--- trunk/ripplePaper/ripple.tex	2005/03/28 21:36:59	2143
+++ trunk/ripplePaper/ripple.tex	2005/05/31 20:43:32	2254
@@ -18,7 +18,7 @@
 
 \begin{document}
 
-\title{Ripple Phase of the Lipid Bilayers: A Monte Carlo Simulation}
+\title{Symmetry breaking and the Ripple phase}
 \author{Xiuquan Sun and J. Daniel Gezelter\footnote{Corresponding author. Email: gezelter@nd.edu} \\ 
 Department of Chemistry and Biochemistry \\ 
 University of Notre Dame \\ 
@@ -29,20 +29,27 @@ The molecular explanation for the origin and propertie
 \maketitle
 
 \begin{abstract}
-The molecular explanation for the origin and properties of the ripple
-phase is addressed in this paper. A model which contains the surface
-tension and dipole-dipole interactions is used to describe the
-potential for a monolayer of simple point dipoles. The simulations are
-carried out using Monte Carlo method. It is shown asymmetry of the
-translational freedom of the dipoles breaks the symmetry of the
-hexagonal lattice and allow antiferroelectric ordering of the
-dipoles. The existence of the ripples only depends on the dipolar
-property of the system. The structure of the ripples is affected by
-surface tension. Only close to the hexagonal lattice, can the ripple
-phase be reached. Surface has the lowest transition temperature on
-hexagonal lattice elucidates the reason of the existence of the ripple
-phase in organism. A mechanism for the phase transition of the lipid
-bilayer is proposed.
+The ripple phase in phosphatidylcholine (PC) bilayers has never been
+explained. Our group has developed some simple (XYZ) spin-lattice
+models that allow spins to vary their elevation as well as their
+orientation. The extra degree of freedom allows hexagonal lattices of
+spins to find states that break out of the normally frustrated
+randomized states and are stabilized by long-range anti-ferroelectric
+ordering. To break out of the frustrated states, the spins must form
+``rippled'' phases that make the lattices effectively non-hexagonal. Our
+XYZ models contain surface tension and dipole-dipole interactions to
+describe the interaction potential for monolayers and bilayers of
+model lipid molecules. The existence of the ripples depends primarily
+on the strength and lattice spacing of the dipoles, while the shape
+(wavelength and amplitude) of the ripples is only weakly sensitive to
+the applied surface tension. Additionally, the wave vector for the
+ripple is always perpendicular to the director axis for the
+dipoles. Non-hexagonal lattices of dipoles are not inherently
+frustrated, and are therefore less likely to form ripple phases
+because they can easily form low-energy anti-ferroelectric states.
+Indeed, we see that the dipolar order-disorder transition is
+substantially lower for hexagonal lattices and the ordered phase for
+this lattice is clearly rippled.
 \end{abstract}
 
 \section{Introduction}
