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\citation{Kaasgaard03} |
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\citation{Kubica02} |
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\citation{Bannerjee02} |
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\citation{Ayton02} |
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\citation{Jiang04} |
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\citation{Brannigan04a} |
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\citation{Harden2006} |
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\citation{Harden2006} |
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\@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{2}{}} |
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\@writefile{toc}{\contentsline {section}{\numberline {II}2-D Dipolar Membrane}{4}{}} |
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\newlabel{sec:model}{{II}{4}{}{}{}} |
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\newlabel{eq:pot}{{2.1}{4}{}{}{}} |
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\@writefile{toc}{\contentsline {section}{\numberline {III}Results and Analysis}{5}{}} |
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\newlabel{sec:results}{{III}{5}{}{}{}} |
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\@writefile{toc}{\contentsline {subsection}{\numberline {A}Dipolar Ordering and Coexistence Temperatures}{5}{}} |
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\newlabel{eq:opmatrix}{{3.2}{5}{}{}{}} |
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Top panel: The $P_2$ dipolar order parameter as a function of temperature for both triangular ($\gamma = 1.732$) and distorted ($\gamma = 1.875$) lattices. Bottom Panel: The phase diagram for the dipolar membrane model. The line denotes the division between the dipolar ordered (anti-ferroelectric) and disordered phases. An enlarged view near the triangular lattice is shown inset.}}{6}{}} |
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\newlabel{phase}{{1}{6}{}{}{}} |
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Top and Side views of a representative configuration for the dipolar ordered phase supported on the triangular lattice. Note the anti-ferroelectric ordering and the long wavelength buckling of the membrane. Dipolar ordering has been observed in all three equivalent directions on the triangular lattice, and the ripple direction is always perpendicular to the director axis for the dipoles.}}{8}{}} |
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\newlabel{fig:snapshot}{{2}{8}{}{}{}} |
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Contours of the height-dipole correlation function as a function of the dot product between the dipole ($\mathaccent "705E\relax {\mu }$) and inter-dipole separation vector ($\mathaccent "705E\relax {r}$) and the distance ($r$) between the dipoles. Perfect height correlation (contours approaching 1) are present in the ordered phase when the two dipoles are in the same head-to-tail line. Anti-correlation (contours below 0) is only seen when the inter-dipole vector is perpendicular to the dipoles. In the dipole-disordered portion of the phase diagram, there is only weak correlation in the dipole direction and this correlation decays rapidly to zero for intermolecular vectors that are not dipole-aligned.}}{9}{}} |
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\newlabel{fig:CrossCorrelation}{{3}{9}{}{}{}} |
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\citation{Safran94} |
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\citation{Seifert97} |
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\citation{Safran94} |
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\@writefile{toc}{\contentsline {subsection}{\numberline {B}Discriminating Ripples from Thermal Undulations}{10}{}} |
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\newlabel{eq:fit}{{3.5}{10}{}{}{}} |
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\newlabel{eq:fit2}{{3.6}{10}{}{}{}} |
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\@writefile{toc}{\contentsline {subsection}{\numberline {C}Effects of Potential Parameters on Amplitude and Wavelength}{11}{}} |
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Evidence that the observed ripples are {\em not} thermal undulations is obtained from the 2-d Fourier transform $\delimiter "426830A |h^{*}(\mathaccent "017E\relax {q})|^2 \delimiter "526930B $ of the height profile ($\delimiter "426830A h^{*}(x,y) \delimiter "526930B $). Rippled samples show low-wavelength peaks that are outliers on the Landau free energy fits by an order of magnitude. Samples exhibiting only thermal undulations fit Eq. 3.5{}{}{}\hbox {} remarkably well.}}{12}{}} |
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\citation{Kaasgaard03} |
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\@writefile{toc}{\contentsline {subsection}{\numberline {D}Distorted lattices}{13}{}} |
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces a) The amplitude $A^{*}$ of the ripples vs. temperature for a triangular lattice. b) The amplitude $A^{*}$ of the ripples vs. dipole strength ($\mu ^{*}$) for both the triangular lattice (circles) and distorted lattice (squares). The reduced temperatures were kept fixed at $T^{*} = 94$ for the triangular lattice and $T^{*} = 106$ for the distorted lattice (approximately 2/3 of the order-disorder transition temperature for each lattice).}}{14}{}} |
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\newlabel{fig:Amplitude}{{5}{14}{}{}{}} |
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces The ripple wavelength (top) and amplitude (bottom) as a function of system size for a triangular lattice ($\gamma =1.732$) at $T^{*} = 122$.}}{15}{}} |
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\newlabel{fig:systemsize}{{6}{15}{}{}{}} |
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\@writefile{toc}{\contentsline {subsection}{\numberline {E}Effects of System Size}{15}{}} |
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\@writefile{toc}{\contentsline {section}{\numberline {IV}Discussion}{16}{}} |
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| 82 |
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| 83 |
\bibcite{Mutz1991}{{4}{1991}{{Mutz et~al.}}{{Mutz, Bensimon, and Brienne}}} |
| 84 |
\bibcite{Sun96}{{5}{1996}{{Sun et~al.}}{{Sun, Tristram-Nagle, Suter, and Nagle}}} |
| 85 |
\bibcite{Katsaras00}{{6}{2000}{{Katsaras et~al.}}{{Katsaras, Tristram-Nagle, Liu, Headrick, E.Fontes, Mason, and Nagle}}} |
| 86 |
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| 87 |
\bibcite{Meyer96}{{8}{1996}{{Meyer}}{{}}} |
| 88 |
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| 89 |
\bibcite{Cevc87}{{10}{1980}{{Cevc and Marsh}}{{}}} |
| 90 |
\bibcite{Marder84}{{11}{1984}{{Marder et~al.}}{{Marder, Frisch, Langer, and McConnell}}} |
| 91 |
\bibcite{Goldstein88}{{12}{1988}{{Goldstein and Leibler}}{{}}} |
| 92 |
\bibcite{McCullough90}{{13}{1990}{{McCullough and Scott}}{{}}} |
| 93 |
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| 94 |
\bibcite{Misbah98}{{15}{1998}{{Misbah et~al.}}{{Misbah, Duplat, and Houchmandzadeh}}} |
| 95 |
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| 96 |
\bibcite{Kubica02}{{17}{2002}{{Kubica}}{{}}} |
| 97 |
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| 98 |
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| 99 |
\bibcite{Jiang04}{{20}{2004}{{Jiang et~al.}}{{Jiang, Bouret, and Kindt}}} |
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\@writefile{toc}{\contentsline {section}{\numberline {}Acknowledgments}{18}{}} |
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\bibcite{deVries05}{{22}{2005}{{de~Vries et~al.}}{{de~Vries, Yefimov, Mark, and Marrink}}} |
| 104 |
\bibcite{deJoannis06}{{23}{2006}{{de~Joannis et~al.}}{{de~Joannis, Jiang, and Kindt}}} |
| 105 |
\bibcite{Todorova2004}{{24}{2004}{{Todorova et~al.}}{{Todorova, Angelov, Marinov, and Petrov}}} |
| 106 |
\bibcite{Harden2006}{{25}{2006}{{Harden et~al.}}{{Harden, Mbanga, Eber, Fodor-Csorba, Sprunt, Gleeson, and Jakli}}} |
| 107 |
\bibcite{Petrov2006}{{26}{2006}{{Petrov}}{{}}} |
| 108 |
\bibcite{Raphael2000}{{27}{2000}{{Raphael et~al.}}{{Raphael, Popel, and Brownell}}} |
| 109 |
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| 110 |
\bibcite{Marland1979}{{29}{1979}{{Marland and Betts}}{{}}} |
| 111 |
\bibcite{Renard1966}{{30}{1966}{{Renard and Garland}}{{}}} |
| 112 |
\bibcite{Zhu2005}{{31}{2005}{{Zhu et~al.}}{{Zhu, Tavazza, and Landau}}} |
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\bibcite{Zhu2006}{{32}{2006}{{Zhu and Landau}}{{}}} |
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\bibcite{Jiang2006}{{33}{2006}{{Jiang and Emig}}{{}}} |
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| 119 |
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