Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds
Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Krause, Andrew L. [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2018 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© The Author(s) 2018 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Bulletin of mathematical biology - Springer US, 1973, 81(2018), 3 vom: 03. Dez., Seite 759-799 |
|---|---|
| Übergeordnetes Werk: |
volume:81 ; year:2018 ; number:3 ; day:03 ; month:12 ; pages:759-799 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11538-018-0535-y |
|---|
| Katalog-ID: |
OLC2087103518 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2087103518 | ||
| 003 | DE-627 | ||
| 005 | 20230401103505.0 | ||
| 007 | tu | ||
| 008 | 230302s2018 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s11538-018-0535-y |2 doi | |
| 035 | |a (DE-627)OLC2087103518 | ||
| 035 | |a (DE-He213)s11538-018-0535-y-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 570 |a 510 |q VZ |
| 084 | |a 12 |2 ssgn | ||
| 084 | |a BIODIV |q DE-30 |2 fid | ||
| 084 | |a 42.00 |2 bkl | ||
| 100 | 1 | |a Krause, Andrew L. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds |
| 264 | 1 | |c 2018 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © The Author(s) 2018 | ||
| 520 | |a Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. | ||
| 650 | 4 | |a Turing patterns | |
| 650 | 4 | |a Growing surfaces | |
| 650 | 4 | |a Anisotropic growth | |
| 650 | 4 | |a Pattern selection | |
| 650 | 4 | |a Pattern robustness | |
| 700 | 1 | |a Ellis, Meredith A. |4 aut | |
| 700 | 1 | |a Van Gorder, Robert A. |0 (orcid)0000-0002-8506-3961 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Bulletin of mathematical biology |d Springer US, 1973 |g 81(2018), 3 vom: 03. Dez., Seite 759-799 |w (DE-627)129391719 |w (DE-600)184905-0 |w (DE-576)014776863 |x 0092-8240 |7 nnns |
| 773 | 1 | 8 | |g volume:81 |g year:2018 |g number:3 |g day:03 |g month:12 |g pages:759-799 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s11538-018-0535-y |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a FID-BIODIV | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_4012 | ||
| 936 | b | k | |a 42.00 |q VZ |
| 951 | |a AR | ||
| 952 | |d 81 |j 2018 |e 3 |b 03 |c 12 |h 759-799 | ||
| author_variant |
a l k al alk m a e ma mae g r a v gra grav |
|---|---|
| matchkey_str |
article:00928240:2018----::nlecocrauerwhnaiorpotevltootrnp |
| hierarchy_sort_str |
2018 |
| bklnumber |
42.00 |
| publishDate |
2018 |
| allfields |
10.1007/s11538-018-0535-y doi (DE-627)OLC2087103518 (DE-He213)s11538-018-0535-y-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Krause, Andrew L. verfasserin aut Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. Turing patterns Growing surfaces Anisotropic growth Pattern selection Pattern robustness Ellis, Meredith A. aut Van Gorder, Robert A. (orcid)0000-0002-8506-3961 aut Enthalten in Bulletin of mathematical biology Springer US, 1973 81(2018), 3 vom: 03. Dez., Seite 759-799 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:81 year:2018 number:3 day:03 month:12 pages:759-799 https://doi.org/10.1007/s11538-018-0535-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 42.00 VZ AR 81 2018 3 03 12 759-799 |
| spelling |
10.1007/s11538-018-0535-y doi (DE-627)OLC2087103518 (DE-He213)s11538-018-0535-y-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Krause, Andrew L. verfasserin aut Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. Turing patterns Growing surfaces Anisotropic growth Pattern selection Pattern robustness Ellis, Meredith A. aut Van Gorder, Robert A. (orcid)0000-0002-8506-3961 aut Enthalten in Bulletin of mathematical biology Springer US, 1973 81(2018), 3 vom: 03. Dez., Seite 759-799 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:81 year:2018 number:3 day:03 month:12 pages:759-799 https://doi.org/10.1007/s11538-018-0535-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 42.00 VZ AR 81 2018 3 03 12 759-799 |
| allfields_unstemmed |
10.1007/s11538-018-0535-y doi (DE-627)OLC2087103518 (DE-He213)s11538-018-0535-y-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Krause, Andrew L. verfasserin aut Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. Turing patterns Growing surfaces Anisotropic growth Pattern selection Pattern robustness Ellis, Meredith A. aut Van Gorder, Robert A. (orcid)0000-0002-8506-3961 aut Enthalten in Bulletin of mathematical biology Springer US, 1973 81(2018), 3 vom: 03. Dez., Seite 759-799 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:81 year:2018 number:3 day:03 month:12 pages:759-799 https://doi.org/10.1007/s11538-018-0535-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 42.00 VZ AR 81 2018 3 03 12 759-799 |
| allfieldsGer |
10.1007/s11538-018-0535-y doi (DE-627)OLC2087103518 (DE-He213)s11538-018-0535-y-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Krause, Andrew L. verfasserin aut Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. Turing patterns Growing surfaces Anisotropic growth Pattern selection Pattern robustness Ellis, Meredith A. aut Van Gorder, Robert A. (orcid)0000-0002-8506-3961 aut Enthalten in Bulletin of mathematical biology Springer US, 1973 81(2018), 3 vom: 03. Dez., Seite 759-799 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:81 year:2018 number:3 day:03 month:12 pages:759-799 https://doi.org/10.1007/s11538-018-0535-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 42.00 VZ AR 81 2018 3 03 12 759-799 |
| allfieldsSound |
10.1007/s11538-018-0535-y doi (DE-627)OLC2087103518 (DE-He213)s11538-018-0535-y-p DE-627 ger DE-627 rakwb eng 570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Krause, Andrew L. verfasserin aut Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. Turing patterns Growing surfaces Anisotropic growth Pattern selection Pattern robustness Ellis, Meredith A. aut Van Gorder, Robert A. (orcid)0000-0002-8506-3961 aut Enthalten in Bulletin of mathematical biology Springer US, 1973 81(2018), 3 vom: 03. Dez., Seite 759-799 (DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 0092-8240 nnns volume:81 year:2018 number:3 day:03 month:12 pages:759-799 https://doi.org/10.1007/s11538-018-0535-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 42.00 VZ AR 81 2018 3 03 12 759-799 |
| language |
English |
| source |
Enthalten in Bulletin of mathematical biology 81(2018), 3 vom: 03. Dez., Seite 759-799 volume:81 year:2018 number:3 day:03 month:12 pages:759-799 |
| sourceStr |
Enthalten in Bulletin of mathematical biology 81(2018), 3 vom: 03. Dez., Seite 759-799 volume:81 year:2018 number:3 day:03 month:12 pages:759-799 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Turing patterns Growing surfaces Anisotropic growth Pattern selection Pattern robustness |
| dewey-raw |
570 |
| isfreeaccess_bool |
false |
| container_title |
Bulletin of mathematical biology |
| authorswithroles_txt_mv |
Krause, Andrew L. @@aut@@ Ellis, Meredith A. @@aut@@ Van Gorder, Robert A. @@aut@@ |
| publishDateDaySort_date |
2018-12-03T00:00:00Z |
| hierarchy_top_id |
129391719 |
| dewey-sort |
3570 |
| id |
OLC2087103518 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2087103518</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230401103505.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230302s2018 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11538-018-0535-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2087103518</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11538-018-0535-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">570</subfield><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">12</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIODIV</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">42.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krause, Andrew L.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Turing patterns</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Growing surfaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anisotropic growth</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pattern selection</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pattern robustness</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ellis, Meredith A.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van Gorder, Robert A.</subfield><subfield code="0">(orcid)0000-0002-8506-3961</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Bulletin of mathematical biology</subfield><subfield code="d">Springer US, 1973</subfield><subfield code="g">81(2018), 3 vom: 03. Dez., Seite 759-799</subfield><subfield code="w">(DE-627)129391719</subfield><subfield code="w">(DE-600)184905-0</subfield><subfield code="w">(DE-576)014776863</subfield><subfield code="x">0092-8240</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:81</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:3</subfield><subfield code="g">day:03</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:759-799</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11538-018-0535-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-BIODIV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">42.00</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">81</subfield><subfield code="j">2018</subfield><subfield code="e">3</subfield><subfield code="b">03</subfield><subfield code="c">12</subfield><subfield code="h">759-799</subfield></datafield></record></collection>
|
| author |
Krause, Andrew L. |
| spellingShingle |
Krause, Andrew L. ddc 570 ssgn 12 fid BIODIV bkl 42.00 misc Turing patterns misc Growing surfaces misc Anisotropic growth misc Pattern selection misc Pattern robustness Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds |
| authorStr |
Krause, Andrew L. |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)129391719 |
| format |
Article |
| dewey-ones |
570 - Life sciences; biology 510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0092-8240 |
| topic_title |
570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds Turing patterns Growing surfaces Anisotropic growth Pattern selection Pattern robustness |
| topic |
ddc 570 ssgn 12 fid BIODIV bkl 42.00 misc Turing patterns misc Growing surfaces misc Anisotropic growth misc Pattern selection misc Pattern robustness |
| topic_unstemmed |
ddc 570 ssgn 12 fid BIODIV bkl 42.00 misc Turing patterns misc Growing surfaces misc Anisotropic growth misc Pattern selection misc Pattern robustness |
| topic_browse |
ddc 570 ssgn 12 fid BIODIV bkl 42.00 misc Turing patterns misc Growing surfaces misc Anisotropic growth misc Pattern selection misc Pattern robustness |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Bulletin of mathematical biology |
| hierarchy_parent_id |
129391719 |
| dewey-tens |
570 - Life sciences; biology 510 - Mathematics |
| hierarchy_top_title |
Bulletin of mathematical biology |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)129391719 (DE-600)184905-0 (DE-576)014776863 |
| title |
Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds |
| ctrlnum |
(DE-627)OLC2087103518 (DE-He213)s11538-018-0535-y-p |
| title_full |
Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds |
| author_sort |
Krause, Andrew L. |
| journal |
Bulletin of mathematical biology |
| journalStr |
Bulletin of mathematical biology |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2018 |
| contenttype_str_mv |
txt |
| container_start_page |
759 |
| author_browse |
Krause, Andrew L. Ellis, Meredith A. Van Gorder, Robert A. |
| container_volume |
81 |
| class |
570 510 VZ 12 ssgn BIODIV DE-30 fid 42.00 bkl |
| format_se |
Aufsätze |
| author-letter |
Krause, Andrew L. |
| doi_str_mv |
10.1007/s11538-018-0535-y |
| normlink |
(ORCID)0000-0002-8506-3961 |
| normlink_prefix_str_mv |
(orcid)0000-0002-8506-3961 |
| dewey-full |
570 510 |
| title_sort |
influence of curvature, growth, and anisotropy on the evolution of turing patterns on growing manifolds |
| title_auth |
Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds |
| abstract |
Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. © The Author(s) 2018 |
| abstractGer |
Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. © The Author(s) 2018 |
| abstract_unstemmed |
Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth. © The Author(s) 2018 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC FID-BIODIV SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 |
| container_issue |
3 |
| title_short |
Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds |
| url |
https://doi.org/10.1007/s11538-018-0535-y |
| remote_bool |
false |
| author2 |
Ellis, Meredith A. Van Gorder, Robert A. |
| author2Str |
Ellis, Meredith A. Van Gorder, Robert A. |
| ppnlink |
129391719 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s11538-018-0535-y |
| up_date |
2024-07-03T13:39:34.579Z |
| _version_ |
1803565373406052352 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2087103518</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230401103505.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230302s2018 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11538-018-0535-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2087103518</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11538-018-0535-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">570</subfield><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">12</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIODIV</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">42.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krause, Andrew L.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction–diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains. We find that in some parameter regimes, some of these factors have a negligible effect on the long-time patterned state. On the other hand, we find that some of these factors play a role in determining the patterns formed on surfaces and that anisotropic growth can produce qualitatively different patterns to those formed under isotropic growth.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Turing patterns</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Growing surfaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Anisotropic growth</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pattern selection</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pattern robustness</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ellis, Meredith A.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van Gorder, Robert A.</subfield><subfield code="0">(orcid)0000-0002-8506-3961</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Bulletin of mathematical biology</subfield><subfield code="d">Springer US, 1973</subfield><subfield code="g">81(2018), 3 vom: 03. Dez., Seite 759-799</subfield><subfield code="w">(DE-627)129391719</subfield><subfield code="w">(DE-600)184905-0</subfield><subfield code="w">(DE-576)014776863</subfield><subfield code="x">0092-8240</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:81</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:3</subfield><subfield code="g">day:03</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:759-799</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11538-018-0535-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-BIODIV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">42.00</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">81</subfield><subfield code="j">2018</subfield><subfield code="e">3</subfield><subfield code="b">03</subfield><subfield code="c">12</subfield><subfield code="h">759-799</subfield></datafield></record></collection>
|
| score |
7.401636 |