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\u306f\u3058\u3081\u306b<\/h2>\n\n\n\n

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\u00a0\u30ad\u30fc\u30ef\u30fc\u30c9:<\/strong>\u3000\u3000<\/td>\u30bd\u30d5\u30c8\u30de\u30bf\u30fc\u7269\u7406\u3001\u7d71\u8a08\u7269\u7406\u3001\u9ad8\u5206\u5b50\u7269\u7406\u3001\u30c8\u30dd\u30ed\u30b8\u30fc\u3001\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u3001\u81ea\u5df1\u6392\u9664\u30a6\u30a9\u30fc\u30af\u3001\u7d50\u3073\u76ee\u3068\u7d61\u307f\u76ee\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3001\u30b0\u30e9\u30d5\u7406\u8ad6\u3001\u6e2c\u5ea6\u8ad6<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u9ad8\u5206\u5b50\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u5883\u754c\u6f14\u7b97\u5b50\u3092\u5229\u7528\u3057\u305f\u89e3\u6790<\/h1>\n\n\n\n

\u80cc\u666f<\/h2>\n\n\n\n

\u9ad8\u5206\u5b50\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u4e00\u90e8\u3092\u7a7a\u9593\u7684\u306b\u56fa\u5b9a\u3057\u305f\u5834\u5408\u306e\u5206\u914d\u95a2\u6570\u306f\u3001James\u306b\u3088\u3063\u3066Kirchhoff\u884c\u5217\u306e\u884c\u5217\u5f0f\u3092\u4f7f\u3063\u3066\u793a\u3055\u308c\u307e\u3057\u305f[1]\u3002\u96fb\u6c17\u56de\u8def\u3068\u306e\u30a2\u30ca\u30ed\u30b8\u30fc\u304b\u3089\u3001\u9ad8\u5206\u5b50\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u5f3e\u6027\u306f\u62b5\u6297\u8ddd\u96e2\u306b\u3088\u3063\u3066\u8868\u3055\u308c\u307e\u3059\u3002\u30d5\u30a1\u30f3\u30c8\u30e0\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u67b6\u6a4b\u9396\u30d9\u30af\u30c8\u30eb\u306e\u63fa\u3089\u304e\u306f\u3001\u67b6\u6a4b\u70b9\u306e\u5206\u5c90\u6570\u3092f\u3068\u3059\u308b\u30682\/\ud835\udc53\u306b\u6bd4\u4f8b\u3059\u308b\u3068Flory\u306b\u3088\u3063\u3066\u4e88\u60f3\u3055\u308c\u307e\u3057\u305f[2]\u3002Kloczkowski\u306f\u5185\u90e8\u306b\u591a\u6570\u306e\u679d\u5206\u304b\u308c\u3092\u542b\u3080\u9ad8\u5206\u5b50\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u3001\u7aef\u3092\u56fa\u5b9a\u3057\u305f\u7121\u9650\u306b\u5927\u304d\u3044\u6728\u69cb\u9020\u306e\u30b0\u30e9\u30d5\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3057\u3001Flory\u306e\u4e88\u60f3\u304c\u3053\u306e\u5834\u5408\u306b\u304a\u3044\u3066\u6b63\u3057\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f[3-4]\u3002Kloczkowski\u306e\u30e2\u30c7\u30eb\u306e\u7814\u7a76\u306f\u73fe\u5728\u3067\u3082\u7d9a\u3051\u3089\u308c\u3066\u304a\u308a\u3001\u6700\u8fd1\u3067\u306f\u30eb\u30fc\u30d7\u3084\u30c0\u30f3\u30b0\u30ea\u30f3\u30b0\u306a\u3069\u69cb\u9020\u306b\u4e0d\u5747\u4e00\u306a\u90e8\u5206\u3092\u542b\u3080\u5834\u5408\u306e\u89e3\u304c\u8a08\u7b97\u3055\u308c\u3066\u3044\u307e\u3059[5-7]\u3002<\/p>\n\n\n\n

[1]H.M. James, “Statistical Properties of Networks of Flexible Chains”, J. Chem. Phys. 15 (1947).
[2]P.J. Flory, “Statistical thermodynamics of random networks”, Proc. R. Soc. Lond. A 351 (1976).
[3]A. Kloczkowski, J.E. Mark and B. Erman, “Chain Dimensions and Fluctuations in Random Elastomeric Networks. 1. Phantom Gaussian Networks in the Undeformed State”, Macromolecules 22 (1989).
[4]B. Erman, A. Kloczkowski and J.E. Mark, “Chain Dimensions and Fluctuations in Random Elastomeric Networks. 2. Dependence of Chain Dimensions and Fluctuations on Macroscopic Strain”, Macromolecules 22 (1989).
[5]M. Zhong et al., “Quantifying the impact of molecular defects on polymer network elasticity”, Science 353 (2016).
[6]M. Lang, “On the Elasticity of Polymer Model Networks Containing Finite Loops”, Macromolecules 52 (2019).
[7]T.-S. Lin et al., “Revisiting the Elasticity Theory for Real Gaussian Phantom Networks”, Macromolecules 52 (2019).<\/p>\n\n\n\n

\u51fa\u53e3\u7814\u7a76\u5ba4\u306e\u7814\u7a76\u306e\u4f8b<\/h2>\n\n\n\n

\u3000\u5f93\u6765\u306e\u7406\u8ad6\u3067\u306f\u3001\u9ad8\u5206\u5b50\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u4e00\u90e8\u3092\u7a7a\u9593\u306b\u56fa\u5b9a\u3057\u306a\u3044\u3068\u5206\u914d\u95a2\u6570\u304c\u767a\u6563\u3057\u3066\u3057\u307e\u3044\u307e\u3057\u305f\u3002\u4e00\u65b9\u3067\u3001\u63fa\u3089\u304e\u306e\u8a08\u7b97\u7d50\u679c\u306f\u3001\u3069\u306e\u70b9\u3092\u56fa\u5b9a\u3059\u308b\u304b\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u51fa\u53e3\u7814\u7a76\u5ba4\u3067\u306f\u3001\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3057\u3001\u56fa\u5b9a\u70b9\u306e\u306a\u3044\u9ad8\u5206\u5b50\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e2\u70b9\u76f8\u95a2\u3092\u30b0\u30e9\u30d5\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u306e\u64ec\u9006\u884c\u5217\u3092\u4f7f\u3063\u3066\u8868\u3057\u307e\u3057\u305f\u3002\u3053\u306e\u65b9\u6cd5\u306b\u3088\u308b\u89e3\u6790\u3067\u3001\u591a\u69d8\u306a\u7a2e\u985e\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u63fa\u3089\u304e\u306b\u3064\u3044\u3066\u306e\u4e88\u60f32\/\ud835\udc53\u304c\u6210\u7acb\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u3088\u3063\u3066\u691c\u8a3c\u3057\u3001\u4e00\u90e8\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u3064\u3044\u3066\u306f2\/\ud835\udc53\u306b\u6f38\u8fd1\u3059\u308b\u53b3\u5bc6\u89e3\u3092\u5f97\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

 \u2460\u683c\u5b50\u72b6\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u67b6\u6a4b\u9396\u30d9\u30af\u30c8\u30eb\u306e\u63fa\u3089\u304e:\u4e00\u8fba\u306e\u683c\u5b50\u70b9\u6570\u304c\ud835\udc41\u306e\ud835\udc37\u6b21\u5143\u5468\u671f\u5883\u754c\u6761\u4ef6\u3092\u6301\u3064\u7acb\u65b9\u683c\u5b50\u306e\u67b6\u6a4b\u9396\u30d9\u30af\u30c8\u30eb\u306e\u63fa\u3089\u304e\u306f\u3001\u67b6\u6a4b\u70b9\u306e\u5206\u5c90\u6570\ud835\udc53=2\ud835\udc37\u3068\u3057\u3066\u3001\u53b3\u5bc6\u306b\u3001<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u3068\u306a\u308b\u3053\u3068\u3092\u793a\u305b\u307e\u3059\u3002\u3053\u308c\u306fN\u304c\u5341\u5206\u5927\u304d\u3044\u6642\u306bFlory\u306e\u4e88\u60f32\/f\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u2461\u6b63\u5247\u30b0\u30e9\u30d5\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u67b6\u6a4b\u9396\u30d9\u30af\u30c8\u30eb\u306e\u63fa\u3089\u304e:McKay\u306e\u6c42\u3081\u305f\u6b63\u5247\u30b0\u30e9\u30d5\u306e\u56fa\u6709\u5024\u30b9\u30da\u30af\u30c8\u30e9\u30e0[1]\u304b\u3089\u5c0e\u304b\u308c\u3001<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u00a0\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\ud835\udc53\u304c\u5927\u304d\u3044\u6642\u306b2\/\ud835\udc53\u306b\u4e00\u81f4\u3057\u307e\u3059\u3002\u6b63\u5247\u30b0\u30e9\u30d5\u306f\u5c40\u6240\u7684\u306b\u306f\u30c4\u30ea\u30fc\u69cb\u9020\u306b\u8fd1\u3044\u305f\u3081\u3001\u5f93\u6765\u306e\u30c4\u30ea\u30fc\u578b\u30b0\u30e9\u30d5\u3092\u7528\u3044\u305f\u30e2\u30c7\u30eb\u306e\u7d50\u679c[2]\u306b\u5bfe\u5fdc\u3059\u308b\u3068\u8003\u3048\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u2462\u5206\u5c90\u6570\u3092\u4fdd\u5b58\u3057\u305f\u307e\u307e\u30e9\u30f3\u30c0\u30e0\u5165\u308c\u66ff\u3048\u3092\u884c\u3063\u305f\u30cd\u30c3\u30c8\u30ef\u30fc\u30af(\u4e0b\u56f3)\u306e\u67b6\u6a4b\u9396\u30d9\u30af\u30c8\u30eb\u306e\u63fa\u3089\u304e:\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u7528\u3044\u3066\u3001\ud835\udc53=3\u223c8\u306e\u9593\u3067\u307b\u307c2\/\ud835\udc53\u3067\u3042\u308b\u3053\u3068\u3092\u691c\u8a3c\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

[1]B.D. McKay, “The Expected Eigenvalue Distribution of a Large Regular Graph”,\u00a0Linear Algebra and its Applications<\/em>\u00a040<\/strong>\u00a0(1981).[2]A. Kloczkowski, J.E. Mark and B. Erman, “Chain Dimensions and Fluctuations in Random Elastomeric Networks. 1. Phantom Gaussian Networks in the Undeformed State”,\u00a0Macromolecules<\/em>\u00a022<\/strong>\u00a0(1989).

\u95a2\u9023\u3059\u308b\u51fa\u53e3\u7814\u7a76\u5ba4\u306e\u696d\u7e3e(\u4e00\u90e8)<\/strong>
[1]J. Cantarella, T. Deguchi, C. Shonkwiler and E. Uehara, “Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers”,\u00a0arXiv<\/em>:2004.06199 (2020).
[2]J. Cantarella, T. Deguchi, C. Shonkwiler and E. Uehara, “Gaussian Random Embeddings of Multigraphs”,\u00a0arXiv<\/em>:2001.11709 (2020).
[3]J. Cantarella, T. Deguchi, C. Shonkwiler and E. Uehara, “Random graph embeddings with general edge potentials”,\u00a0arXiv<\/em>:2205.09049 (2022).
[4]\u51fa\u53e3\u54f2\u751f\u3001J. \u30ab\u30f3\u30bf\u30ec\u30e9\u3001C. \u30b7\u30e7\u30fc\u30f3\u30af\u30ef\u30a4\u30e9\u30fc\u3001\u4e0a\u539f\u6075\u7406\u9999\u3001\u65e5\u672c\u7269\u7406\u5b66\u4f1a77\u56de\u5e74\u6b21\u5927\u4f1a\u3000\u53e3\u982d\u8b1b\u6f14

\u203b\u3053\u306e\u30c6\u30fc\u30de\u306fCREST\u53d7\u8a17\u7814\u7a76\u300c\u9ad8\u5206\u5b50\u5f3e\u6027\u306e\u30db\u30e2\u30ed\u30b8\u30fc\u7684\u30c8\u30dd\u30ed\u30b8\u30fc\u7406\u8ad6\u306e\u69cb\u7bc9\u3068\u74b0\u72b6\u6df7\u5408\u30c7\u30d0\u30a4\u30b9(\u7814\u7a76\u4ee3\u8868\u8005:\u51fa\u53e3\u54f2\u751f)\u300d\u306e\u652f\u63f4\u306e\u3082\u3068\u884c\u308f\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u9ad8\u5206\u5b50\u9396\u306e\u7d61\u307f\u5408\u3044\u3001\u7d50\u3073\u76ee\u306e\u7814\u7a76\u00a0<\/h1>\n\n\n\n

\u80cc\u666f\u00a0<\/h2>\n\n\n\n

\u3000\u5927\u8178\u83cc\u306a\u3069\u4e00\u90e8\u306e\u7d30\u83cc\u306f\u74b0\u72b6DNA\u3092\u6301\u3063\u3066\u304a\u308a\u3001DNA\u30c8\u30dd\u30a4\u30bd\u30e1\u30e9\u30fc\u30bc\u3092\u4f7f\u3046\u3053\u3068\u3067DNA\u306b\u7d50\u3073\u76ee\u3092\u751f\u3058\u308b\u3053\u3068\u304c\u3001\u96fb\u5b50\u9855\u5fae\u93e1\u5199\u771f\u3067\u76f4\u63a5\u78ba\u8a8d\u3055\u308c\u3066\u3044\u307e\u3059[1]\u3002\u7d50\u3073\u76ee\u3092\u751f\u3058\u305f\u9ad8\u5206\u5b50\u306f\u901a\u5e38\u3088\u308a\u5c0f\u3055\u304f\u306a\u308b\u306e\u3067\u3001\u6eb6\u5a92\u4e2d\u3067\u306e\u79fb\u52d5\u901f\u5ea6\u304c\u5909\u5316\u3057\u3001\u96fb\u6c17\u6cf3\u52d5\u306b\u3088\u3063\u3066\u5206\u96e2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059[2]\u3002\u307e\u305f\u6700\u8fd1\u3067\u3082\u3001\u7d50\u3073\u76eeDNA\u3092\u7d30\u5b54\u3092\u901a\u3057\u3066\u5206\u96e2\u3059\u308b\u5b9f\u9a13\u304c\u884c\u308f\u308c\u307e\u3057\u305f[3]\u3002\u3053\u308c\u3089\u306e\u5b9f\u9a13\u306f\u3001\u9ad8\u5206\u5b50\u540c\u58eb\u306e\u7d61\u307f\u5408\u3044\u304c\u5b9f\u969b\u306b\u7269\u6027\u306b\u5f71\u97ff\u3059\u308b\u3053\u3068\u3092\u7aef\u7684\u306b\u793a\u3057\u3066\u304a\u308a\u3001\u30d0\u30eb\u30af\u306e\u7269\u8cea\u3067\u3082\u7d61\u307f\u5408\u3044\u304c\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

[1]M.A. Krasnow, A. Stasiak, S.J. Spengler, F. Dean, T. Koller and N.R. Cozzarelli, “Determination of the absolute handedness of knots and catenanes of DNA”,\u00a0Nature<\/em>\u00a0304<\/strong>\u00a0(1983).
[2]V.V. Rybenkov,\u00a0et al.<\/em>, “Probability of DNA knotting and the effective diameter of the DNA double helix”,\u00a0PNAS USA<\/em>\u00a090<\/strong>\u00a0(1993).[3]C. Plesa,\u00a0et al.<\/em>, “Direct observation of DNA knots using a solid-state nanopore”,\u00a0Nature Nanotech.<\/em>\u00a011<\/strong>\u00a0(2016).<\/p>\n\n\n\n

\u51fa\u53e3\u7814\u7a76\u5ba4\u306e\u7814\u7a76\u306e\u4f8b\u00a0<\/h2>\n\n\n\n

\u3000\u51fa\u53e3\u7814\u7a76\u5ba4\u3067\u958b\u767a\u3057\u305f\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u3092\u4f7f\u3044\u3001\u74b0\u72b6\u9ad8\u5206\u5b50\u9396\u306e\u7d50\u3073\u76ee\u78ba\u7387\u304a\u3088\u3073\u6163\u6027\u534a\u5f84\u306e\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u6307\u6570\u3092\u8a08\u7b97\u3057\u3066\u3044\u307e\u3059[1]\u3002\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u306e\u958b\u767a\u3092\u884c\u3046\u4e2d\u3067\u3001\u5f93\u6765\u306f\u96e3\u3057\u304b\u3063\u305f\u675f\u7e1b\u6761\u4ef6\u306e\u3042\u308b\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306e\u9ad8\u901f\u751f\u6210\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u958b\u767a\u3057\u3001\u6761\u4ef6\u3092\u6e80\u305f\u3059\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u3092\u7d71\u8a08\u7684\u306b\u4e00\u69d8\u306b\u72b6\u614b\u7a7a\u9593\u304b\u3089\u53d6\u308a\u51fa\u305b\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f[2,3]\u3002\u6700\u8fd1\u3067\u306f\u74b0\u72b6\u4ee5\u5916\u306e\u69d8\u3005\u306a\u5f62\u72b6\u306e\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306b\u304a\u3051\u308b\u81ea\u5df1\u7d61\u307f\u5408\u3044\u306e\u78ba\u7387\u3092\u8a08\u7b97\u3057[4]\u3001\u307e\u305f\u4f38\u9577\u3057\u305f\u3068\u304d\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306e\u5909\u5316\u304b\u3089\u5f3e\u6027\u529b\u3092\u8a55\u4fa1\u3057\u3001\u30d5\u30a1\u30f3\u30c8\u30e0\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u304a\u3051\u308bMooney-Rivlin\u5247\u306e\u518d\u73fe\u3092\u76ee\u6307\u3057\u3066\u3044\u307e\u3059[5]\u3002<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

\u00a0\u95a2\u9023\u3059\u308b\u51fa\u53e3\u7814\u7a76\u5ba4\u306e\u696d\u7e3e(\u4e00\u90e8)<\/h4>\n\n\n\n

[1]N. Hirayama, K. Tsurusaki and T. Deguchi, “Linking probabilities of off-lattice self-avoiding polygons and the effects of excluded volume”,\u00a0J. Phys. A: Math. Theor.<\/em>\u00a042<\/strong>\u00a0(2009) 105001.
[2]J. Cantarella, T. Deguchi and C. Shonkwiler, “Probability Theory of Random Polygons from the Quaternionic Viewpoint”,\u00a0Comm. Pure Appl. Math.<\/em>\u00a067<\/strong>\u00a0(2014) 1658-1699.
[3]J. Cantarella, B. Duplantier, C. Shonkwiler, and E. Uehara, “A fast direct sampling algorithm for equilateral closed polygons”,\u00a0J. Phys. A: Math. Theor.<\/em>\u00a049<\/strong>\u00a0(2016) 275202.
[4]E. Uehara and T. Deguchi, “Statistical and hydrodynamic properties of double-ring polymers with a fixed linking number between twin rings”,\u00a0J. Chem. Phys.<\/em>\u00a0140<\/strong>\u00a0(2014) 044902.
[5]in preparation.<\/em><\/p>\n\n\n\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

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