3,523 research outputs found
Membrane morphology induced by anisotropic proteins
There are a great many proteins that localize to and collectively generate
curvature in biological fluid membranes. We study changes in the topology of
fluid membranes due to the presence of highly anisotropic, curvature-inducing
proteins. Generically, we find a surprisingly rich phase diagram with phases of
both positive and negative Gaussian curvature. As a concrete example modeled on
experiments, we find that a lamellar phase in a negative Gaussian curvature
regime exhibits a propensity to form screw dislocations of definite burgers
scalar but of both chirality. The induced curvature depends strongly on the
membrane rigidity, suggesting membrane composition can be a factor regulating
membrane sculpting to to curvature-inducing proteins.Comment: 4 pages, 4 figure
Boundary conditions in the Dirac approach to graphene devices
We study a family of local boundary conditions for the Dirac problem
corresponding to the continuum limit of graphene, both for nanoribbons and
nanodots. We show that, among the members of such family, MIT bag boundary
conditions are the ones which are in closest agreement with available
experiments. For nanotubes of arbitrary chirality satisfying these last
boundary conditions, we evaluate the Casimir energy via zeta function
regularization, in such a way that the limit of nanoribbons is clearly
determined.Comment: 10 pages, no figure. Section on Casimir energy adde
Self-Assembly on a Cylinder: A Model System for Understanding the Constraint of Commensurability
A crystal lattice, when confined to the surface of a cylinder, must have a
periodic structure that is commensurate with the cylinder circumference. This
constraint can frustrate the system, leading to oblique crystal lattices or to
structures with a chiral seam known as a "line slip" phase, neither of which
are stable for isotropic particles in equilibrium on flat surfaces. In this
study, we use molecular dynamics simulations to find the steady-state structure
of spherical particles with short-range repulsion and long-range attraction far
below the melting temperature. We vary the range of attraction using the
Lennard-Jones and Morse potentials and find that a shorter-range attraction
favors the line-slip. We develop a simple model based only on geometry and bond
energy to predict when the crystal or line-slip phases should appear, and find
reasonable agreement with the simulations. The simplicity of this model allows
us to understand the influence of the commensurability constraint, an
understanding that might be extended into the more general problem of
self-assembling particles in strongly confined spaces.Comment: 12 pages, 9 figures. Submitted for publication, 201
Zeroes of combinations of Bessel functions and mean charge of graphene nanodots
We establish some properties of the zeroes of sums and differences of
contiguous Bessel functions of the first kind. As a byproduct, we also prove
that the zeroes of the derivatives of Bessel functions of the first kind of
different orders are interlaced the same way as the zeroes of Bessel functions
themselves. As a physical motivation, we consider gated graphene nanodots
subject to Berry-Mondragon boundary conditions. We determine the allowed energy
levels and calculate the mean charge at zero temperature. We discuss in detail
its dependence on the gate (chemical) potential.Comment: vesrion accepted to Theoretical and Mathematical Physics, 18 pages, 1
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