REFLECTION FROM A BARRIER AND OSCILLATIONS IN A POTENTIAL
WELL 171 9.4.1 WEBER EQUATION AND FUNCTIONS 171 9.4.2 ASYMPTOTIC
SOLUTION TO ONE-DIMENSIONAL REFLECTION FROM A BARRIER 172 9.4.3
PENETRATION OF A PLANE WAVE THROUGH A BARRIER 174 9.4.4 ASYMPTOTIC
REPRESENTATION OF THE FIELD FOR A BARRIER WITH VARIABLE PARAMETERS 176
9.4.5 WAVEGUIDING CAUSTICS 178 9.4.6 CAUSTICS CONFINING BOUNCING BALL
OSCILLATIONS 181 9.4.7 APPLICABILITY OF THE WEBER ASYMPTOTIC 182 9.5
STANDARD FUNCTIONS INDUCED BY ORDINARY DIFFERENTIAL EQUATIONS 184 9.5.1
USING SECOND-ORDER DIFFERENTIAL EQUATIONS AS STANDARDS 184 9.5.2 UNIFORM
ASYMPTOTICS OF 3-D WAVE PROBLEMS DEVELOPED WITH 1-D STANDARD FUNCTIONS
185 9.5.3 CAUSTICS FOR AN ELLIPSOID CAVITY 186 9.5.4 EXTENSION OF EM
OSCILLATIONS 188 9.5.5 MULTIBARRIER PROBLEMS: COUPLED OSCILLATIONS 188
9.5.6 CAUSTICS WITH ARBITRARY ORDER OF RAY CONTACT 188 9.5.7 STANDARD
EQUATIONS OF ORDER HIGHER THAN TWO 189 9.5.8 INTERPOLATION FORMULAS FOR
OSCILLATING INTEGRALS 189 10 CAUSTICS REVISITED 190 10.1 CAUSTICS IN
DISPERSIVE MEDIA 190 10.1.1 SPACE-TIME CAUSTICS 190 10.1.2 A UNIFORM
FIELD ASYMPTOTIC FOR SPACE-TIME CAUSTICS 192 10.1.3 CAUSTICS WITH
ANOMALOUS PHASE SHIFT 193 10.1.4 BROKEN SPACE-TIME CAUSTICS 193 10.1.5
SPACE-TIME LENSES 193 10.1.6 UNIFORM ASYMPTOTICS IN MEDIA WITH SPATIAL
DISPERSION 194 10.2 CAUSTICS IN ANISOTROPIC MEDIA 194 10.2.1 DESCRIPTION
OF CAUSTIC FIELDS 194 10.2.2 EXCEPTIONAL DIRECTIONS OF RADIATIVE
TRANSFER 195 10.2.3 FOCUSING OF WAVES AT THE INTERFACE OF ANISOTROPIC
AND ISOTROPIC MEDIA 196 10.2.4 CAUSTICS WITH ANOMALOUS PHASE SHIFT 195
10.3 COMPLEX CAUSTICS 197 10.4 RANDOM CAUSTICS 198 10.5 CAUSTICS IN
QUANTUM MECHANICAL PROBLEMS 200 10.6 CONCLUDING REMARKS 201 REFERENCES
202 LIST OF SYMBOLS 214 SUBJECT INDEX 215
|
| any_adam_object | 1 |
| author | Kravcov, Jurij A. 1937- Orlov, Jurij I. |
| author_GND | (DE-588)120181665 |
| author_facet | Kravcov, Jurij A. 1937- Orlov, Jurij I. |
| author_role | aut aut |
| author_sort | Kravcov, Jurij A. 1937- |
| author_variant | j a k ja jak j i o ji jio |
| building | Verbundindex |
| bvnumber | BV011995555 |
| callnumber-first | Q - Science |
| callnumber-label | QC383 |
| callnumber-raw | QC383 |
| callnumber-search | QC383 |
| callnumber-sort | QC 3383 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 SK 560 UH 5080 |
| ctrlnum | (OCoLC)39299144 (DE-599)BVBBV011995555 |
| dewey-full | 535/.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 535 - Light and related radiation |
| dewey-raw | 535/.32 |
| dewey-search | 535/.32 |
| dewey-sort | 3535 232 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV011995555 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:54Z |
| institution | BVB |
| isbn | 3540642277 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008118338 |
| oclc_num | 39299144 |
| open_access_boolean | |
| owner | DE-703 DE-188 |
| owner_facet | DE-703 DE-188 |
| physical | XII, 216 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Springer series on wave phenomena |
| series2 | Springer series on wave phenomena |
| spelling | Kravcov, Jurij A. 1937- Verfasser (DE-588)120181665 aut Caustics, catastrophes and wave fields Yu. A. Kravtsov ; Yu. I. Orlov 2. ed. Berlin [u.a.] Springer 1999 XII, 216 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series on wave phenomena 15 Literaturverz. S. 202 - 213. - Bildet Forts. zu: Kravcov, Jurij A.: Geometrical optics of inhomogeneous media Mathematik Catastrophes (Mathematics) Caustics (Optics) Mathematics Geometrical optics Mathematics Katastrophentheorie (DE-588)4029930-2 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Inhomogenes Medium (DE-588)4228459-4 gnd rswk-swf Wellenoptik (DE-588)4189552-6 gnd rswk-swf Geometrische Optik (DE-588)4020241-0 gnd rswk-swf Wellenfeld (DE-588)4189544-7 gnd rswk-swf Kaustik (DE-588)4135840-5 gnd rswk-swf Kaustik (DE-588)4135840-5 s Wellenfeld (DE-588)4189544-7 s Katastrophentheorie (DE-588)4029930-2 s DE-604 Geometrische Optik (DE-588)4020241-0 s Inhomogenes Medium (DE-588)4228459-4 s Wellenoptik (DE-588)4189552-6 s Asymptotische Entwicklung (DE-588)4112609-9 s Orlov, Jurij I. Verfasser aut Springer series on wave phenomena 15 (DE-604)BV000022763 15 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118338&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kravcov, Jurij A. 1937- Orlov, Jurij I. Caustics, catastrophes and wave fields Springer series on wave phenomena Mathematik Catastrophes (Mathematics) Caustics (Optics) Mathematics Geometrical optics Mathematics Katastrophentheorie (DE-588)4029930-2 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Inhomogenes Medium (DE-588)4228459-4 gnd Wellenoptik (DE-588)4189552-6 gnd Geometrische Optik (DE-588)4020241-0 gnd Wellenfeld (DE-588)4189544-7 gnd Kaustik (DE-588)4135840-5 gnd |
| subject_GND | (DE-588)4029930-2 (DE-588)4112609-9 (DE-588)4228459-4 (DE-588)4189552-6 (DE-588)4020241-0 (DE-588)4189544-7 (DE-588)4135840-5 |
| title | Caustics, catastrophes and wave fields |
| title_auth | Caustics, catastrophes and wave fields |
| title_exact_search | Caustics, catastrophes and wave fields |
| title_full | Caustics, catastrophes and wave fields Yu. A. Kravtsov ; Yu. I. Orlov |
| title_fullStr | Caustics, catastrophes and wave fields Yu. A. Kravtsov ; Yu. I. Orlov |
| title_full_unstemmed | Caustics, catastrophes and wave fields Yu. A. Kravtsov ; Yu. I. Orlov |
| title_short | Caustics, catastrophes and wave fields |
| title_sort | caustics catastrophes and wave fields |
| topic | Mathematik Catastrophes (Mathematics) Caustics (Optics) Mathematics Geometrical optics Mathematics Katastrophentheorie (DE-588)4029930-2 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Inhomogenes Medium (DE-588)4228459-4 gnd Wellenoptik (DE-588)4189552-6 gnd Geometrische Optik (DE-588)4020241-0 gnd Wellenfeld (DE-588)4189544-7 gnd Kaustik (DE-588)4135840-5 gnd |
| topic_facet | Mathematik Catastrophes (Mathematics) Caustics (Optics) Mathematics Geometrical optics Mathematics Katastrophentheorie Asymptotische Entwicklung Inhomogenes Medium Wellenoptik Geometrische Optik Wellenfeld Kaustik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118338&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022763 |
| work_keys_str_mv | AT kravcovjurija causticscatastrophesandwavefields AT orlovjuriji causticscatastrophesandwavefields |