Fractal Properties of “Disordered Surfaces” and The Termite Problem View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1991

AUTHORS

H. Eugene Stanley , A. Bunde , A. Coniglio , D. C. Hong , P. Meakin , T. A. Witten

ABSTRACT

In this second lecture, I shall turn to the topic of fractal surfaces, for which knowledge of only “the” fractal dimension df is not sufficient to describe the essential physics. In fact, we must distinguish between the entire external perimeter or “hull,” with its corresponding fractal dimension dh, and the unscreened portion of the external perimeter and its fractal dimension d. A very simple argument gives rise to an expression for du in terms of df and dp, the fractal dimension of the particles used to probe the surface. We shell see that the concept of the unscreened perimeter is at the heart of transport in a two-component random medium made up of superconductors and normal resistors. In particular, the exponent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde s = s/v$$\end{document} for characterizing the divergence of the macroscopic conductivity at the percolation threshold pc is identically equal to du. More... »

PAGES

307-333

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4757-1402-9_26

DOI

http://dx.doi.org/10.1007/978-1-4757-1402-9_26

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1017799711


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Engineering", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0903", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biomedical Engineering", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA", 
          "id": "http://www.grid.ac/institutes/grid.189504.1", 
          "name": [
            "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Stanley", 
        "givenName": "H. Eugene", 
        "id": "sg:person.0767651144.84", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0767651144.84"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA", 
          "id": "http://www.grid.ac/institutes/grid.189504.1", 
          "name": [
            "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Bunde", 
        "givenName": "A.", 
        "id": "sg:person.013610102705.28", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013610102705.28"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA", 
          "id": "http://www.grid.ac/institutes/grid.189504.1", 
          "name": [
            "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Coniglio", 
        "givenName": "A.", 
        "id": "sg:person.01227217136.16", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01227217136.16"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA", 
          "id": "http://www.grid.ac/institutes/grid.189504.1", 
          "name": [
            "Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hong", 
        "givenName": "D. C.", 
        "id": "sg:person.07530236015.75", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07530236015.75"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Central Research and Development Department, E. I. DuPont de Nemours and Company, 19898, Wilmington, DE, USA", 
          "id": "http://www.grid.ac/institutes/grid.416832.a", 
          "name": [
            "Central Research and Development Department, E. I. DuPont de Nemours and Company, 19898, Wilmington, DE, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Meakin", 
        "givenName": "P.", 
        "id": "sg:person.011210412314.30", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011210412314.30"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Corporate Research Science Laboratories, Exxon Research and Engineering Company, 08801, Annandale, NJ, USA", 
          "id": "http://www.grid.ac/institutes/grid.421234.2", 
          "name": [
            "Corporate Research Science Laboratories, Exxon Research and Engineering Company, 08801, Annandale, NJ, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Witten", 
        "givenName": "T. A.", 
        "id": "sg:person.01176156165.31", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01176156165.31"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1991", 
    "datePublishedReg": "1991-01-01", 
    "description": "In this second lecture, I shall turn to the topic of fractal surfaces, for which knowledge of only \u201cthe\u201d fractal dimension df is not sufficient to describe the essential physics. In fact, we must distinguish between the entire external perimeter or \u201chull,\u201d with its corresponding fractal dimension dh, and the unscreened portion of the external perimeter and its fractal dimension d. A very simple argument gives rise to an expression for du in terms of df and dp, the fractal dimension of the particles used to probe the surface. We shell see that the concept of the unscreened perimeter is at the heart of transport in a two-component random medium made up of superconductors and normal resistors. In particular, the exponent \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\tilde s = s/v$$\\end{document} for characterizing the divergence of the macroscopic conductivity at the percolation threshold pc is identically equal to du.", 
    "editor": [
      {
        "familyName": "Pynn", 
        "givenName": "Roger", 
        "type": "Person"
      }, 
      {
        "familyName": "Skjeltorp", 
        "givenName": "Arne", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-1-4757-1402-9_26", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-1-4757-1404-3", 
        "978-1-4757-1402-9"
      ], 
      "name": "Scaling Phenomena in Disordered Systems", 
      "type": "Book"
    }, 
    "keywords": [
      "normal resistor", 
      "external perimeter", 
      "macroscopic conductivity", 
      "fractal dimension D.", 
      "fractal surfaces", 
      "fractal dimension dH", 
      "surface", 
      "essential physics", 
      "two-component random medium", 
      "fractal dimension Df", 
      "fractal dimension", 
      "percolation threshold pc", 
      "conductivity", 
      "dimension df", 
      "resistors", 
      "unscreened perimeter", 
      "particles", 
      "fractal properties", 
      "superconductors", 
      "perimeter", 
      "properties", 
      "threshold pc", 
      "transport", 
      "disordered surfaces", 
      "random media", 
      "exponent", 
      "simple argument", 
      "physics", 
      "DH", 
      "PC", 
      "DF", 
      "problem", 
      "medium", 
      "dimensions", 
      "terms", 
      "concept", 
      "termite problem", 
      "rise", 
      "DP", 
      "portion", 
      "dimension d.", 
      "fact", 
      "topic", 
      "DU", 
      "divergence", 
      "knowledge", 
      "D.", 
      "second lecture", 
      "lectures", 
      "heart", 
      "argument", 
      "expression", 
      "entire external perimeter", 
      "corresponding fractal dimension dh", 
      "dimension dh", 
      "unscreened portion", 
      "terms of df", 
      "heart of transport"
    ], 
    "name": "Fractal Properties of \u201cDisordered Surfaces\u201d and The Termite Problem", 
    "pagination": "307-333", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1017799711"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4757-1402-9_26"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4757-1402-9_26", 
      "https://app.dimensions.ai/details/publication/pub.1017799711"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2021-12-01T20:09", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/chapter/chapter_405.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-1-4757-1402-9_26"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-1-4757-1402-9_26'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4757-1402-9_26'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4757-1402-9_26'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4757-1402-9_26'


 

This table displays all metadata directly associated to this object as RDF triples.

164 TRIPLES      23 PREDICATES      84 URIs      77 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4757-1402-9_26 schema:about anzsrc-for:09
2 anzsrc-for:0903
3 schema:author N3fa05298c8994975845bc50d283e3634
4 schema:datePublished 1991
5 schema:datePublishedReg 1991-01-01
6 schema:description In this second lecture, I shall turn to the topic of fractal surfaces, for which knowledge of only “the” fractal dimension df is not sufficient to describe the essential physics. In fact, we must distinguish between the entire external perimeter or “hull,” with its corresponding fractal dimension dh, and the unscreened portion of the external perimeter and its fractal dimension d. A very simple argument gives rise to an expression for du in terms of df and dp, the fractal dimension of the particles used to probe the surface. We shell see that the concept of the unscreened perimeter is at the heart of transport in a two-component random medium made up of superconductors and normal resistors. In particular, the exponent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde s = s/v$$\end{document} for characterizing the divergence of the macroscopic conductivity at the percolation threshold pc is identically equal to du.
7 schema:editor Nfe77658d62c04cddae501da2c85010de
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf N997b43ee89304a26bb7c5ce1df2d1781
12 schema:keywords D.
13 DF
14 DH
15 DP
16 DU
17 PC
18 argument
19 concept
20 conductivity
21 corresponding fractal dimension dh
22 dimension d.
23 dimension df
24 dimension dh
25 dimensions
26 disordered surfaces
27 divergence
28 entire external perimeter
29 essential physics
30 exponent
31 expression
32 external perimeter
33 fact
34 fractal dimension
35 fractal dimension D.
36 fractal dimension Df
37 fractal dimension dH
38 fractal properties
39 fractal surfaces
40 heart
41 heart of transport
42 knowledge
43 lectures
44 macroscopic conductivity
45 medium
46 normal resistor
47 particles
48 percolation threshold pc
49 perimeter
50 physics
51 portion
52 problem
53 properties
54 random media
55 resistors
56 rise
57 second lecture
58 simple argument
59 superconductors
60 surface
61 termite problem
62 terms
63 terms of df
64 threshold pc
65 topic
66 transport
67 two-component random medium
68 unscreened perimeter
69 unscreened portion
70 schema:name Fractal Properties of “Disordered Surfaces” and The Termite Problem
71 schema:pagination 307-333
72 schema:productId Ne660970394434b7b8ec9e66470b46ae9
73 Nf72b56977f834ca5a254f9bf4fd78ed0
74 schema:publisher Nd669b1ae55794eeea741d06de56b71c2
75 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017799711
76 https://doi.org/10.1007/978-1-4757-1402-9_26
77 schema:sdDatePublished 2021-12-01T20:09
78 schema:sdLicense https://scigraph.springernature.com/explorer/license/
79 schema:sdPublisher Nfe27c36f6b374faa9a4174132cedc610
80 schema:url https://doi.org/10.1007/978-1-4757-1402-9_26
81 sgo:license sg:explorer/license/
82 sgo:sdDataset chapters
83 rdf:type schema:Chapter
84 N03d91d294ecf4edebfd7df45df575a5c rdf:first sg:person.01227217136.16
85 rdf:rest Nc30a222358654be1a302eef328655627
86 N071d331ccf7142098b3b34a7959eff1e rdf:first Nc671c8fa52f743599405529399e9fc97
87 rdf:rest rdf:nil
88 N3fa05298c8994975845bc50d283e3634 rdf:first sg:person.0767651144.84
89 rdf:rest N9ee7778482a549c6a0365450a7ed9c61
90 N84ed5f094efb4c1082d4f8e3a04e2a70 rdf:first sg:person.011210412314.30
91 rdf:rest Nfc23acccac064fe1b431357d5f02c207
92 N997b43ee89304a26bb7c5ce1df2d1781 schema:isbn 978-1-4757-1402-9
93 978-1-4757-1404-3
94 schema:name Scaling Phenomena in Disordered Systems
95 rdf:type schema:Book
96 N9ee7778482a549c6a0365450a7ed9c61 rdf:first sg:person.013610102705.28
97 rdf:rest N03d91d294ecf4edebfd7df45df575a5c
98 Na0305386dd3f43f2a122b614fe1338cf schema:familyName Pynn
99 schema:givenName Roger
100 rdf:type schema:Person
101 Nc30a222358654be1a302eef328655627 rdf:first sg:person.07530236015.75
102 rdf:rest N84ed5f094efb4c1082d4f8e3a04e2a70
103 Nc671c8fa52f743599405529399e9fc97 schema:familyName Skjeltorp
104 schema:givenName Arne
105 rdf:type schema:Person
106 Nd669b1ae55794eeea741d06de56b71c2 schema:name Springer Nature
107 rdf:type schema:Organisation
108 Ne660970394434b7b8ec9e66470b46ae9 schema:name doi
109 schema:value 10.1007/978-1-4757-1402-9_26
110 rdf:type schema:PropertyValue
111 Nf72b56977f834ca5a254f9bf4fd78ed0 schema:name dimensions_id
112 schema:value pub.1017799711
113 rdf:type schema:PropertyValue
114 Nfc23acccac064fe1b431357d5f02c207 rdf:first sg:person.01176156165.31
115 rdf:rest rdf:nil
116 Nfe27c36f6b374faa9a4174132cedc610 schema:name Springer Nature - SN SciGraph project
117 rdf:type schema:Organization
118 Nfe77658d62c04cddae501da2c85010de rdf:first Na0305386dd3f43f2a122b614fe1338cf
119 rdf:rest N071d331ccf7142098b3b34a7959eff1e
120 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
121 schema:name Engineering
122 rdf:type schema:DefinedTerm
123 anzsrc-for:0903 schema:inDefinedTermSet anzsrc-for:
124 schema:name Biomedical Engineering
125 rdf:type schema:DefinedTerm
126 sg:person.011210412314.30 schema:affiliation grid-institutes:grid.416832.a
127 schema:familyName Meakin
128 schema:givenName P.
129 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011210412314.30
130 rdf:type schema:Person
131 sg:person.01176156165.31 schema:affiliation grid-institutes:grid.421234.2
132 schema:familyName Witten
133 schema:givenName T. A.
134 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01176156165.31
135 rdf:type schema:Person
136 sg:person.01227217136.16 schema:affiliation grid-institutes:grid.189504.1
137 schema:familyName Coniglio
138 schema:givenName A.
139 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01227217136.16
140 rdf:type schema:Person
141 sg:person.013610102705.28 schema:affiliation grid-institutes:grid.189504.1
142 schema:familyName Bunde
143 schema:givenName A.
144 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013610102705.28
145 rdf:type schema:Person
146 sg:person.07530236015.75 schema:affiliation grid-institutes:grid.189504.1
147 schema:familyName Hong
148 schema:givenName D. C.
149 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07530236015.75
150 rdf:type schema:Person
151 sg:person.0767651144.84 schema:affiliation grid-institutes:grid.189504.1
152 schema:familyName Stanley
153 schema:givenName H. Eugene
154 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0767651144.84
155 rdf:type schema:Person
156 grid-institutes:grid.189504.1 schema:alternateName Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA
157 schema:name Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA
158 rdf:type schema:Organization
159 grid-institutes:grid.416832.a schema:alternateName Central Research and Development Department, E. I. DuPont de Nemours and Company, 19898, Wilmington, DE, USA
160 schema:name Central Research and Development Department, E. I. DuPont de Nemours and Company, 19898, Wilmington, DE, USA
161 rdf:type schema:Organization
162 grid-institutes:grid.421234.2 schema:alternateName Corporate Research Science Laboratories, Exxon Research and Engineering Company, 08801, Annandale, NJ, USA
163 schema:name Corporate Research Science Laboratories, Exxon Research and Engineering Company, 08801, Annandale, NJ, USA
164 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...