Positional, Reorientational and Bond Orientational Order in DNA Mesophases

We investigate the orientational order of transverse polarization vectors of long, stiff polymer molecules and their coupling to bond orientational and positional order in high density mesophases. Homogeneous ordering of transverse polarization vector promotes distortions in the hexatic phase, whereas inhomogeneous ordering precipitates crystalization of the 2D sections with different orientations of the transverse polarization vector on each molecule in the unit cell. We propose possible scenarios for going from the hexatic phase, through the distorted hexatic phase to the crystalline phase with an orthorhombic unit cell observed experimentally for the case of DNA.Comment: 4 pages, 2 figure

FixFit: using parameter-compression to solve the inverse problem in overdetermined models

All fields of science depend on mathematical models. One of the fundamental problems with using complex nonlinear models is that data-driven parameter estimation often fails because interactions between model parameters lead to multiple parameter sets fitting the data equally well. Here, we develop a new method to address this problem, FixFit, which compresses a given mathematical model's parameters into a latent representation unique to model outputs. We acquire this representation by training a neural network with a bottleneck layer on data pairs of model parameters and model outputs. The bottleneck layer nodes correspond to the unique latent parameters, and their dimensionality indicates the information content of the model. The trained neural network can be split at the bottleneck layer into an encoder to characterize the redundancies and a decoder to uniquely infer latent parameters from measurements. We demonstrate FixFit in two use cases drawn from classical physics and neuroscience

Coupling between Smectic and Twist Modes in Polymer Intercalated Smectics

We analyse the elastic energy of an intercalated smectic where orientationally ordered polymers with an average orientation varying from layer to layer are intercalated between smectic planes. The lowest order terms in the coupling between polymer director and smectic layer curvature are added to the smectic elastic energy. Integration over the smectic degrees of freedom leaves an effective polymer twist energy that has to be included into the total polymer elastic energy leading to a fluctuational renormalization of the intercalated polymer twist modulus. If the polymers are chiral this in its turn leads to a renormalization of the cholesteric pitch.Comment: 8 pages, 1 fig in ps available from [email protected] Replaced version also contains title and abstract in the main tex

Boundary Effects in Chiral Polymer Hexatics

Boundary effects in liquid-crystalline phases can be large due to long-ranged orientational correlations. We show that the chiral hexatic phase can be locked into an apparent three-dimensional N+6 phase via such effects. Simple numerical estimates suggest that the recently discovered "polymer hexatic" may actually be this locked phase.Comment: 4 pages, RevTex, 3 included eps figure

A twist in chiral interaction between biological helices

Using an exact solution for the pair interaction potential, we show that long, rigid, chiral molecules with helical surface charge patterns have a preferential interaxial angle ~((RH)^1/2)/L, where L is the length of the molecules, R is the closest distance between their axes, and H is the helical pitch. Estimates based on this formula suggest a solution for the puzzle of small interaxial angles in a-helix bundles and in cholesteric phases of DNA.Comment: 7 pages, 2 figures, PDF file onl

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_\xi]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_\xi$, which corresponds to the area of the membrane coarse-grained at the mesh size $\xi$. We show that the meshwork modifies the membrane tension $\sigma$ both below and above the scale $\xi$, inducing a tension-jump $\Delta\sigma=dF_\mathrm{el}/dA_\xi$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane area. We also predict an observable tension jump for membranes decorated with polymer "brushes"

Interfaces of Modulated Phases

Numerically minimizing a continuous free-energy functional which yields several modulated phases, we obtain the order-parameter profiles and interfacial free energies of symmetric and non-symmetric tilt boundaries within the lamellar phase, and of interfaces between coexisting lamellar, hexagonal, and disordered phases. Our findings agree well with chevron, omega, and T-junction tilt-boundary morphologies observed in diblock copolymers and magnetic garnet films.Comment: 4 page

Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties

Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $\mu$m range and slits widths spanning continuously the 50--1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is non-monotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for three-dimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure

Homogeneous Bubble Nucleation driven by local hot spots: a Molecular Dynamics Study

We report a Molecular Dynamics study of homogenous bubble nucleation in a Lennard-Jones fluid. The rate of bubble nucleation is estimated using forward-flux sampling (FFS). We find that cavitation starts with compact bubbles rather than with ramified structures as had been suggested by Shen and Debenedetti (J. Chem. Phys. 111:3581, 1999). Our estimate of the bubble-nucleation rate is higher than predicted on the basis of Classical Nucleation Theory (CNT). Our simulations show that local temperature fluctuations correlate strongly with subsequent bubble formation - this mechanism is not taken into account in CNT

Thermodynamics and structure of self-assembled networks

We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. The model is solved in the mean field approximation. It is found that despite the absence of any specific interaction between the chains, the entropy of the junctions induces an effective attraction between the monomers, which in the case of three-fold junctions leads to a first order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. Independent of the phase separation, we predict the percolation (connectivity) transition at which an infinite network is formed that partially overlaps with the first-order transition. The percolation transition is a continuous, non thermodynamic transition that describes a change in the topology of the system. Our treatment which predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation correlation has a usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying an onset of medium-range order in the system. Implications of the results for different physical systems are discussed.Comment: Submitted to Phys. Rev.