Actuation of magnetoelastic membranes in precessing magnetic fields.

Superparamagnetic nanoparticles incorporated into elastic media offer the possibility of creating actuators driven by external fields in a multitude of environments. Here, magnetoelastic membranes are studied through a combination of continuum mechanics and molecular dynamics simulations. We show how induced magnetic interactions affect the buckling and the configuration of magnetoelastic membranes in rapidly precessing magnetic fields.

Contractile actuation and dynamical gel assembly of paramagnetic filaments in fast precessing fields.

Flexible superparamagnetic filaments are studied under the influence of fast precessing magnetic fields using simulations and a continuum approximation analysis. We find that individual filaments can be made to exert controllable tensile forces along the precession axis. These forces are exploited for microscopic actuation.

Constriction by Dynamin: Elasticity versus Adhesion.

Any cellular fission process is completed when the neck connecting almost-separate membrane compartments is severed. This crucial step is somehow accomplished by proteins from the dynamin family, which polymerize into helical spirals around such necks. Much research has been devoted to elucidating the specifics of that somehow, but despite no shortage of ideas, the question is not settled.

Cylindrical confinement of semiflexible polymers.

Equilibrium states of a closed semiflexible polymer binding to a cylinder are described. This may be either by confinement or by constriction. Closed completely bound states are labeled by two integers: the number of oscillations, n, and the number of times it winds the cylinder, p, the latter being a topological invariant.

Direct and remote constriction of membrane necks.

The physical properties of membrane necks are relevant in vesiculation, a process that plays an essential role in cellular physiology. Because the neck's radius is, in general, finite, membrane scission and the consequent pinching off of the vesicle can only occur if it is narrowed to permit the necessary membrane topological reformation. Here we examine, in a simple single phase lipid vesicle, how external forces can promote neck constriction not only by direct compression at the neck but also, counterintuitively, by dilation at remote locations.

Force dipoles and stable local defects on fluid vesicles.

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area- and volume-preserving conformal transformations, which breaks the symmetry between the two points.

Confinement of semiflexible polymers.

A variational framework is developed to examine the equilibrium states of a semiflexible polymer that is constrained to lie on a fixed surface. As an application the confinement of a closed polymer loop of fixed length 2π R within a spherical cavity of smaller radius, R(0), is considered. It is shown that an infinite number of distinct periodic completely attached equilibrium states exist, labeled by two integers: n = 2,3,4,.

Spinor representation of surfaces and complex stresses on membranes and interfaces.

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the 1990s, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature.