Ontology type: schema:ScholarlyArticle
2021-10-06
AUTHORSV. Sharanya, B. Sri Padmavati, G. P. Raja Sekhar
ABSTRACTIn this paper, we consider a viscous droplet migrating in a viscous fluid of a different viscosity. Further, we assume that the surface of the droplet is partially contaminated with a stagnant layer of surfactant (surface active agent which reduces the interfacial tension). We analyze the effects of the following phenomena associated with the thermocapillary migration of a droplet in a transient Stokes flow. The first is the influence of surfactant cap for an arbitrary cap angle which is partially coated on the droplet surface for both high and low surface Péclet number cases. The second is the influence of the energy changes associated with stretching and shrinkage of the interfacial area elements, when the droplet is in motion. It can be noted that for the vanishing cap angle, both high and low surface Péclet number limits reduce to the case of a pure thermocapillary migration of a droplet in a transient Stokes flow. For a given ambient flow, the migration of the droplet is controlled by the magnitude of the ambient velocity and the surface tension variations due to temperature and surfactant concentration. In particular, these surface tension variations balance the tangential stress balance. Considering axisymmetric transient Stokes flow, we obtain analytical solutions in two limiting cases, namely low and high surface Péclet number. This work considers linear variation of interfacial tension on both thermal and surfactant gradients. The main contribution is pertaining to the capillary drift and the corresponding surfactant transport on the droplet for an axisymmetric hydrodynamic as well as thermal and surfactant fields. We have analyzed the level curves corresponding to stream function and temperature fields, i.e., streamlines and isotherms for various parameters in order to develop a realistic picture of the migration pattern and the influence of thermal fields. We observe that the streamlines in the vicinity of rear end of the droplet show asymmetry due to the surfactant accumulation at that region. Increasing cap angle breaks the symmetry of the induced stream. It is seen that increasing values of nondimensional parameter that accounts for the stretching and shrinkage of the droplet surface immobilizes the surface and offers retardation to the migrating droplet. The variation of migration velocity with time suggests a control mechanism for the migration of the drop under external/surface gradients and hence may serve as a useful tool in applications like targeted drug delivery systems. More... »
PAGES783-806
http://scigraph.springernature.com/pub.10.1007/s00162-021-00592-w
DOIhttp://dx.doi.org/10.1007/s00162-021-00592-w
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1141669145
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/2008/0915",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Interdisciplinary Engineering",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Department of Mathematics, Madanapalle Institute of Technology and Science, 517325, Angallu, Andhra Pradesh, India",
"id": "http://www.grid.ac/institutes/grid.459547.e",
"name": [
"Department of Mathematics, Madanapalle Institute of Technology and Science, 517325, Angallu, Andhra Pradesh, India"
],
"type": "Organization"
},
"familyName": "Sharanya",
"givenName": "V.",
"id": "sg:person.07555144151.65",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07555144151.65"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "School of Mathematics and Statistics, University of Hyderabad, P.O. Central University, 500046, Hyderabad, Telangana, India",
"id": "http://www.grid.ac/institutes/grid.18048.35",
"name": [
"School of Mathematics and Statistics, University of Hyderabad, P.O. Central University, 500046, Hyderabad, Telangana, India"
],
"type": "Organization"
},
"familyName": "Padmavati",
"givenName": "B. Sri",
"id": "sg:person.012727116431.30",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012727116431.30"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India",
"id": "http://www.grid.ac/institutes/grid.429017.9",
"name": [
"Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India"
],
"type": "Organization"
},
"familyName": "Raja Sekhar",
"givenName": "G. P.",
"id": "sg:person.016630736336.54",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016630736336.54"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1023/a:1017979029814",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1001192436",
"https://doi.org/10.1023/a:1017979029814"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1038/s41598-019-40069-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1112603562",
"https://doi.org/10.1038/s41598-019-40069-9"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1023/a:1004180322668",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1056301748",
"https://doi.org/10.1023/a:1004180322668"
],
"type": "CreativeWork"
}
],
"datePublished": "2021-10-06",
"datePublishedReg": "2021-10-06",
"description": "In this paper, we consider a viscous droplet migrating in a viscous fluid of a different viscosity. Further, we assume that the surface of the droplet is partially contaminated with a stagnant layer of surfactant (surface active agent which reduces the interfacial tension). We analyze the effects of the following phenomena associated with the thermocapillary migration of a droplet in a transient Stokes flow. The first is the influence of surfactant cap for an arbitrary cap angle which is partially coated on the droplet surface for both high and low surface P\u00e9clet number cases. The second is the influence of the energy changes associated with stretching and shrinkage of the interfacial area elements, when the droplet is in motion. It can be noted that for the vanishing cap angle, both high and low surface P\u00e9clet number limits reduce to the case of a pure thermocapillary migration of a droplet in a transient Stokes flow. For a given ambient flow, the migration of the droplet is controlled by the magnitude of the ambient velocity and the surface tension variations due to temperature and surfactant concentration. In particular, these surface tension variations balance the tangential stress balance. Considering axisymmetric transient Stokes flow, we obtain analytical solutions in two limiting cases, namely low and high surface P\u00e9clet number. This work considers linear variation of interfacial tension on both thermal and surfactant gradients. The main contribution is pertaining to the capillary drift and the corresponding surfactant transport on the droplet for an axisymmetric hydrodynamic as well as thermal and surfactant fields. We have analyzed the level curves corresponding to stream function and temperature fields, i.e., streamlines and isotherms for various parameters in order to develop a realistic picture of the migration pattern and the influence of thermal fields. We observe that the streamlines in the vicinity of rear end of the droplet show asymmetry due to the surfactant accumulation at that region. Increasing cap angle breaks the symmetry of the induced stream. It is seen that increasing values of nondimensional parameter that accounts for the stretching and shrinkage of the droplet surface immobilizes the surface and offers retardation to the migrating droplet. The variation of migration velocity with time suggests a control mechanism for the migration of the drop under external/surface gradients and hence may serve as a useful tool in applications like targeted drug delivery systems.",
"genre": "article",
"id": "sg:pub.10.1007/s00162-021-00592-w",
"inLanguage": "en",
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1052938",
"issn": [
"0935-4964",
"1432-2250"
],
"name": "Theoretical and Computational Fluid Dynamics",
"publisher": "Springer Nature",
"type": "Periodical"
},
{
"issueNumber": "6",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "35"
}
],
"keywords": [
"transient Stokes flow",
"surface tension variation",
"Stokes flow",
"thermocapillary migration",
"tension variation",
"droplet surface",
"cap angle",
"surface P\u00e9clet number",
"temperature field",
"thermal field",
"tangential stress balance",
"viscous droplets",
"surfactant transport",
"ambient flow",
"stagnant layer",
"ambient velocity",
"nondimensional parameters",
"stagnant cap",
"interfacial tension",
"viscous fluid",
"P\u00e9clet number",
"spherical droplets",
"number cases",
"different viscosities",
"analytical solution",
"surface gradient",
"rear end",
"stress balance",
"droplets",
"number limit",
"linear variation",
"surfactant gradient",
"transient Stokes",
"streamlines",
"flow",
"surface",
"drug delivery systems",
"migration velocity",
"surfactant layer",
"layer",
"velocity",
"surfactant concentration",
"shrinkage",
"angle",
"area elements",
"hydrodynamics",
"surfactant field",
"field",
"main contribution",
"parameters",
"gradient",
"influence",
"energy change",
"viscosity",
"isotherms",
"stretching",
"temperature",
"delivery system",
"drop",
"motion",
"surfactant accumulation",
"variation",
"Stokes",
"fluid",
"applications",
"control mechanisms",
"transport",
"solution",
"surfactants",
"cap",
"drift",
"vicinity",
"tension",
"streams",
"realistic picture",
"level curves",
"magnitude",
"system",
"work",
"phenomenon",
"curves",
"order",
"elements",
"limit",
"symmetry",
"useful tool",
"values",
"concentration",
"time",
"effect",
"cases",
"balance",
"tool",
"mechanism",
"region",
"contribution",
"migration",
"end",
"number",
"function",
"changes",
"asymmetry",
"patterns",
"accumulation",
"picture",
"retardation",
"migration patterns",
"paper"
],
"name": "Transient Stokes flow past a spherical droplet with a stagnant cap due to contaminated surfactant layer",
"pagination": "783-806",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1141669145"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s00162-021-00592-w"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s00162-021-00592-w",
"https://app.dimensions.ai/details/publication/pub.1141669145"
],
"sdDataset": "articles",
"sdDatePublished": "2022-05-10T10:31",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_899.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1007/s00162-021-00592-w"
}
]
Download the RDF metadata as: json-ld nt turtle xml License info
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/s00162-021-00592-w'
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/s00162-021-00592-w'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00162-021-00592-w'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00162-021-00592-w'
This table displays all metadata directly associated to this object as RDF triples.
198 TRIPLES
22 PREDICATES
136 URIs
125 LITERALS
6 BLANK NODES
Subject | Predicate | Object | |
---|---|---|---|
1 | sg:pub.10.1007/s00162-021-00592-w | schema:about | anzsrc-for:09 |
2 | ″ | ″ | anzsrc-for:0915 |
3 | ″ | schema:author | N76b8fe18703e4b7598da48e15ed951b5 |
4 | ″ | schema:citation | sg:pub.10.1023/a:1004180322668 |
5 | ″ | ″ | sg:pub.10.1023/a:1017979029814 |
6 | ″ | ″ | sg:pub.10.1038/s41598-019-40069-9 |
7 | ″ | schema:datePublished | 2021-10-06 |
8 | ″ | schema:datePublishedReg | 2021-10-06 |
9 | ″ | schema:description | In this paper, we consider a viscous droplet migrating in a viscous fluid of a different viscosity. Further, we assume that the surface of the droplet is partially contaminated with a stagnant layer of surfactant (surface active agent which reduces the interfacial tension). We analyze the effects of the following phenomena associated with the thermocapillary migration of a droplet in a transient Stokes flow. The first is the influence of surfactant cap for an arbitrary cap angle which is partially coated on the droplet surface for both high and low surface Péclet number cases. The second is the influence of the energy changes associated with stretching and shrinkage of the interfacial area elements, when the droplet is in motion. It can be noted that for the vanishing cap angle, both high and low surface Péclet number limits reduce to the case of a pure thermocapillary migration of a droplet in a transient Stokes flow. For a given ambient flow, the migration of the droplet is controlled by the magnitude of the ambient velocity and the surface tension variations due to temperature and surfactant concentration. In particular, these surface tension variations balance the tangential stress balance. Considering axisymmetric transient Stokes flow, we obtain analytical solutions in two limiting cases, namely low and high surface Péclet number. This work considers linear variation of interfacial tension on both thermal and surfactant gradients. The main contribution is pertaining to the capillary drift and the corresponding surfactant transport on the droplet for an axisymmetric hydrodynamic as well as thermal and surfactant fields. We have analyzed the level curves corresponding to stream function and temperature fields, i.e., streamlines and isotherms for various parameters in order to develop a realistic picture of the migration pattern and the influence of thermal fields. We observe that the streamlines in the vicinity of rear end of the droplet show asymmetry due to the surfactant accumulation at that region. Increasing cap angle breaks the symmetry of the induced stream. It is seen that increasing values of nondimensional parameter that accounts for the stretching and shrinkage of the droplet surface immobilizes the surface and offers retardation to the migrating droplet. The variation of migration velocity with time suggests a control mechanism for the migration of the drop under external/surface gradients and hence may serve as a useful tool in applications like targeted drug delivery systems. |
10 | ″ | schema:genre | article |
11 | ″ | schema:inLanguage | en |
12 | ″ | schema:isAccessibleForFree | false |
13 | ″ | schema:isPartOf | N255cec744a314ec79960f439c53e22cd |
14 | ″ | ″ | N715ccf99cff84bec8f8e88c9fe423670 |
15 | ″ | ″ | sg:journal.1052938 |
16 | ″ | schema:keywords | Péclet number |
17 | ″ | ″ | Stokes |
18 | ″ | ″ | Stokes flow |
19 | ″ | ″ | accumulation |
20 | ″ | ″ | ambient flow |
21 | ″ | ″ | ambient velocity |
22 | ″ | ″ | analytical solution |
23 | ″ | ″ | angle |
24 | ″ | ″ | applications |
25 | ″ | ″ | area elements |
26 | ″ | ″ | asymmetry |
27 | ″ | ″ | balance |
28 | ″ | ″ | cap |
29 | ″ | ″ | cap angle |
30 | ″ | ″ | cases |
31 | ″ | ″ | changes |
32 | ″ | ″ | concentration |
33 | ″ | ″ | contribution |
34 | ″ | ″ | control mechanisms |
35 | ″ | ″ | curves |
36 | ″ | ″ | delivery system |
37 | ″ | ″ | different viscosities |
38 | ″ | ″ | drift |
39 | ″ | ″ | drop |
40 | ″ | ″ | droplet surface |
41 | ″ | ″ | droplets |
42 | ″ | ″ | drug delivery systems |
43 | ″ | ″ | effect |
44 | ″ | ″ | elements |
45 | ″ | ″ | end |
46 | ″ | ″ | energy change |
47 | ″ | ″ | field |
48 | ″ | ″ | flow |
49 | ″ | ″ | fluid |
50 | ″ | ″ | function |
51 | ″ | ″ | gradient |
52 | ″ | ″ | hydrodynamics |
53 | ″ | ″ | influence |
54 | ″ | ″ | interfacial tension |
55 | ″ | ″ | isotherms |
56 | ″ | ″ | layer |
57 | ″ | ″ | level curves |
58 | ″ | ″ | limit |
59 | ″ | ″ | linear variation |
60 | ″ | ″ | magnitude |
61 | ″ | ″ | main contribution |
62 | ″ | ″ | mechanism |
63 | ″ | ″ | migration |
64 | ″ | ″ | migration patterns |
65 | ″ | ″ | migration velocity |
66 | ″ | ″ | motion |
67 | ″ | ″ | nondimensional parameters |
68 | ″ | ″ | number |
69 | ″ | ″ | number cases |
70 | ″ | ″ | number limit |
71 | ″ | ″ | order |
72 | ″ | ″ | paper |
73 | ″ | ″ | parameters |
74 | ″ | ″ | patterns |
75 | ″ | ″ | phenomenon |
76 | ″ | ″ | picture |
77 | ″ | ″ | realistic picture |
78 | ″ | ″ | rear end |
79 | ″ | ″ | region |
80 | ″ | ″ | retardation |
81 | ″ | ″ | shrinkage |
82 | ″ | ″ | solution |
83 | ″ | ″ | spherical droplets |
84 | ″ | ″ | stagnant cap |
85 | ″ | ″ | stagnant layer |
86 | ″ | ″ | streamlines |
87 | ″ | ″ | streams |
88 | ″ | ″ | stress balance |
89 | ″ | ″ | stretching |
90 | ″ | ″ | surface |
91 | ″ | ″ | surface Péclet number |
92 | ″ | ″ | surface gradient |
93 | ″ | ″ | surface tension variation |
94 | ″ | ″ | surfactant accumulation |
95 | ″ | ″ | surfactant concentration |
96 | ″ | ″ | surfactant field |
97 | ″ | ″ | surfactant gradient |
98 | ″ | ″ | surfactant layer |
99 | ″ | ″ | surfactant transport |
100 | ″ | ″ | surfactants |
101 | ″ | ″ | symmetry |
102 | ″ | ″ | system |
103 | ″ | ″ | tangential stress balance |
104 | ″ | ″ | temperature |
105 | ″ | ″ | temperature field |
106 | ″ | ″ | tension |
107 | ″ | ″ | tension variation |
108 | ″ | ″ | thermal field |
109 | ″ | ″ | thermocapillary migration |
110 | ″ | ″ | time |
111 | ″ | ″ | tool |
112 | ″ | ″ | transient Stokes |
113 | ″ | ″ | transient Stokes flow |
114 | ″ | ″ | transport |
115 | ″ | ″ | useful tool |
116 | ″ | ″ | values |
117 | ″ | ″ | variation |
118 | ″ | ″ | velocity |
119 | ″ | ″ | vicinity |
120 | ″ | ″ | viscosity |
121 | ″ | ″ | viscous droplets |
122 | ″ | ″ | viscous fluid |
123 | ″ | ″ | work |
124 | ″ | schema:name | Transient Stokes flow past a spherical droplet with a stagnant cap due to contaminated surfactant layer |
125 | ″ | schema:pagination | 783-806 |
126 | ″ | schema:productId | N1147280b6d1a475297b242d8d7768f1c |
127 | ″ | ″ | Nbc7e2f5247914edbb697c887d16bb00d |
128 | ″ | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1141669145 |
129 | ″ | ″ | https://doi.org/10.1007/s00162-021-00592-w |
130 | ″ | schema:sdDatePublished | 2022-05-10T10:31 |
131 | ″ | schema:sdLicense | https://scigraph.springernature.com/explorer/license/ |
132 | ″ | schema:sdPublisher | N47d0a204ea10443482b7bc14888f4e1d |
133 | ″ | schema:url | https://doi.org/10.1007/s00162-021-00592-w |
134 | ″ | sgo:license | sg:explorer/license/ |
135 | ″ | sgo:sdDataset | articles |
136 | ″ | rdf:type | schema:ScholarlyArticle |
137 | N1147280b6d1a475297b242d8d7768f1c | schema:name | doi |
138 | ″ | schema:value | 10.1007/s00162-021-00592-w |
139 | ″ | rdf:type | schema:PropertyValue |
140 | N255cec744a314ec79960f439c53e22cd | schema:volumeNumber | 35 |
141 | ″ | rdf:type | schema:PublicationVolume |
142 | N2c8a4f42cdcd471d999697eae1ca9554 | rdf:first | sg:person.016630736336.54 |
143 | ″ | rdf:rest | rdf:nil |
144 | N47d0a204ea10443482b7bc14888f4e1d | schema:name | Springer Nature - SN SciGraph project |
145 | ″ | rdf:type | schema:Organization |
146 | N65d489bee7b04fa8970c0db67881c8ec | rdf:first | sg:person.012727116431.30 |
147 | ″ | rdf:rest | N2c8a4f42cdcd471d999697eae1ca9554 |
148 | N715ccf99cff84bec8f8e88c9fe423670 | schema:issueNumber | 6 |
149 | ″ | rdf:type | schema:PublicationIssue |
150 | N76b8fe18703e4b7598da48e15ed951b5 | rdf:first | sg:person.07555144151.65 |
151 | ″ | rdf:rest | N65d489bee7b04fa8970c0db67881c8ec |
152 | Nbc7e2f5247914edbb697c887d16bb00d | schema:name | dimensions_id |
153 | ″ | schema:value | pub.1141669145 |
154 | ″ | rdf:type | schema:PropertyValue |
155 | anzsrc-for:09 | schema:inDefinedTermSet | anzsrc-for: |
156 | ″ | schema:name | Engineering |
157 | ″ | rdf:type | schema:DefinedTerm |
158 | anzsrc-for:0915 | schema:inDefinedTermSet | anzsrc-for: |
159 | ″ | schema:name | Interdisciplinary Engineering |
160 | ″ | rdf:type | schema:DefinedTerm |
161 | sg:journal.1052938 | schema:issn | 0935-4964 |
162 | ″ | ″ | 1432-2250 |
163 | ″ | schema:name | Theoretical and Computational Fluid Dynamics |
164 | ″ | schema:publisher | Springer Nature |
165 | ″ | rdf:type | schema:Periodical |
166 | sg:person.012727116431.30 | schema:affiliation | grid-institutes:grid.18048.35 |
167 | ″ | schema:familyName | Padmavati |
168 | ″ | schema:givenName | B. Sri |
169 | ″ | schema:sameAs | https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012727116431.30 |
170 | ″ | rdf:type | schema:Person |
171 | sg:person.016630736336.54 | schema:affiliation | grid-institutes:grid.429017.9 |
172 | ″ | schema:familyName | Raja Sekhar |
173 | ″ | schema:givenName | G. P. |
174 | ″ | schema:sameAs | https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016630736336.54 |
175 | ″ | rdf:type | schema:Person |
176 | sg:person.07555144151.65 | schema:affiliation | grid-institutes:grid.459547.e |
177 | ″ | schema:familyName | Sharanya |
178 | ″ | schema:givenName | V. |
179 | ″ | schema:sameAs | https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07555144151.65 |
180 | ″ | rdf:type | schema:Person |
181 | sg:pub.10.1023/a:1004180322668 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1056301748 |
182 | ″ | ″ | https://doi.org/10.1023/a:1004180322668 |
183 | ″ | rdf:type | schema:CreativeWork |
184 | sg:pub.10.1023/a:1017979029814 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1001192436 |
185 | ″ | ″ | https://doi.org/10.1023/a:1017979029814 |
186 | ″ | rdf:type | schema:CreativeWork |
187 | sg:pub.10.1038/s41598-019-40069-9 | schema:sameAs | https://app.dimensions.ai/details/publication/pub.1112603562 |
188 | ″ | ″ | https://doi.org/10.1038/s41598-019-40069-9 |
189 | ″ | rdf:type | schema:CreativeWork |
190 | grid-institutes:grid.18048.35 | schema:alternateName | School of Mathematics and Statistics, University of Hyderabad, P.O. Central University, 500046, Hyderabad, Telangana, India |
191 | ″ | schema:name | School of Mathematics and Statistics, University of Hyderabad, P.O. Central University, 500046, Hyderabad, Telangana, India |
192 | ″ | rdf:type | schema:Organization |
193 | grid-institutes:grid.429017.9 | schema:alternateName | Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India |
194 | ″ | schema:name | Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India |
195 | ″ | rdf:type | schema:Organization |
196 | grid-institutes:grid.459547.e | schema:alternateName | Department of Mathematics, Madanapalle Institute of Technology and Science, 517325, Angallu, Andhra Pradesh, India |
197 | ″ | schema:name | Department of Mathematics, Madanapalle Institute of Technology and Science, 517325, Angallu, Andhra Pradesh, India |
198 | ″ | rdf:type | schema:Organization |