Theodore W. Burkhardt

A generalized kinetic equation for crystal growth

Abstract A kinetic equation describing the growth of a crystal is formulated in the spirit of the time-dependent Ginzburg-Landau theory. The equation, which is applicable to two and three-dimensional problems, takes into account the anisotropy of the edge free energy γ and of a transport coefficient D as well as spatial and temporal variations in the chemical-potential difference. Anisotropic expressions for γ and D are obtained from a microscopic model. Numerical solutions of the generalized kinetic equation are presented which show the influence of the anisotropy on the two-dimensional growth spiral of a screw dislocation.

Free energy and extension of a semiflexible polymer in cylindrical confining geometries.

We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime D<<P<<L the free energy of confinement DeltaF and the length of the channel R parallel occupied by the polymer are given by Odijks relations DeltaF/R parallel=A(o)kB(TP)-1/3 D(-2/3) and R parallel =L[1-alpha(o)(D/P)2/3], where A(o) and alpha(o) are dimensionless amplitudes. Using a simulation algorithm inspired by the pruned enriched Rosenbluth method, which yields results for very long polymers, we determine A(o) and alpha(o) and the analogous amplitudes for a channel with a rectangular cross section. For a semiflexible polymer confined to the surface of a cylinder, the corresponding amplitudes are derived with an exact analytic approach. The results are relevant for interpreting experiments on biopolymers in microchannels or microfluidic devices.

Free energy of a semiflexible polymer in a tube and statistics of a randomly-accelerated particle

The confinement free energy per unit length of a continuous semiflexible polymer or wormlike chain in a tube with a rectangular cross section is derived in the regime of strong confinement. Here P is the persistence length, and and are the sides of the rectangle. The result is also interpreted in terms of the escape probability of a randomly-accelerated particle from a rectangular domain.

Fluctuations of a long, semiflexible polymer in a narrow channel

We consider an inextensible, semiflexible polymer or wormlike chain, with persistence length P and contour length L, fluctuating in a cylindrical channel of diameter D. In the regime D<<P<<L , corresponding to a long, tightly confined polymer, the average length of the channel occupied by the polymer and the mean-square deviation from the average vary as =[1-α(∘)(D/P)(2/3)]L and =β(∘)(D(2)P)L , respectively, where α(∘) and β(∘) are dimensionless amplitudes. In earlier work we determined α(∘) and the analogous amplitude α(square) for a channel with a rectangular cross section from simulations of very long chains. In this paper, we estimate β(∘) and β(square) from the simulations. The estimates are compared with exact analytical results for a semiflexible polymer confined in the transverse direction by a parabolic potential instead of a channel and with a recent experiment. For the parabolic confining potential we also obtain a simple analytic result for the distribution of R(∥) or radial distribution function, which is asymptotically exact for large L and has the skewed shape seen experimentally.

Ordinary, extraordinary, and normal surface transitions: Extraordinary-normal equivalence and simple explanation of ||T-Tc||2- alpha singularities.

With simple, exact arguments we show that the surface magnetization

Conformal theory of energy correlations in the semi-infinite two-dimensional O(N) model

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Free energy of a semiflexible polymer confined along an axis

at the extraordinary and normal transitions and the surface energy density

Localisation-delocalisation transition in a solid-on-solid model with a pinning potential

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Semiflexible polymer in the half plane and statistics of the integral of a brownian curve

at the ordinary, extraordinary, and normal transitions of semi-infinite

Conformal invariance and critical systems with mixed boundary conditions

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