Phase transitions on non-uniformly curved surfaces: coupling between phase and location

Abstract

For particles confined to two dimensions, any curvature of the surface affects the structural, kinetic and thermodynamic properties of the system. If the curvature is non-uniform, an even richer range...

Packing core–corona particles on a spherical surface

“…1b. Standard Monte Carlo (MC) simulations based on the canonical ensemble (NVT simulations) on a sphere of radius R have been carried out using the generalized Metropolis algorithm 45,46 as follows. An initial random distribution of particles on the sphere is generated.…”

“…We construct the vector t = dv ˆ+ r ˆ(i) and normalize it to obtain the trial orientation vector 45 that is then accepted or rejected using the generalized Metropolis algorithm. 46 The scale factor d is initially set to d = 0.2 and optimized by updating it such that the acceptance probability is maintained at around 50%. We have used s 0 and e as the length and energy units, respectively, set l = 2, and studied the pattern formation dependence on R* R/s 0 , reduced temperature T* k B T/e, where k B is the Boltzmann's constant; and the number of particles N. The structural diversity and phase behavior is explored in detail for a small number of particles N r 12 although runs with other values of N are considered, with the largest value N = 400 as an example of a large system.…”

Effects of orientational order on modulated cylindrical interfaces

“…ii) In our model the order parameter field is not coupled to any extrinsic or mean curvature terms in Equation 8. Such a coupling exists more or less prominently in various systems, from interactions through the bulk phase between hexatically arranged spheres [29] to the prominently mean-curvature-inducing properties of ordered domains of inclusions [30]. The focus on extrinsic curvature coupling has allowed us to study a field theory with unbroken continuous O n symmetry and the associated vortex state.…”

Packing and emergence of the ordering of rods in a spherical monolayer

“…25 Curvature driven dynamics also play an important role in different biological processes [26][27][28] as well as in different properties of colloidal systems. [29][30][31] Three dimensional uniaxial nematics are orientationally ordered fluids, and can be characterized by the three component unit director n ˆ= (n x (x,y,z),n y (x,y,z),n z (x,y,z)), whereas the unit director of two dimensional a Centre for Condensed Matter Theory, Department of Physics, Indian Institute of nematics in a plane has two components: n ˆ= (n x (x,y),n y (x,y)). On a curved surface such as a sphere, the two dimensional nematic director lies in the local tangent plane to the sphere.…”