CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="390"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "royalsocietypublishing.org",cType: 'managed',cRay: '928bef8e9f4ef92c',cH: '5afxP4SmpPsTvaFcXTN1SR0moxcNX8bBk5FKpsBQ1qY-1743383098-1.2.1.1-KicAzcaHB.6GAF_7sqjo0t_.yKhWChnfCV9f.Ecz3m6EFlTS9eDRMlACmrU7kUN2',cUPMDTk: "\/doi\/10.1098\/rspa.2006.1760?__cf_chl_tk=htLGLo9XxG4J3_V4YnADak0FFtcBPs6t9RSL4MUtgDE-1743383098-1.0.1.1-BsKBXoQEjn_Wxt53LYSQXk_OE3oFbfBVkxllxeNrq3U",cFPWv: 'b',cITimeS: '1743383098',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/doi\/10.1098\/rspa.2006.1760?__cf_chl_f_tk=htLGLo9XxG4J3_V4YnADak0FFtcBPs6t9RSL4MUtgDE-1743383098-1.0.1.1-BsKBXoQEjn_Wxt53LYSQXk_OE3oFbfBVkxllxeNrq3U",md: "KFQJl5c8qCasVtZP1389VZ4tejMDyV8RYbpTfnRwNOU-1743383098-1.2.1.1-D4Th84cdfEqq.2gwaHXhrPnTppARwjQRHUPz2AFPiKHllYOrYfUWgnX9YVkNzE0TMs1cCYggDO3OZ53Qwzxw7f6fJUed7jk.kyjrWvfdSlWNf2ZyZ5KhHZsToZppuvR6vDtF5DXDPjUGdbbWEn4jrEWtQNPnkj3YNblmDjdXuc_kBfuD9cGrXDtfRvymLS7kB7KeKTwrIcM9ZDQUVvxI_Q5SKaHFES.wOrtLJeoikazNeMs3qVPa2oPE8zY99Plo0d7JEZ_K3IsSF7xuB75YwhcDhE61kuoD0HW2DArzX1UXFiH0DwYf6tlSkYKWPvfZsYf6eUam6_fJTZttuT7A5Nx1UmkWOr3kaHnDTzdDPpIUTmNq83fatTWBoWvRyYJLfeohkMt75Cr0CKWct9zFlo9QFqwdy4S8M6vpv6LwVxkaIaUZsD5Y69kzHGvt7L1mdsprit19HlVWOOH0PwAnioupyUl2W7fTkTJaAZccepF2Mbt_Fk.Cu3AiM6q.ZYoOuCM4Rsjw4ZA3kFAGo3vyCiKAIi.OQ9pCGMq3TkPEwPrLKkrkATiJcCFHtNphNLerk_Z0MGN339R_gyMeAfkw91mEeZdq6mNxR.r7DI5X8DuLDZ_nmu.pwK2_wQBOw6oecz14mTeOtkDDKleC1hAFSd5cyWsgwt7JTQUN134H3gAxJhYOfcwGTu7nGJ9AIjDX2i0k1Viv9rkBkFCtgkLlkmgkvmZdyOEONtg6fxpxkhZGU5SSMDz3dTXcaueN8DqotOW7yLPg4nRXXo_EcT.x0YENScfLoHy5mLAlmhViKZaMI8.9uIbwLcoSH9C3rkbSKGca7iUBVqEnf0pr3QtWOd200_yRh2tJ7L71DDWaxCBaNjaXAEid6fepvvlWS0mIQkyirviZ2W6WuDSzec.RRGTx9UKRvnvJfrIEyzLz6QC88OXKx1CeNqRRXffpNNZ4UHOPGAESdWGoaPvXBfS9.hEibHXQkw7p0CWZPHng4fS8hHfD7_jQDe6lH4zpQlS26w6_7wQ9YJQ0ZIbDw35RnUVmpB5SpkOvA4yh_CE4QRvYS7k0G47ms7HoUoC9x7pIXP.DEN0n5Hw9lMahx9uAzdiQwh.D3_XpdFm1kGGo6R6btmm3CYFusOoGOdopoyduJDfxz1bF50ppnWPAfomljWMdbGily2JQ40QU6OIWNKWPHcekFz47tmAgcEuN5nJEW1WiVcUuFhQKQOec9C0hkxY1zKN_nZI5peypJIVmHIUoqjBKxRuA9ilJbLsyyghcxCTHTJHKwMFlc4MuGseg9g",mdrd: "C7NVuFxRBUBU2yzBQab.i3y9C1eqYPKaBv0IUIQ7hck-1743383098-1.2.1.1-KranBndYGbr5feoXFTHOA2hfQXu8SYIR_UtGa6Ryx3Ie.BAOXGvRM9S8XRlz1gZzcFjHdyyJe0A2lzmsryrOjA66QNsESnOnXiXrCdWarMuCc6xlOHnbxB9fIB_nijyloH.myGAKzGhpyJpthcCpMAZCDey9n3tJtSs9OGqV7PQUd7G1_DiYWER6BVBK3Bs.bFnDTm22k7T_Bal7VcuQkqv3IKx6aURyaYUjx3J0aj_1Fs3XedqrRbA6XW3YtWYXXYi13KGZ_ZUB87T2siZcP9k7HJ2Qv8vjjnr_Zpz_3sD72Rd.3UP3IUUJnosJUVG2YLlyHgsrcj9r.ZIcZhv9P7Yoru.RsuSU0h_xoAqZII4iniHx5s6hzdGOeAHWeTKveP8XCUado8QisvdL2n6o4DvIUaqcHhbKP6yky_yfuBme_wEDztoyd1ze4CmknZSg8MkCxUpIscK6VparV.4.UQPWyDBmnjNKOiwQK2eGPvRQHTnCWog5g16KmhO.UzVq5D.go8rWShLtuf40m.c1AQFLdj36tWWuDAo5KMn49UZblJegEGL4SByGtpTIUVFBRz0LEnworq2O_8bhPIyO5J1hymBJF767EDpQ31QCzUEp0VZgippVFKZoyKLbUenUqK3Fl37VCC0SmS3LGb.RsbG4lqhjcN38QQluC8uEokYbqOdGpjcruo3uH2NjFP6hF2GMTTVe3e__tOZNPm6JVyvkENbFHIm6K7oXsZXoHK.5qhREkUioy2387AuwZ9PXeWk8hHEdxSz2Qz.bW1GXkb0XrxNZaAX2GZZ_vZrh3mI3xP3kX_X7pW1nlOLjiSqgfW2Dc6tmSiJxb2AItizlP_VLsXIirEQzSpO9_2ko2pBM4jIYq9XM85MqoqIAVlCq8iwfqGpWduJg7bk8LVs0nXWUog4I18i_Rlo2s36UMQyv3_IpGwJCovfVJHsofPed.BR0aVmA0A.AQuuQQ3h1GYNWWRJiiYqDXZXvUAR28nyBJPcplB8QEtM.ognKGv9YJHvQF6vMOY3ogg4xMU01HWGxek0x2ZGieDwQwA1H2QfjOUi8BBSuSuDD4vd5z_P4dXwA8gF8_bsjgNV5g11jsKygS5zvfZCwqmT2DMM1aTf5AMlzRd2gwRfdEEay1J_l3OqyKLU_94uMQcMnJo1PcC.8cdAtM1DsraGPkzaqi28c0SKbrCj6Nig_LaIDZmPEzjQtbBca9ZN2WUWJWUuilqBKRdcyaq2IM7tggdVWtP8jjh5pyqyxuMbJ4TRY7dO7iJbEahIqCG_ehE7PcDSLHhu_3Xbx5SliFOuDv2euzG3ehghNGFjQ1.AkHkrAPM1dcCjS4UIsXf8Vo0nNFznFDUwvk0A4Eh4Cj8jagF.etAogiK3V1soY7AE.j9xEPnRyhRpvXVEIbf3oJojZ4pISpfOXuuWfeco8MoBuk8Y2.k4dsbuNO8a6HzPdM_t69tEjq7ACR8oUIm_lrGgYDbXjRZEXYqB0vYMlcLG9liLIXrlOYjdIbp.7iffChJ3dBOIBN_m.0xmj8aqZ5jp44UUpb8h5VB20AGe52CYWLML1T3IYneUMrDIKJ0tR5MVYgl3rnN6.8SR0XkL8sWqy1wHqXg7xbA.tzkly4QsvxoIWbI5Lql.7tOwp8y3Wf3Whou6qWrcuyMMTa4pudy3M2kLXyC.GPtf8TqbeZ9ivrKmD1DI8Ush2AKdcNLcQbSuZGinCOVHDjEy4ZcMAP5FPR3esbB.O1rDbAGAK4VvBET_zef0Ebmz0eu4wVYbmTxtt7hBDv68bnJMU7Bvdm52B63ShaWTn8B1vBkmz5_XbG7jI9mTdl6p7kuTFQybBUMQ2OUDKwrDsp5.QU12gJejF9kNCKGggamC6z9PTUGHWYkgL4NT4qVC5s.3GbSvbHungz6KL9_OIfK255Hhdg_U7IHiipV2EtYIQcZ01TAtMTOnQefp4jahvCFG.hA4W3lrm_89V1PamR6RaxXdjwLlQK.kAvjfCYSDsW0ZaHbVYv_tQ2KKK4XEoKtAJP1rZklqeZDruGYGbqxp3AhzJ06KubZQ5AQAp9ffZP59JVm5VEuCrE9Y"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=928bef8e9f4ef92c';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/doi\/10.1098\/rspa.2006.1760?__cf_chl_rt_tk=htLGLo9XxG4J3_V4YnADak0FFtcBPs6t9RSL4MUtgDE-1743383098-1.0.1.1-BsKBXoQEjn_Wxt53LYSQXk_OE3oFbfBVkxllxeNrq3U" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>