Lorenz Kramer

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Lorenz Kramer liquid
crystals (1985-2005)
LKI started my scientific career (diploma in
1967) in nonlinear physics (and even pattern
formation) using GL theory to study type II
superconductors.
Flow properties of superfluid 4He
Pattern dynamics in nematics
1982 sabbatical in SB, thanks to P.Hohenberg and
J.Langer!
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L.Kramer, E.Ben-Jacob, H.Brand, M.C.Cross
Wavelength selection in systems far
from equilibrium, PRL,
Vol.49, 1891 (1982) My entrance into pattern
forming, non-equilibrium systems occurred with a
work on wavelength selection by control
parameter ramps, which was inspired by an
experiment with surface barriers in
superconductors. E.Ben-Jacob, H.Brand,
G.Dee, L.Kramer, J.S.Langer Pattern propagation
in nonlinear, dissipative systems, Physica
D, Vol. 14, 348 (1985) L.Kramer,
P.C.Hohenberg Effects of boundaries on spatially
periodic structures, Physica D, Vol.13, 357
(1984)
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1983-84 I also started to work on real systems,
in particular EC in nematics.

• Electroconvection (EC, RB) (1985- )
• Transient patterns in the Freedericksz
  transition (1989-92)
• Interfacial growth of N-SB (1994-2000)
• Shear (oscillatory, elliptic) induced
  instabilities (1993- ) - Light induced
  structures, nonlinear optics (1999- )

LK Liquid crystals have just the right kind
and right amount of nonlinearity
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At threshold, increasing f (planar, sigmaa gt 0,
epsa lt 0)
OR
NR
n
TW
DR
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Entering the field of LCs
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E.Bodenschatz, W.Zimmermann, and L.Kramer On
electrically driven pattern-forming
instabilities in planar nematics. J.Phys. France
Vol.49, 1875 (1988)-November

• 3-d theory, rigid free boundary conditions,
  ac-drive
• q(qx, py) - NR and OR, Uc(f), qc(f)
• neutral curve U(q), wavenumber band
• - linear stability, weakly nonlinear analysis
• 1-mode analytic threshold formula
• conductive and dielectric modes

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100 years of liquid crystals
A.Buka, T.Vicsek, J.Kertesz, Nature, 323, 424
(1986)
Ingo Rehberg Bernhard Winkler M. De la Torre
Juarez S.Rasenat
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Transient patterns in the Freedericksz transition
A.Buka, M.de la Torre Juarez, L.Kramer,
I.Rehberg, PRA, 40, 7427 (1989)
y
Linear theory no structure secondary
bifurcation
x
n
Splay (not twist), E (not H), large ?a (not
small ?a)
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Nonlinear theory (nx, 0, 0 (nx, ny, nz)
(vx, 0, 0) (vx, vy, vz)
(0, 0, Ez) grad U

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Nonlinear theory of transient patterns in the
Freedericksz transition
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Interfacial patterns, nonequilibrium mesophase
growth
Planar smectic in planar nematic
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Homeotropic smectic in planar nematic
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Aspen Center for Physics, Summer program (August
2000)
Pattern Formation in Physics and Biology
Cross-Hohenberg tour
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European workshop center Nonequilibrium in
Physics and Biology(www.szfki.hu/physbio) Scope
advanced training research in an open
environment Peyresq (2002), Benasque (2003)
St.Etienne de Tinnee (2004-05)
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Nonlinear Evolution of Spatio-Temporal Structures
in Dissipative Continous Systems and Pattern
Formation in LCs

• Bayreuth/Streitberg (1989) F.H.Busse and L.
  Kramer
• Kitakyushu (1991) S.Kai
• Santa Fe (1993) P.Cladis and P.Palffy-Muhoray
• Copenhagen (1995) T.Bohr
• Budapest (1997) A.B.
• Waischenfeld (1999) L.K.
• Peking (2001) L.Lam

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Extreme sports
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On the top of a mountain
High Tatras, 1997
Cote dAzur, 1994
Himalaya, 1998
Peyresq, 2002
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CKP, 2002
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