메뉴 건너뛰기




Volumn 84, Issue 3, 2006, Pages 281-299

Twisted elastic rings and the rediscoveries of Michell's instability

Author keywords

Elastic rings; Instability; Kirchhoff rods; Twist

Indexed keywords

COMPUTATION THEORY; DNA; PROBLEM SOLVING;

EID: 33746032175     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-006-9055-3     Document Type: Article
Times cited : (75)

References (61)
  • 1
    • 1142290570 scopus 로고
    • On the stability of a bent and twisted wire
    • Michell, J.H.: On the stability of a bent and twisted wire. Messenger of Math. 11, 181-184, (1889-1990)
    • (1889) Messenger of Math. , vol.11 , pp. 181-184
    • Michell, J.H.1
  • 3
    • 0018451173 scopus 로고
    • An elastic model of the large structure of duplex DNA
    • Benham, C.J.: An elastic model of the large structure of duplex DNA. Bioploymers 18, 609-623 (1979)
    • (1979) Bioploymers , vol.18 , pp. 609-623
    • Benham, C.J.1
  • 4
    • 0020856954 scopus 로고
    • Geometry and mechanics of DNA superhelicity
    • Benham, C.J.: Geometry and mechanics of DNA superhelicity. Biopolymers 22, 2477-2495 (1983)
    • (1983) Biopolymers , vol.22 , pp. 2477-2495
    • Benham, C.J.1
  • 6
    • 0000323998 scopus 로고    scopus 로고
    • A continuum rod model of sequence-dependent DNA structure
    • Manning, R.S., Maddocks, J.H., Kahn, J.D.: A continuum rod model of sequence-dependent DNA structure. J. Chem. Phys. 105, 5626-5646 (1996)
    • (1996) J. Chem. Phys. , vol.105 , pp. 5626-5646
    • Manning, R.S.1    Maddocks, J.H.2    Kahn, J.D.3
  • 7
    • 38249021749 scopus 로고
    • On the curving and twining of stems
    • Silk, W.K.; On the curving and twining of stems. Environmental Exp. Bot. 29, 95-109 (1989)
    • (1989) Environmental Exp. Bot. , vol.29 , pp. 95-109
    • Silk, W.K.1
  • 8
    • 0001031397 scopus 로고    scopus 로고
    • Spontaneous helix-hand reversal and tendril perversion in climbing plants
    • Goriely, A., Tabor, M.: Spontaneous helix-hand reversal and tendril perversion in climbing plants. Phys. Rev. Lett. 80, 1564-1567 (1998)
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 1564-1567
    • Goriely, A.1    Tabor, M.2
  • 10
    • 33746036631 scopus 로고    scopus 로고
    • Bifurcation theory, symmetry breaking and homogenization in continuum mechanics descriptions of DNA
    • Givoli, M.J., Grote, D., Papanicolaou, G. (eds.) Kluwer
    • Maddocks, J.H.: Bifurcation theory, symmetry breaking and homogenization in continuum mechanics descriptions of DNA. In: Givoli, M.J., Grote, D., Papanicolaou, G. (eds.) A Celebration of Mathematical Modeling: The Joseph B. Keller Anniversary Volume, pp. 113-136. Kluwer (2004)
    • (2004) A Celebration of Mathematical Modeling: The Joseph B. Keller Anniversary Volume , pp. 113-136
    • Maddocks, J.H.1
  • 12
    • 0001773307 scopus 로고
    • The small deformation of curves and surfaces with applications to the vibration of a helix and a circular ring
    • Michell, J.H.: The small deformation of curves and surfaces with applications to the vibration of a helix and a circular ring. Messenger of Math. 19, 68-82 (1889-90)
    • (1889) Messenger of Math. , vol.19 , pp. 68-82
    • Michell, J.H.1
  • 14
    • 3042748647 scopus 로고
    • The wave resistance formula of J.H. Michell (1898) and its significance to recent research in ship hydrodynamics
    • Tuck, E.O.: The wave resistance formula of J.H. Michell (1898) and its significance to recent research in ship hydrodynamics. J. Austral. Math. Soc. Ser. B 30, 365-377 (1989)
    • (1989) J. Austral. Math. Soc. Ser. B , vol.30 , pp. 365-377
    • Tuck, E.O.1
  • 17
    • 1142266283 scopus 로고
    • On the deformation of thin elastic wires
    • Basset, A.B.: On the deformation of thin elastic wires. Amer. J. Math. 17, 281-317 (1895)
    • (1895) Amer. J. Math. , vol.17 , pp. 281-317
    • Basset, A.B.1
  • 19
    • 0019668063 scopus 로고
    • Large buckled states of nonlinearly elastic rods under torsion, thrust and gravity
    • Antman, S.S., Kenney, C.S.: Large buckled states of nonlinearly elastic rods under torsion, thrust and gravity. Arch. Ration. Mech. Analysis 84, 289-338 (1981)
    • (1981) Arch. Ration. Mech. Analysis , vol.84 , pp. 289-338
    • Antman, S.S.1    Kenney, C.S.2
  • 20
    • 85024530638 scopus 로고
    • Stability of two planar loop elasticas
    • March
    • Zajac, E.E.: Stability of two planar loop elasticas. ASME J. Applied Mech. 29, 136-142 (March 1962)
    • (1962) ASME J. Applied Mech. , vol.29 , pp. 136-142
    • Zajac, E.E.1
  • 21
    • 0015040327 scopus 로고
    • The writhing number of a space curve
    • Fuller, F.B.: The writhing number of a space curve. Proc. Nat. Acad. Sci. 68, 815-819 (1971)
    • (1971) Proc. Nat. Acad. Sci. , vol.68 , pp. 815-819
    • Fuller, F.B.1
  • 22
    • 0017886919 scopus 로고
    • Decomposition of the linking number of a closed ribbon: A problem from molecular biology
    • Fuller, F.B.: Decomposition of the linking number of a closed ribbon: A problem from molecular biology. Proc. Natl. Acad. Sci. 78, 3557-3561 (1978)
    • (1978) Proc. Natl. Acad. Sci. , vol.78 , pp. 3557-3561
    • Fuller, F.B.1
  • 23
    • 0000816797 scopus 로고
    • Elastic model of supercoiling
    • Benham, C.J.: Elastic model of supercoiling. Proc. Nat. Acad. Sci. USA 74, 2397-2401 (1977)
    • (1977) Proc. Nat. Acad. Sci. USA , vol.74 , pp. 2397-2401
    • Benham, C.J.1
  • 24
    • 0018393775 scopus 로고
    • Catastrophic variations of twist and writhing of circular DNA with constraint?
    • LeBret, M.: Catastrophic variations of twist and writhing of circular DNA with constraint? Biopolymers 18, 1709-1725 (1979)
    • (1979) Biopolymers , vol.18 , pp. 1709-1725
    • LeBret, M.1
  • 25
    • 0021133086 scopus 로고
    • Twist and writhing in short circular DNA according to first-order elasticity
    • LeBret, M.: Twist and writhing in short circular DNA according to first-order elasticity. Biopolymers 23, 1835-1867 (1984)
    • (1984) Biopolymers , vol.23 , pp. 1835-1867
    • LeBret, M.1
  • 26
    • 0000511427 scopus 로고
    • Onset of writhing in circular elastic polymers
    • Benham, C.J.: Onset of writhing in circular elastic polymers. Phys. Rev. A 39, 2582-2586 (1989)
    • (1989) Phys. Rev. A , vol.39 , pp. 2582-2586
    • Benham, C.J.1
  • 28
    • 0027577107 scopus 로고
    • The effect of intrinsic curvature on supercoiling-Predictions of elasticity theory
    • Tobias, I., Olson, W.K.: The effect of intrinsic curvature on supercoiling-Predictions of elasticity theory. Biopolymers 33, 639-646 (1993)
    • (1993) Biopolymers , vol.33 , pp. 639-646
    • Tobias, I.1    Olson, W.K.2
  • 29
    • 0000091323 scopus 로고
    • Finite element analysis of DNA supercoiling
    • Yang, Y., Tobias, I., Olson, W.K.: Finite element analysis of DNA supercoiling. J. Chem. Phys. 98, 1673-1686 (1993)
    • (1993) J. Chem. Phys. , vol.98 , pp. 1673-1686
    • Yang, Y.1    Tobias, I.2    Olson, W.K.3
  • 30
    • 21344484976 scopus 로고
    • A new twist in the kinematics and elastic dynamics of thin filaments and ribbons
    • Klapper, I., Tabor, M.: A new twist in the kinematics and elastic dynamics of thin filaments and ribbons. J. Phys. A 27, 4919-4924 (1994)
    • (1994) J. Phys. A , vol.27 , pp. 4919-4924
    • Klapper, I.1    Tabor, M.2
  • 31
    • 0029066852 scopus 로고
    • Modeling superhelical DNA: Recent analytical and dynamical approaches
    • Schlick, T.: Modeling superhelical DNA: Recent analytical and dynamical approaches. Curr. Opin. Struct. Biol. 5, 245-262 (1995)
    • (1995) Curr. Opin. Struct. Biol. , vol.5 , pp. 245-262
    • Schlick, T.1
  • 32
    • 0001192419 scopus 로고
    • Formulae for the calculation and estimation of writhe
    • Aldinger, J., Klapper, I., Tabor, M.: Formulae for the calculation and estimation of writhe. J. Knot Theory 4, 243-372 (1995)
    • (1995) J. Knot Theory , vol.4 , pp. 243-372
    • Aldinger, J.1    Klapper, I.2    Tabor, M.3
  • 33
    • 0002803267 scopus 로고    scopus 로고
    • Nonlinear dynamics of filaments I: Dynamical instabilities
    • Goriely, A., Tabor, M.: Nonlinear dynamics of filaments I: Dynamical instabilities. Physica D 105, 20-44 (1997)
    • (1997) Physica D , vol.105 , pp. 20-44
    • Goriely, A.1    Tabor, M.2
  • 34
    • 0030825156 scopus 로고    scopus 로고
    • Configurational transitions in Fourier series-represented DNA supercoils
    • Liu, G.H., Schlick, T., Olson, A.J., Olson, W.K.: Configurational transitions in Fourier series-represented DNA supercoils. Biophys. J. 73, 1742-1762 (1997)
    • (1997) Biophys. J. , vol.73 , pp. 1742-1762
    • Liu, G.H.1    Schlick, T.2    Olson, A.J.3    Olson, W.K.4
  • 35
    • 0031559721 scopus 로고    scopus 로고
    • Modeling self-contact forces in the elastic theory of DNA supercoiling
    • Westcott, T.P., Tobias, I., Olson, W.K.: Modeling self-contact forces in the elastic theory of DNA supercoiling. J. Chem. Phys. 107, 3967-3980 (1997)
    • (1997) J. Chem. Phys. , vol.107 , pp. 3967-3980
    • Westcott, T.P.1    Tobias, I.2    Olson, W.K.3
  • 36
    • 0035950960 scopus 로고    scopus 로고
    • Biopolymer mechanics: Stability, dynamics, and statistics
    • Wiggins, C.H.: Biopolymer mechanics: Stability, dynamics, and statistics. Math. Methods Appl. Sci. 24, 1325-1335 (2001)
    • (2001) Math. Methods Appl. Sci. , vol.24 , pp. 1325-1335
    • Wiggins, C.H.1
  • 37
    • 22244457390 scopus 로고    scopus 로고
    • Nonlinear dynamics of filaments. II, Nonlinear analysis
    • Goriely, A., Tabor, M.: Nonlinear dynamics of filaments. II, Nonlinear analysis. Physica D 105, 45-61 (1997)
    • (1997) Physica D , vol.105 , pp. 45-61
    • Goriely, A.1    Tabor, M.2
  • 38
    • 33746795125 scopus 로고    scopus 로고
    • Nonlinear dynamics of filaments. III. Instabilities of helical rods
    • Goriely, A., Tabor, M.: Nonlinear dynamics of filaments. III. Instabilities of helical rods. Proc. Roy. Soc. London (A) 453, 2583-2601 (1997)
    • (1997) Proc. Roy. Soc. London (A) , vol.453 , pp. 2583-2601
    • Goriely, A.1    Tabor, M.2
  • 39
    • 33746386391 scopus 로고    scopus 로고
    • Nonlinear dynamics of filaments. IV. The spontaneous looping of twisted elastic rods
    • Goriely, A., Tabor, M.: Nonlinear dynamics of filaments. IV. The spontaneous looping of twisted elastic rods. Proc. Roy. Soc. London (A) 455, 3183-3202 (1998)
    • (1998) Proc. Roy. Soc. London (A) , vol.455 , pp. 3183-3202
    • Goriely, A.1    Tabor, M.2
  • 40
    • 0034894261 scopus 로고    scopus 로고
    • Stability of n-covered circles for elastic rods with constant planar intrinsic curvature
    • Manning, R.S., Hoffman, K.A.: Stability of n-covered circles for elastic rods with constant planar intrinsic curvature. J. Elasticity 62, 456-479 (2001)
    • (2001) J. Elasticity , vol.62 , pp. 456-479
    • Manning, R.S.1    Hoffman, K.A.2
  • 41
    • 0141960819 scopus 로고    scopus 로고
    • Link, twist, energy, and the stability of DNA minicircles
    • Hoffman, K.A., Manning, R.S., Maddocks, J.H.: Link, twist, energy, and the stability of DNA minicircles. Biopolymers 70, 145-157 (2003)
    • (2003) Biopolymers , vol.70 , pp. 145-157
    • Hoffman, K.A.1    Manning, R.S.2    Maddocks, J.H.3
  • 42
    • 0037253308 scopus 로고    scopus 로고
    • On the stability of elastic annular rods
    • Lembo, M.: On the stability of elastic annular rods. Int. J. Solids. Structures 40, 317-330 (2003)
    • (2003) Int. J. Solids. Structures , vol.40 , pp. 317-330
    • Lembo, M.1
  • 43
    • 3042528270 scopus 로고    scopus 로고
    • Methods for determining stability in continuum elastic rod-models of DNA
    • Hoffman, K.A.: Methods for determining stability in continuum elastic rod-models of DNA. Phil. Trans. R. Soc. Lond. A 362, 1301-1315 (2004)
    • (2004) Phil. Trans. R. Soc. Lond. A , vol.362 , pp. 1301-1315
    • Hoffman, K.A.1
  • 44
    • 0005613646 scopus 로고    scopus 로고
    • Knot types, homotopies and stability of closed elastic rods
    • Ivey, T.A., Singer, D.A.: Knot types, homotopies and stability of closed elastic rods. Proc. London Math. Soc. 3, 429-450 (1999)
    • (1999) Proc. London Math. Soc. , vol.3 , pp. 429-450
    • Ivey, T.A.1    Singer, D.A.2
  • 45
    • 0000417766 scopus 로고    scopus 로고
    • A class of exact dynamical solutions in the elastic rod model of DNA with implications for the theory of fluctuations in the torsional motion of plasmids
    • Tobias, I., Coleman, B.D., Lembo, M.: A class of exact dynamical solutions in the elastic rod model of DNA with implications for the theory of fluctuations in the torsional motion of plasmids. J. Chem. Phys. 105, 2517-2526 (1996)
    • (1996) J. Chem. Phys. , vol.105 , pp. 2517-2526
    • Tobias, I.1    Coleman, B.D.2    Lembo, M.3
  • 46
    • 0032452370 scopus 로고    scopus 로고
    • Terminal twist induced continuous writhe of a circular rod with intrinsic curvature
    • Qian, H., White, J.H.: Terminal twist induced continuous writhe of a circular rod with intrinsic curvature. J. Biomol. Struct. Dyn. 16, 663-669 (1998)
    • (1998) J. Biomol. Struct. Dyn. , vol.16 , pp. 663-669
    • Qian, H.1    White, J.H.2
  • 47
    • 0000450212 scopus 로고    scopus 로고
    • Spontaneous curvature-induced dynamical instability of Kirchhoff filaments: Application to DNA kink deformations
    • Haijun, Z., Zhong can, O.-Y.: Spontaneous curvature-induced dynamical instability of Kirchhoff filaments: Application to DNA kink deformations. J. Chem. Phys. 110, 1247-1251 (1999)
    • (1999) J. Chem. Phys. , vol.110 , pp. 1247-1251
    • Haijun, Z.1    Zhong Can, O.-Y.2
  • 48
    • 0000216631 scopus 로고    scopus 로고
    • On the dynamics of helical strips
    • Shipman, P., Goriely, A.: On the dynamics of helical strips. Phys. Rev. E 61, 4508-4517 (2000)
    • (2000) Phys. Rev. E , vol.61 , pp. 4508-4517
    • Shipman, P.1    Goriely, A.2
  • 51
    • 22044441704 scopus 로고    scopus 로고
    • Kirchhoff's problem of helical equilibria of uniform rods
    • Chouaieb, N., Maddocks, J.H.: Kirchhoff's problem of helical equilibria of uniform rods. J. Elast. 77, 221-247 (2005)
    • (2005) J. Elast. , vol.77 , pp. 221-247
    • Chouaieb, N.1    Maddocks, J.H.2
  • 52
    • 0033874539 scopus 로고    scopus 로고
    • Nonlinear dynamics of filaments
    • Goriely, A., Tabor, M.: Nonlinear dynamics of filaments. Nonlinear Dyn. 21, 101-133 (2000)
    • (2000) Nonlinear Dyn. , vol.21 , pp. 101-133
    • Goriely, A.1    Tabor, M.2
  • 53
    • 0033764926 scopus 로고    scopus 로고
    • Elastic stability of DNA configurations. I. General theory
    • Tobias, I., Swigon, D., Coleman, B.D.: Elastic stability of DNA configurations. I. General theory. Phys. Rev. E 61, 747-758 (2000)
    • (2000) Phys. Rev. E , vol.61 , pp. 747-758
    • Tobias, I.1    Swigon, D.2    Coleman, B.D.3
  • 54
    • 0033754160 scopus 로고    scopus 로고
    • Elastic stability of DNA configurations. II. Supercoiled plasmids with self-contact
    • Coleman, B.D., Swigon, S., Tobias, I.: Elastic stability of DNA configurations. II. Supercoiled plasmids with self-contact. Phys. Rev. E 61, 759-770 (2000)
    • (2000) Phys. Rev. E , vol.61 , pp. 759-770
    • Coleman, B.D.1    Swigon, S.2    Tobias, I.3
  • 55
    • 0034965398 scopus 로고    scopus 로고
    • Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids
    • Coleman, B.D., Swigon, D.: Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids. J. Elast. 60, 173-221 (2000)
    • (2000) J. Elast. , vol.60 , pp. 173-221
    • Coleman, B.D.1    Swigon, D.2
  • 56
    • 3042586213 scopus 로고    scopus 로고
    • Equilibrium configurations of a thin elastic rod with self-contacts
    • PAMM
    • Starostin, E.L.: Equilibrium configurations of a thin elastic rod with self-contacts. PAMM, Proc. Appl. Math. Mech. 1, 137-138 (2002)
    • (2002) Proc. Appl. Math. Mech. , vol.1 , pp. 137-138
    • Starostin, E.L.1
  • 57
    • 1142303893 scopus 로고    scopus 로고
    • Dynamic supercoiling bifurcation of growing elastic filaments
    • Wolgemuth, C.W., Goldstein, R.E., Powers, T.R.: Dynamic supercoiling bifurcation of growing elastic filaments. Phys. D 190, 266-289 (2004)
    • (2004) Phys. D , vol.190 , pp. 266-289
    • Wolgemuth, C.W.1    Goldstein, R.E.2    Powers, T.R.3
  • 58
    • 0042872746 scopus 로고    scopus 로고
    • Hidden symmetry of global solutions in twisted elastic rings
    • Domokos, G., Healey, T.: Hidden symmetry of global solutions in twisted elastic rings. J. Nonlinear Sci. 11, 47-67 (2001)
    • (2001) J. Nonlinear Sci. , vol.11 , pp. 47-67
    • Domokos, G.1    Healey, T.2
  • 60
    • 0035395730 scopus 로고    scopus 로고
    • Fluctuating elastic rings: Statics and dynamics
    • #0011909
    • Panyukov, S., Rabin, Y.: Fluctuating elastic rings: Statics and dynamics. Phys. Rev. E. 64:#0011909 (2001)
    • (2001) Phys. Rev. E , vol.64
    • Panyukov, S.1    Rabin, Y.2
  • 61
    • 0031957256 scopus 로고    scopus 로고
    • A theory of thermal fluctuations in DNA miniplasmids
    • Tobias, I.: A theory of thermal fluctuations in DNA miniplasmids. Biophysical J. 74, 2545-2553 (1998)
    • (1998) Biophysical J. , vol.74 , pp. 2545-2553
    • Tobias, I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.