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曲面の幾何による進行波のカオス散乱
阪大 理,*東大 理


堀部和也,*廣中謙一,松下勝義,藤本仰一
1
Noneq WS 18/12/27
2
• 1細胞・多細胞組織の表面
https://sites.google.com/site/cienciashumanismocultura/reino-protista
アメーバ細胞
突起(仮足)の形成
PIP3
Collision Fusion Split
[Taniguchi et al. 2013]
仮足
大脳皮質
神経繊維
Rat
• 曲面上の進行波
[Fujita et al. 2015]
脳表面(大脳皮質)
視覚情報処理 Voltage-sensitive dye
実験:生物の表面上では生命現象を駆動する
多彩な進行波が見られる
対象
3
実験:進行波の進行方向が曲面の幾何の
影響を受けることが示唆された
[Santos et al. 2014]
Visual Cortex
Collision
Intrinsic optical signal imaging
皮質のしわの方向に従って進行波が整流される
目的:理論的側面から曲面上の進行波を調べる
ことで生物の形の機能を理解したい
Pig
目的
4
[Kneer et al. 2014]
Donuts
[Macdonald et.al 2013]
Heart
背景
• 曲面による波の進行方向変化 • 曲面による波のトポロジー変化
時間
[in preparation]
モデル:曲面に従って進行波は変形する
曲面の測地線を用いて進行波の経時変化を予測できる
時間 [in preparation]
• 曲面の測地線(最短経路)と進行波が一致する
5
最終的には細胞膜上,器官上の進行波の経時変化を予測・制御したい
• 局所的な設計原理を用いて大域的な進行波の経時変化の設計
• 進行波の局所的な設計原理
Stable
Unstable
0
0
0
0.2
0.4
0.6
0.8
1.0
Gaussian curvature
Positive
Negative
0
x
y
Neutral
問い&戦略
問い:測地線を用いて進行波の経時変化を
設計できるか?
6
方法
モデル:曲面上の進行波
• 反応拡散方程式による進行波
[Nishiura et al. 2005]
u
t = u(1 u)(u a) v
+ d u
v
t = u v
ut = Du u
uv2
1 + f2w
+ f0(1 u)
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vt = Dv v
uv2
1 + f2w
+ (f0 + f1)v
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⌧wt = Dw w + f3(v w)
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d2
xi
dt2
+ i
jk
dxj
dt
dxk
dt
= 0
i
jk =
1
2
gil glj
xk
+
glk
xj
gjk
xl
:Position(i=1,2)
xi
gil
• 測地線方程式(曲面上の最短経路)
:Metric tensor
Christoffel symbols of the second kind
Geodesic equation
3変数のGray-Scott型
ガウス関数
7
曲面による進行波の経時変化の設計例
結果の概要
x
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<latexit sha1_base64="T5eNG1t/rh/1LJqdf1tI18J36qA=">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</latexit>
y
<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit>
<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit>
<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit>
<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit>
z
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
波の進行方向を“そろえる”
波の進行方向を”散らす”
• 波の離合集散を実現するには?
カオス散乱のように”散らす”ことができる
8
b = 0.7
<latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">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</latexit>
<latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">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</latexit>
<latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">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</latexit>
<latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">AAACaHichVHLSsNAFD2Nr1ofrbpQcSMWxVW5EUERhKIbl33YKqhIEkcdTJOQpIVa/AE3LlVcKYiIn+HGH3DRT1CXFdy48DYNiIp6h5k5c+aeO2dmdMeUnk9Ujyht7R2dXdHuWE9vX388MTBY9Oyya4iCYZu2u65rnjClJQq+9E2x7rhCK+mmWNMPlpv7axXhetK2Vv2qI7ZK2p4ld6Wh+UwV9EVKzW0nkpSiIMZ/AjUESYSRsRM32MQObBgoowQBCz5jExo8bhtQQXCY20KNOZeRDPYFjhBjbZmzBGdozB7wuMerjZC1eN2s6QVqg08xubusHMckPdItNeiB7uiJ3n+tVQtqNL1UedZbWuFsx49H8m//qko8+9j/VP3p2ccu5gOvkr07AdO8hdHSVw5PG/mF3GRtiq7ohf1fUp3u+QZW5dW4zorcBWL8Aer35/4JijMplVJqdjaZXgq/IooxTGCa33sOaawggwKfK3GCM5xHnpWEMqyMtlKVSKgZwpdQJj4ABtKK3A==</latexit>
設定: 初期位置を変化させる
x
y
z
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
b
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
曲面を通過後の波の進行方向は測地線で予測できる
b = 0.5
<latexit sha1_base64="HTIAwHa1mlbeO72rqjEI5Hl6+84=">AAACaHichVFNLwNBGH66vqq+igPiIhri1LwrhEgkDRfHFv1ISmR3DSbd7m52t02q8QdcHBEnEhHxM1z8AQc/AUcSFwdvt5sIgncyM8888z7vPDOjO6b0fKKHiNLS2tbeEe2MdXX39PbF+wdynl1xDZE1bNN2C7rmCVNaIutL3xQFxxVaWTdFXi8tN/bzVeF60rbW/ZojNsvariV3pKH5TGX1RUrObsUTlKQgxn4CNQQJhJG241fYwDZsGKigDAELPmMTGjxuRaggOMxtos6cy0gG+wIHiLG2wlmCMzRmSzzu8qoYshavGzW9QG3wKSZ3l5VjmKB7uqYXuqMbeqT3X2vVgxoNLzWe9aZWOFt9h8Nrb/+qyjz72PtU/enZxw7mA6+SvTsB07iF0dRX949f1hZWJ+qTdEHP7P+cHuiWb2BVX43LjFg9Q4w/QP3+3D9BbjqpUlLNzCRSS+FXRDGKcUzxe88hhRWkkeVzJY5wgtPIkxJXhpSRZqoSCTWD+BLK+AcC0ora</latexit>
<latexit sha1_base64="HTIAwHa1mlbeO72rqjEI5Hl6+84=">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</latexit>
<latexit sha1_base64="HTIAwHa1mlbeO72rqjEI5Hl6+84=">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</latexit>
<latexit sha1_base64="HTIAwHa1mlbeO72rqjEI5Hl6+84=">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</latexit>
b = 0.8
進行波と測地線を比較する
進行スポットの経時変化は測地線と一致した
結果
z(x, y) = h exp( (x2
+ y2
))
<latexit sha1_base64="CwwUwyZGdq80AchHvz3ZWq+bjm0=">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</latexit>
<latexit sha1_base64="CwwUwyZGdq80AchHvz3ZWq+bjm0=">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</latexit>
<latexit sha1_base64="CwwUwyZGdq80AchHvz3ZWq+bjm0=">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</latexit>
<latexit sha1_base64="CwwUwyZGdq80AchHvz3ZWq+bjm0=">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</latexit>
9
曲面を通過後のスポットの進行方向(散乱角φ)
は初期位置bに対して連続的に変化する
1000 2000 3000 4000 5000
-1.5
-1.0
-0.5
0.5
1.0
1.5
b
φ
結果
10
h=5
h=1 h=3
h=7
高さhに依存せず散乱角φは連続的に変化する
結果
1000 2000 3000 4000 5000
-0.6
-0.4
-0.2
0.2
0.4
0.6
1000 2000 3000 4000 5000
-1.5
-1.0
-0.5
0.5
1.0
1.5
1000 2000 3000 4000 5000
-1.5
-1.0
-0.5
0.5
1.0
1.5
1000 2000 3000 4000 5000
-1.5
-1.0
-0.5
0.5
1.0
1.5
b
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
0
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2.7
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2.7
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b
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0
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2.7
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2.7
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b
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0
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2.7
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2.7
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b
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0
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<latexit sha1_base64="HFqcAbZDYt70XV1gMAiePXX1DQM=">AAACZHichVHLSsNAFD2Nr1ofrYogCFIsFVflRgTFVdGNS9taW1CRJE5raJqEJC3U4g/oVnHhSkFE/Aw3/oALf0AQlxXcuPA2DYgW9Q4zc+bMPXfOzKi2obse0VNI6unt6x8ID0aGhkdGo7Gx8S3XqjmayGuWYTlFVXGFoZsi7+meIYq2I5SqaoiCWllr7xfqwnF1y9z0GrbYrSplUy/pmuIxlaG9WIJS5Ee8G8gBSCCIDSt2gx3sw4KGGqoQMOExNqDA5bYNGQSbuV00mXMY6f6+wBEirK1xluAMhdkKj2VebQesyet2TddXa3yKwd1hZRxJeqRbatED3dELffxaq+nXaHtp8Kx2tMLeix5P5d7/VVV59nDwpfrTs4cSln2vOnu3faZ9C62jrx+et3Ir2WRzjq7olf1f0hPd8w3M+pt2nRHZC0T4A+Sfz90NthZSMqXkzGIivRp8RRjTmMU8v/cS0ljHBvJ8rsAJTnEWepaGpQlpspMqhQLNBL6FNPMJZkyJsA==</latexit>
2.7
<latexit sha1_base64="ZaM3osAnKuyFuD+9kGdp78PM8Gk=">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</latexit>
<latexit sha1_base64="ZaM3osAnKuyFuD+9kGdp78PM8Gk=">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</latexit>
<latexit sha1_base64="ZaM3osAnKuyFuD+9kGdp78PM8Gk=">AAACZnichVHLSsNAFD2Nr1pfVREFN8WiuCo3Rai4Krpx2YetQi2SxLEG0yQkaaEWf0BwaxeuFETEz3DjD7joHyguK7hx4W0aEBX1DjNz5sw9d87MqLahux5ROyT19Q8MDoWHIyOjY+MT0cmpomvVHE0UNMuwnB1VcYWhm6Lg6Z4hdmxHKFXVENvq0UZ3f7suHFe3zC2vYYtyVamY+oGuKR5T+WQitReNU4L8iP0EcgDiCCJjRW+wi31Y0FBDFQImPMYGFLjcSpBBsJkro8mcw0j39wVOEGFtjbMEZyjMHvFY4VUpYE1ed2u6vlrjUwzuDitjWKRHuqUOPdAdPdP7r7Wafo2ulwbPak8r7L2J07n827+qKs8eDj9Vf3r2cIBV36vO3m2f6d5C6+nrx61Ofi232FyiK3ph/5fUpnu+gVl/1a6zIneBCH+A/P25f4JiMiFTQs6uxNPrwVeEMY8FLPN7p5DGJjIo8LkVnOEcrdCTNC7NSLO9VCkUaKbxJaTYB3+viis=</latexit>
<latexit sha1_base64="ZaM3osAnKuyFuD+9kGdp78PM8Gk=">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</latexit>
2.7
<latexit sha1_base64="GVezLnUH5o+M+5CjsXavEpN2pko=">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</latexit>
<latexit sha1_base64="GVezLnUH5o+M+5CjsXavEpN2pko=">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</latexit>
<latexit sha1_base64="GVezLnUH5o+M+5CjsXavEpN2pko=">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</latexit>
<latexit sha1_base64="GVezLnUH5o+M+5CjsXavEpN2pko=">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</latexit>
11
b = 1.6
<latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit>
<latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit>
<latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit>
<latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit>
b = 1.7
<latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">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</latexit>
<latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">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</latexit>
<latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">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</latexit>
<latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">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</latexit>
b = 1.8
<latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">AAACaHichVHLSsNAFD2Nr1ofrbpQcSMWxVW5EUERhKIbl33YKqhIEkcdTJOQpIVa/AE3LlVcKYiIn+HGH3DRT1CXFdy48DYNiIp6h5k5c+aeO2dmdMeUnk9Ujyht7R2dXdHuWE9vX388MTBY9Oyya4iCYZu2u65rnjClJQq+9E2x7rhCK+mmWNMPlpv7axXhetK2Vv2qI7ZK2p4ld6Wh+UwV9EU1Nb+dSFKKghj/CdQQJBFGxk7cYBM7sGGgjBIELPiMTWjwuG1ABcFhbgs15lxGMtgXOEKMtWXOEpyhMXvA4x6vNkLW4nWzpheoDT7F5O6ychyT9Ei31KAHuqMnev+1Vi2o0fRS5VlvaYWzHT8eyb/9qyrx7GP/U/WnZx+7mA+8SvbuBEzzFkZLXzk8beQXcpO1KbqiF/Z/SXW65xtYlVfjOityF4jxB6jfn/snKM6kVEqp2dlkein8iijGMIFpfu85pLGCDAp8rsQJznAeeVYSyrAy2kpVIqFmCF9CmfgACtSK3g==</latexit>
<latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">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</latexit>
<latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">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</latexit>
<latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">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</latexit>
z(x, y) = hxy exp( (x2
+ y2
))
<latexit sha1_base64="/vV1WGkd7OBhxMWPGxfSg7IrIAk=">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</latexit>
<latexit sha1_base64="/vV1WGkd7OBhxMWPGxfSg7IrIAk=">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</latexit>
<latexit sha1_base64="/vV1WGkd7OBhxMWPGxfSg7IrIAk=">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</latexit>
<latexit sha1_base64="/vV1WGkd7OBhxMWPGxfSg7IrIAk=">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</latexit>
x
y
z
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">AAACZHichVHLSsNAFD2Nr1qrrRZBEKRYFFflRgTFlejGpbX2AVVKEkcNTZOQpIVa/AHdKi5cKYiIn+HGH3DRHxDEZQU3LrxNA6Ki3mFmzpy5586ZGdU2dNcjaoWknt6+/oHwYGQoOjwSi4+O5V2r5mgip1mG5RRVxRWGboqcp3uGKNqOUKqqIQpqZa2zX6gLx9Utc8tr2GKnquyb+p6uKR5TmcNyPEVp8iP5E8gBSCGIDSt+g23swoKGGqoQMOExNqDA5VaCDILN3A6azDmMdH9f4AgR1tY4S3CGwmyFx31elQLW5HWnpuurNT7F4O6wMokZeqRbatMD3dEzvf9aq+nX6Hhp8Kx2tcIux44nsm//qqo8ezj4VP3p2cMelnyvOnu3faZzC62rrx+et7PLmzPNWbqiF/Z/SS265xuY9VftOiM2LxDhD5C/P/dPkJ9Py5SWMwupldXgK8KYxDTm+L0XsYJ1bCDH5wqc4BRnoScpKiWk8W6qFAo0CXwJaeoD+kyJ+g==</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
<latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit>
b
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
<latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit>
進行方向(散乱角φ)は初期位置を
少しずらすと大きく変化する
h=1
設定: 初期位置を変化させる
進行波と測地線を比較する
結果
181226noneq
181226noneq
181226noneq
181226noneq
181226noneq

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181226noneq

  • 2. 2 • 1細胞・多細胞組織の表面 https://sites.google.com/site/cienciashumanismocultura/reino-protista アメーバ細胞 突起(仮足)の形成 PIP3 Collision Fusion Split [Taniguchi et al. 2013] 仮足 大脳皮質 神経繊維 Rat • 曲面上の進行波 [Fujita et al. 2015] 脳表面(大脳皮質) 視覚情報処理 Voltage-sensitive dye 実験:生物の表面上では生命現象を駆動する 多彩な進行波が見られる 対象
  • 3. 3 実験:進行波の進行方向が曲面の幾何の 影響を受けることが示唆された [Santos et al. 2014] Visual Cortex Collision Intrinsic optical signal imaging 皮質のしわの方向に従って進行波が整流される 目的:理論的側面から曲面上の進行波を調べる ことで生物の形の機能を理解したい Pig 目的
  • 4. 4 [Kneer et al. 2014] Donuts [Macdonald et.al 2013] Heart 背景 • 曲面による波の進行方向変化 • 曲面による波のトポロジー変化 時間 [in preparation] モデル:曲面に従って進行波は変形する 曲面の測地線を用いて進行波の経時変化を予測できる 時間 [in preparation] • 曲面の測地線(最短経路)と進行波が一致する
  • 6. 6 方法 モデル:曲面上の進行波 • 反応拡散方程式による進行波 [Nishiura et al. 2005] u t = u(1 u)(u a) v + d u v t = u v ut = Du u uv2 1 + f2w + f0(1 u) <latexit sha1_base64="SA7s6ep9iKDOvb1duLdOG0V9290=">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</latexit> <latexit sha1_base64="SA7s6ep9iKDOvb1duLdOG0V9290=">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</latexit> <latexit sha1_base64="SA7s6ep9iKDOvb1duLdOG0V9290=">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</latexit> <latexit sha1_base64="SA7s6ep9iKDOvb1duLdOG0V9290=">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</latexit> vt = Dv v uv2 1 + f2w + (f0 + f1)v <latexit sha1_base64="0WqknVjBpeJpC1HA2mtH3R++UuY=">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</latexit> <latexit 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  • 7. 7 曲面による進行波の経時変化の設計例 結果の概要 x <latexit sha1_base64="T5eNG1t/rh/1LJqdf1tI18J36qA=">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</latexit> <latexit 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sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit> 波の進行方向を“そろえる” 波の進行方向を”散らす” • 波の離合集散を実現するには? カオス散乱のように”散らす”ことができる
  • 8. 8 b = 0.7 <latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">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</latexit> <latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">AAACaHichVHLSsNAFD2Nr1ofrbpQcSMWxVW5EUERhKIbl33YKqhIEkcdTJOQpIVa/AE3LlVcKYiIn+HGH3DRT1CXFdy48DYNiIp6h5k5c+aeO2dmdMeUnk9Ujyht7R2dXdHuWE9vX388MTBY9Oyya4iCYZu2u65rnjClJQq+9E2x7rhCK+mmWNMPlpv7axXhetK2Vv2qI7ZK2p4ld6Wh+UwV9EVKzW0nkpSiIMZ/AjUESYSRsRM32MQObBgoowQBCz5jExo8bhtQQXCY20KNOZeRDPYFjhBjbZmzBGdozB7wuMerjZC1eN2s6QVqg08xubusHMckPdItNeiB7uiJ3n+tVQtqNL1UedZbWuFsx49H8m//qko8+9j/VP3p2ccu5gOvkr07AdO8hdHSVw5PG/mF3GRtiq7ohf1fUp3u+QZW5dW4zorcBWL8Aer35/4JijMplVJqdjaZXgq/IooxTGCa33sOaawggwKfK3GCM5xHnpWEMqyMtlKVSKgZwpdQJj4ABtKK3A==</latexit> <latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">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</latexit> <latexit sha1_base64="pbfYpJt79hOdkGAuRh+NA3m/kpQ=">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</latexit> 設定: 初期位置を変化させる x y z <latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit> <latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit> <latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit> <latexit sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">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</latexit> b <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">AAACZHichVHLSsNAFD2Nr1ofrYogCFIsFVflRgTFVdGNS9taW1CRJE5raJqEJC3U4g/oVnHhSkFE/Aw3/oALf0AQlxXcuPA2DYgW9Q4zc+bMPXfOzKi2obse0VNI6unt6x8ID0aGhkdGo7Gx8S3XqjmayGuWYTlFVXGFoZsi7+meIYq2I5SqaoiCWllr7xfqwnF1y9z0GrbYrSplUy/pmuIxlVH3YglKkR/xbiAHIIEgNqzYDXawDwsaaqhCwITH2IACl9s2ZBBs5nbRZM5hpPv7AkeIsLbGWYIzFGYrPJZ5tR2wJq/bNV1frfEpBneHlXEk6ZFuqUUPdEcv9PFrraZfo+2lwbPa0Qp7L3o8lXv/V1Xl2cPBl+pPzx5KWPa96uzd9pn2LbSOvn543sqtZJPNObqiV/Z/SU90zzcw62/adUZkLxDhD5B/Pnc32FpIyZSSM4uJ9GrwFWFMYxbz/N5LSGMdG8jzuQInOMVZ6FkaliakyU6qFAo0E/gW0swnykyJ4g==</latexit> <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit> <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit> <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit> 曲面を通過後の波の進行方向は測地線で予測できる b = 0.5 <latexit sha1_base64="HTIAwHa1mlbeO72rqjEI5Hl6+84=">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</latexit> <latexit 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sha1_base64="HTIAwHa1mlbeO72rqjEI5Hl6+84=">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</latexit> <latexit sha1_base64="HTIAwHa1mlbeO72rqjEI5Hl6+84=">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</latexit> b = 0.8 進行波と測地線を比較する 進行スポットの経時変化は測地線と一致した 結果 z(x, y) = h exp( (x2 + y2 )) <latexit 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  • 10. 10 h=5 h=1 h=3 h=7 高さhに依存せず散乱角φは連続的に変化する 結果 1000 2000 3000 4000 5000 -0.6 -0.4 -0.2 0.2 0.4 0.6 1000 2000 3000 4000 5000 -1.5 -1.0 -0.5 0.5 1.0 1.5 1000 2000 3000 4000 5000 -1.5 -1.0 -0.5 0.5 1.0 1.5 1000 2000 3000 4000 5000 -1.5 -1.0 -0.5 0.5 1.0 1.5 b <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit> <latexit 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sha1_base64="GVezLnUH5o+M+5CjsXavEpN2pko=">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</latexit> <latexit sha1_base64="GVezLnUH5o+M+5CjsXavEpN2pko=">AAACZ3ichVHLSsNAFD2Nr1ofrQpScKOWihvLjQiKK9GNy/qoLdRSkjjVYJqEJC3U4g+4cKvgSkFE/Aw3/oALP6G4rODGhTdpQLSod5iZM2fuuXNmRrUN3fWIXiJST29f/0B0MDY0PDIaT4yN77lWzdFETrMMyymoiisM3RQ5T/cMUbAdoVRVQ+TV4w1/P18Xjqtb5q7XsEWpqhyaekXXFM+nFhYzy+VEijIUxHQ3kEOQQhhZK3GHfRzAgoYaqhAw4TE2oMDlVoQMgs1cCU3mHEZ6sC9wihhra5wlOENh9pjHQ14VQ9bktV/TDdQan2Jwd1g5jTQ90z216YkeqEUfv9ZqBjV8Lw2e1Y5W2OX4WXLn/V9VlWcPR1+qPz17qGAl8Kqzdztg/FtoHX395KK9s7qdbs7RDb2y/2t6oUe+gVl/0263xPYVYvwB8s/n7gZ7ixmZMvLWUmptPfyKKKYwi3l+72WsYRNZ5PjcI5zjApeRlhSXJqVkJ1WKhJoJfAtp5hP/mopi</latexit>
  • 11. 11 b = 1.6 <latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit> <latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit> <latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit> <latexit sha1_base64="KXwshrXXb7ckLV5g2p1F0zr2Z/g=">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</latexit> b = 1.7 <latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">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</latexit> <latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">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</latexit> <latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">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</latexit> <latexit sha1_base64="591Ns1f2JqMyEmAWdVcXJ/NapfI=">AAACaHichVHLSsNAFD2Nr1ofrbpQcSMWxVW5EUERhKIbl33YKqhIEkcdTJOQpIVa/AE3LlVcKYiIn+HGH3DRT1CXFdy48DYNiIp6h5k5c+aeO2dmdMeUnk9Ujyht7R2dXdHuWE9vX388MTBY9Oyya4iCYZu2u65rnjClJQq+9E2x7rhCK+mmWNMPlpv7axXhetK2Vv2qI7ZK2p4ld6Wh+UwV9EU1NbedSFKKghj/CdQQJBFGxk7cYBM7sGGgjBIELPiMTWjwuG1ABcFhbgs15lxGMtgXOEKMtWXOEpyhMXvA4x6vNkLW4nWzpheoDT7F5O6ychyT9Ei31KAHuqMnev+1Vi2o0fRS5VlvaYWzHT8eyb/9qyrx7GP/U/WnZx+7mA+8SvbuBEzzFkZLXzk8beQXcpO1KbqiF/Z/SXW65xtYlVfjOityF4jxB6jfn/snKM6kVEqp2dlkein8iijGMIFpfu85pLGCDAp8rsQJznAeeVYSyrAy2kpVIqFmCF9CmfgACNSK3Q==</latexit> b = 1.8 <latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">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</latexit> <latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">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</latexit> <latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">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</latexit> <latexit sha1_base64="/SVPpEYl+FP9yNzQDRakBiIyYXs=">AAACaHichVHLSsNAFD2Nr1ofrbpQcSMWxVW5EUERhKIbl33YKqhIEkcdTJOQpIVa/AE3LlVcKYiIn+HGH3DRT1CXFdy48DYNiIp6h5k5c+aeO2dmdMeUnk9Ujyht7R2dXdHuWE9vX388MTBY9Oyya4iCYZu2u65rnjClJQq+9E2x7rhCK+mmWNMPlpv7axXhetK2Vv2qI7ZK2p4ld6Wh+UwV9EU1Nb+dSFKKghj/CdQQJBFGxk7cYBM7sGGgjBIELPiMTWjwuG1ABcFhbgs15lxGMtgXOEKMtWXOEpyhMXvA4x6vNkLW4nWzpheoDT7F5O6ychyT9Ei31KAHuqMnev+1Vi2o0fRS5VlvaYWzHT8eyb/9qyrx7GP/U/WnZx+7mA+8SvbuBEzzFkZLXzk8beQXcpO1KbqiF/Z/SXW65xtYlVfjOityF4jxB6jfn/snKM6kVEqp2dlkein8iijGMIFpfu85pLGCDAp8rsQJznAeeVYSyrAy2kpVIqFmCF9CmfgACtSK3g==</latexit> z(x, y) = hxy exp( (x2 + y2 )) <latexit 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sha1_base64="9fic6A8G+DmZBGiKEjiO1nNUJwk=">AAACZHichVHLSsNAFD2Nr1qrrRZBEKRYFFflRgTFlejGpbX2AVVKEkcNTZOQpIVa/AHdKi5cKYiIn+HGH3DRHxDEZQU3LrxNA6Ki3mFmzpy5586ZGdU2dNcjaoWknt6+/oHwYGQoOjwSi4+O5V2r5mgip1mG5RRVxRWGboqcp3uGKNqOUKqqIQpqZa2zX6gLx9Utc8tr2GKnquyb+p6uKR5TmcNyPEVp8iP5E8gBSCGIDSt+g23swoKGGqoQMOExNqDA5VaCDILN3A6azDmMdH9f4AgR1tY4S3CGwmyFx31elQLW5HWnpuurNT7F4O6wMokZeqRbatMD3dEzvf9aq+nX6Hhp8Kx2tcIux44nsm//qqo8ezj4VP3p2cMelnyvOnu3faZzC62rrx+et7PLmzPNWbqiF/Z/SS265xuY9VftOiM2LxDhD5C/P/dPkJ9Py5SWMwupldXgK8KYxDTm+L0XsYJ1bCDH5wqc4BRnoScpKiWk8W6qFAo0CXwJaeoD+kyJ+g==</latexit> <latexit 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sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">AAACZHichVHLSsNAFD2Nr1ofrYogCFIsFVflRgTFVdGNS9taW1CRJE5raJqEJC3U4g/oVnHhSkFE/Aw3/oALf0AQlxXcuPA2DYgW9Q4zc+bMPXfOzKi2obse0VNI6unt6x8ID0aGhkdGo7Gx8S3XqjmayGuWYTlFVXGFoZsi7+meIYq2I5SqaoiCWllr7xfqwnF1y9z0GrbYrSplUy/pmuIxlVH3YglKkR/xbiAHIIEgNqzYDXawDwsaaqhCwITH2IACl9s2ZBBs5nbRZM5hpPv7AkeIsLbGWYIzFGYrPJZ5tR2wJq/bNV1frfEpBneHlXEk6ZFuqUUPdEcv9PFrraZfo+2lwbPa0Qp7L3o8lXv/V1Xl2cPBl+pPzx5KWPa96uzd9pn2LbSOvn543sqtZJPNObqiV/Z/SU90zzcw62/adUZkLxDhD5B/Pnc32FpIyZSSM4uJ9GrwFWFMYxbz/N5LSGMdG8jzuQInOMVZ6FkaliakyU6qFAo0E/gW0swnykyJ4g==</latexit> <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit> <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit> <latexit sha1_base64="69XD92zTOgvkRlljhJSuppYvvRQ=">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</latexit> 進行方向(散乱角φ)は初期位置を 少しずらすと大きく変化する h=1 設定: 初期位置を変化させる 進行波と測地線を比較する 結果