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Bibliography

ABWZ02
O. Agam, E. Bettelheim, P. Wiegmann, and A. Zabrodin.
Viscous fingering and the shape of an Electronic droplet in the Quantum hall regime.
Phys. Rev. Lett., 88:236801, 2002.

AM01
Giovanni Alberti and Stefan Müller.
A new approach to variational problems with multiple scales.
Comm. Pure Appl. Math., 54(7):761-825, 2001.

Att84
H. Attouch.
Variational convergence for functions and operators.
Pitman (Advanced Publishing Program), Boston, MA, 1984.

BAP97
M. Ben Amar and Y. Pomeau.
Crumpled paper.
Proc. Roy. Soc. London Ser. A, 453:729, 1997.

Bar79
G. I. Barenblatt.
Similarity, self-similarity, and intermediate asymptotics.
Consultants Bureau [Plenum], New York, 1979.
Translated from the Russian by Norman Stein, Translation edited by Milton Van Dyke, With a foreword by Ya. B. Zel'dovich [Ja. B. Zel'dovic].

BBCDM00
H. Ben Belgacem, S. Conti, A. DeSimone, and S. Müller.
Rigorous bounds for the Föppl-von Kármán theory of isotropically compressed plates.
J. Nonlinear Sci., 10(6):661-683, 2000.

BCK+99
Michael P. Brenner, Peter Constantin, Leo P. Kadanoff, Alain Schenkel, and Shankar C. Venkataramani.
Diffusion, attraction and collapse.
Nonlinearity, 12(4):1071-1098, 1999.

Bet90
Fabrice Bethuel.
Approximation in Sobolev spaces between two manifolds and homotopy groups.
In Variational methods (Paris, 1988), pages 239-249. Birkhäuser Boston, Boston, MA, 1990.

BN98
Piotr Biler and Tadeusz Nadzieja.
A nonlocal singular parabolic problem modelling gravitational interaction of particles.
Adv. Differential Equations, 3(2):177-197, 1998.

Bra75
S. A. Brazovskii.
Phase transition of an isotropic system to a nonuniform state.
Sov. Phys. JETP, 41:85, 1975.

CH93
M. C. Cross and P. C. Hohenberg.
Pattern-formation outside of equilibrium.
Rev. Mod. Phys., 65:854, 1993.

CM98
E. Cerda and L. Mahadevan.
Concical surfaces and crescent singularities in crumpled sheets.
Phys. Rev. Lett., 80:2354, 1998.

CMG98
S. Chaïeb, F. Melo, and J-C. Géminard.
Experimental study of developable cones.
Phys. Rev. Lett., 80:2358, 1998.

Con00
Sergio Conti.
Branched microstructures: scaling and asymptotic self-similarity.
Comm. Pure Appl. Math., 53(11):1448-1474, 2000.

Cop87
S. N. Coppersmith.
Overdamped Frenkel-Kontorova model with randomness as a dynamical system: mode locking and derivation of discrete maps.
Phys. Rev. A (3), 36(7):3375-3382, 1987.

Cro88
M. C. Cross.
Theoretical methods in pattern formation in physics, chemistry and biology.
In Far from equilibrium phase transitions (Sitges, 1988), pages 45-74. Springer, Berlin, 1988.

Dac89
Bernard Dacorogna.
Direct methods in the calculus of variations.
Springer-Verlag, Berlin, 1989.

DGDM83
Ennio De Giorgi and Gianni Dal Maso.
$ \Gamma$-convergence and calculus of variations.
In Mathematical theories of optimization (Genova, 1981), pages 121-143. Springer, Berlin, 1983.

DKM98
P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin.
New results on the equilibrium measure for logarithmic potentials in the presence of an external field.
J. Approx. Theory, 95(3):388-475, 1998.

DKMO00
Antonio DeSimone, Robert V. Kohn, Stefan Müller, and Felix Otto.
Magnetic microstructures--a paradigm of multiscale problems.
In ICIAM 99 (Edinburgh), pages 175-190. Oxford Univ. Press, Oxford, 2000.

DM93
Gianni Dal Maso.
An introduction to $ \Gamma$-convergence.
Birkhäuser Boston Inc., Boston, MA, 1993.

DWVK01
B. A. DiDonna, T. A. Witten, S. C. Venkataramani, and E. M. Kramer.
Singularities, structures and scaling in deformed elastic m-sheets.
To appear in Phys. Rev. E, 2001.

EL78
J. Eells and L. Lemaire.
A report on harmonic maps.
Bull. London Math. Soc., 10(1):1-68, 1978.

EL88
J. Eells and L. Lemaire.
Another report on harmonic maps.
Bull. London Math. Soc., 20(5):385-524, 1988.

Eva90
Lawrence C. Evans.
Weak convergence methods for nonlinear partial differential equations.
Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1990.

Eva98
Lawrence C. Evans.
Partial differential equations.
American Mathematical Society, Providence, RI, 1998.

FKMZ00
C. Fermanian Kammerer, F. Merle, and H. Zaag.
Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view.
Math. Ann., 317(2):347-387, 2000.

FPD01
Mitchell J. Feigenbaum, Itamar Procaccia, and Benny Davidovich.
Dynamics of finger formation in Laplacian growth without surface tension.
J. Statist. Phys., 103(5-6):973-1007, 2001.

GL99
J. P. Gollub and J. S. Langer.
Pattern formation in nonequilibrium physics.
Rev. Mod. Phys., 71:S396, 1999.

Gro86
Mikhael Gromov.
Partial differential relations.
Springer-Verlag, Berlin, 1986.

Hin91
E. J. Hinch.
Perturbation methods.
Cambridge University Press, Cambridge, 1991.

HKD02
Taylor L. Hughes, A. D. Klironomos, and Alan T Dorsey.
Fingering of electron droplets in nonuniform magnetic fields.
preprint, September 2002.

HL98
M. B. Hastings and L. S. Levitov.
Laplacian growth as one-dimensional turbulence.
Physica D, 116(1-2):244-252, 1998.

HMV97
M. A. Herrero, E. Medina, and J. J. L. Velázquez.
Finite-time aggregation into a single point in a reaction-diffusion system.
Nonlinearity, 10(6):1739-1754, 1997.

HMV98
M. A. Herrero, E. Medina, and J. J. L. Velázquez.
Self-similar blow-up for a reaction-diffusion system.
J. Comput. Appl. Math., 97(1-2):99-119, 1998.

HV96
Miguel A. Herrero and Juan J. L. Velázquez.
Chemotactic collapse for the Keller-Segel model.
J. Math. Biol., 35(2):177-194, 1996.

HV97
Miguel A. Herrero and Juan J. L. Velázquez.
A blow-up mechanism for a chemotaxis model.
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24(4):633-683 (1998), 1997.

JK00
W. Jin and R. V. Kohn.
Singular perturbation and the energy of folds.
J. Nonlinear Sci., 10(3):355-390, 2000.

JL92
W. Jäger and S. Luckhaus.
On explosions of solutions to a system of partial differential equations modelling chemotaxis.
Trans. Amer. Math. Soc., 329(2):819-824, 1992.

JS01
Weimin Jin and Peter Sternberg.
Energy estimates for the von Kármán model of thin-film blistering.
J. Math. Phys., 42(1):192-199, 2001.

Kad76
Leo P. Kadanoff.
Scaling, universality and operator algebras.
In Phase transitions and critical phenomena, Vol. 5a, pages 1-34. Academic Press, London, 1976.

Kad00
Leo P. Kadanoff.
Statistical physics.
World Scientific Publishing Co. Inc., River Edge, NJ, 2000.
Statics, dynamics and renormalization.

KKMW+01
I. K. Kostov, I. Krichever, M. Mineev-Weinstein, P. B. Wiegmann, and A. Zabrodin.
The $ \tau$-function for analytic curves.
In Random matrix models and their applications, volume 40 of Math. Sci. Res. Inst. Publ., pages 285-299. Cambridge Univ. Press, Cambridge, 2001.

KM94
Robert V. Kohn and Stefan Müller.
Surface energy and microstructure in coherent phase transitions.
Comm. Pure Appl. Math., 47(4):405-435, 1994.

Kor96
J. Korevaar.
Fekete extreme points and related problems.
In Approximation theory and function series (Budapest, 1995), volume 5 of Bolyai Soc. Math. Stud., pages 35-62. János Bolyai Math. Soc., Budapest, 1996.

KP91
David Kinderlehrer and Pablo Pedregal.
Characterizations of Young measures generated by gradients.
Arch. Rational Mech. Anal., 115(4):329-365, 1991.

Kra97
E. M. Kramer.
The von Karman equations, the stress function, and elastic ridges in high dimensions.
J. Math. Phys., 38:830, 1997.

KS70
E. F. Keller and J. A. Segel.
Initiation of slime mold aggregation viewed as an instability.
J. Theor. Biology, 26:399-415, 1970.

Kui55
Nicolaas H. Kuiper.
On C$ \sp$1-isometric imbeddings. I, II.
Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indag. Math., 17:545-556, 683-689, 1955.

KVO+01
J. W. Kim, J.Y. Vaishnav, E. Ott, S. C. Venkataramani, and W. Losert.
Front propagation of spatiotemporal chaos.
Phys. Rev. E, 64:016215, 2001.

KW97
E. M. Kramer and T. A. Witten.
Stress condensation in crushed elastic manifolds.
Phys. Rev. Lett., 78:1303, 1997.

LGL+95
A. Lobkovsky, S. Gentges, H. Li, D. Morse, and T. A. Witten.
Scaling properties of stretching ridges in a crumpled elastic sheet.
Science, 270:1482, 1995.

LL92
A. J. Lichtenberg and M. A. Lieberman.
Regular and chaotic dynamics.
Springer-Verlag, New York, second edition, 1992.

Lob96
A. E. Lobkovsky.
Boundary layer analysis of the ridge singularity in a thin plate.
Phys. Rev. E., 53:3750, 1996.

LW97
A. E. Lobkovsky and T. A. Witten.
Properties of ridges in elastic membranes.
Phys. Rev. E, 55:1577, 1997.

MŠ96
Stefan Müller and Vladimir Šverák.
Attainment results for the two-well problem by convex integration.
In Geometric analysis and the calculus of variations, pages 239-251. Internat. Press, Cambridge, MA, 1996.

Mül99
Stefan Müller.
Variational models for microstructure and phase transitions.
In Calculus of variations and geometric evolution problems (Cetraro, 1996), pages 85-210. Springer, Berlin, 1999.

MUS95
F. Melo, P. B. Umbanhowar, and H. L. Swinney.
Hexagons, kinks, and disorder in oscillated granular layers.
Phys. Rev. Lett., 75:3838, 1995.

MZ98
F. Merle and H. Zaag.
Refined uniform estimates at blow-up and applications for nonlinear heat equations.
Geom. Funct. Anal., 8(6):1043-1085, 1998.

Nag95
Toshitaka Nagai.
Blow-up of radially symmetric solutions to a chemotaxis system.
Adv. Math. Sci. Appl., 5(2):581-601, 1995.

Nas54
John Nash.
C$ \sp$1 isometric imbeddings.
Ann. of Math. (2), 60:383-396, 1954.

OG94
Michael Ortiz and Gustavo Gioia.
The morphology and folding patterns of buckling-driven thin-film blisters.
J. Mech. Phys. Solids, 42(3):531-559, 1994.

PCK+99
M.L. Povinelli, S.N. Coppersmith, L.P. Kadanoff, S.R. Nagel, and S. C. Venkataramani.
Noise stabilization of self-organized memories.
Phys. Rev. E, 59(5):4970-4982, 1999.

Pom92
Ch. Pommerenke.
Boundary behaviour of conformal maps, volume 299 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences].
Springer-Verlag, Berlin, 1992.

SGAR00
M. A. Scherer, F. Horner G. Ahlers, and I. Rehberg.
Deviations from linear theory for fluctuations below the supercritical primary bifurcation to electroconvection.
Phys. Rev. Lett., 85(18):3754-3757, 2000.

SH77
J. Swift and P. C. Hohenberg.
Hydrodynamic fluctuations at convective instability.
Phys. Rev. A, 15(1):319-328, 1977.

Spr98
David Spring.
Convex integration theory.
Birkhäuser Verlag, Basel, 1998.
Solutions to the h-principle in geometry and topology.

SU84
Richard Schoen and Karen Uhlenbeck.
Regularity of minimizing harmonic maps into the sphere.
Invent. Math., 78(1):89-100, 1984.

Tar79
L. Tartar.
Compensated compactness and applications to partial differential equations.
In Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, pages 136-212. Pitman, Boston, Mass., 1979.

Tar90
Luc Tartar.
H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations.
Proc. Roy. Soc. Edinburgh Sect. A, 115(3-4):193-230, 1990.

Tar92
Luc Tartar.
On mathematical tools for studying partial differential equations of continuum physics: H-measures and Young measures.
In Developments in partial differential equations and applications to mathematical physics (Ferrara, 1991), pages 201-217. Plenum, New York, 1992.

Tar95
Luc Tartar.
Beyond Young measures.
Meccanica, 30(5):505-526, 1995.
Microstructure and phase transitions in solids (Udine, 1994).

UMS96
P. B. Umbanhowar, F. Melo, and H. L. Swinney.
Localized excitations in a vertically vibrated granular layer.
Nature, 382:793, 1996.

UMS98
P. B. Umbanhowar, F. Melo, and H. L. Swinney.
Periodic, aperiodic, and transient patterns in vibrated granular layers.
Phys. Rev. A, 249:1, 1998.

VO98
S. C. Venkataramani and E. Ott.
Spatiotemporal bifurcation phenomena with temporal period doubling: Patterns in vibrated sand.
Phys. Rev. Lett., 80(16):3495-3498, 1998.

VO01
S. C. Venkataramani and E. Ott.
Pattern selection in extended periodically forced systems: A continuum coupled map approach.
Phys. Rev. E, 63:046202, 2001.

VWKG00
S. C. Venkataramani, T. A. Witten, E. M. Kramer, and R. P. Geroch.
Limitations on the smooth confinement of an unstretchable manifold.
J. Math. Phys., 41(7):5107-5128, 2000.

Wil83
Kenneth G. Wilson.
The renormalization group and critical phenomena.
Rev. Modern Phys., 55(3):583-600, 1983.

WL93
T. A. Witten and H. Li.
Asymptotic shape of a fullerene ball.
Europhys. Lett., 23:51-55, 1993.

WZ00
P. B. Wiegmann and A. Zabrodin.
Conformal maps and integrable hierarchies.
Comm. Math. Phys., 213(3):523-538, 2000.

You69
L. C. Young.
Lectures on the calculus of variations and optimal control theory.
W. B. Saunders Co., Philadelphia, 1969.



Shankar 2003-11-29