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Register a new userThermal Properties of Vortices on Curved Surfaces
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We use Monte Carlo simulations to study the finite temperature behavior of vortices in the XY- model for tangent vector order on curved backgrounds. Contrary to naive expectations, we show that the underlying geometry does not affect the proliferation of vortices with temperature respect to what is observed on a flat surface. Long-range order in these systems is analyzed by using the classical two-point correlation functions. As expected, in the case of slightly curved substrates these correlations behave similarly to the plane. However, for high curvatures, the presence of geometry-induced unbounded vortices at low temperatures produces the rapid decay of correlations and an apparent lack of long-range order. Our results shed light on the finite-temperature physics of soft-matter systems and anisotropic magnets deposited on curved substrates.
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We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calulations in the plane and on the sphere. Using an isoperimetric inequality from the differential geometry literature and a theorem on the inequalitys saturation, we show how geometry informs the critical droplet size and shape. This inequality establishes a mean field result for nucleated droplets. We then study the effects of fluctuations on the interfaces of droplets in two dimensions, treating the droplet interface as a fluctuating line. We emphasize that care is needed in deriving the line curvature energy from the Landau-Ginzburg energy functional and in interpreting the scalings of the nucleation rate with the size of the droplet. We end with a comparison of nucleation in the plane and on a sphere.
We present a systematic study of how vortices in superfluid films interact with the spatially varying Gaussian curvature of the underlying substrate. The Gaussian curvature acts as a source for a geometric potential that attracts (repels) vortices towards regions of negative (positive) Gaussian curvature independently of the sign of their topological charge. Various experimental tests involving rotating superfluid films and vortex pinning are first discussed for films coating gently curved substrates that can be treated in perturbation theory from flatness. An estimate of the experimental regimes of interest is obtained by comparing the strength of the geometrical forces to the vortex pinning induced by the varying thickness of the film which is in turn caused by capillary effects and gravity. We then present a non-perturbative technique based on conformal mappings that leads an exact solution for the geometric potential as well as the geometric correction to the interaction between vortices. The conformal mapping approach is illustrated by means of explicit calculations of the geometric effects encountered in the study of some strongly curved surfaces and by deriving universal bounds on their strength.
Comment on Liquids on Topologically Nanopatterned Surfaces by O. Gang et al, Phys. Rev. Lett. 95, 217801 (2005). See also an erratum published by O. Gang et al (Phys Rev Lett, to appear)
The impact of liquid drops on solid surfaces is ubiquitous in nature, and of practical importance in many industrial processes. A drop hitting a flat surface retains a circular symmetry throughout the impact process. Here we show that a drop impinging on Echevaria leaves exhibits asymmetric bouncing dynamics with distinct spreading and retraction along two perpendicular directions. This is a direct consequence of the cylindrical leaves which have a convex/concave architecture of size comparable to the drop. Systematic experimental investigations on mimetic surfaces and lattice Boltzmann simulations reveal that this novel phenomenon results from an asymmetric momentum and mass distribution that allows for preferential fluid pumping around the drop rim. The asymmetry of the bouncing leads to ~40% reduction in contact time.
Recent studies have highlighted the sensitivity of active matter to boundaries and their geometries. Here we develop a general theory for the dynamics and statistics of active particles on curved surfaces and illustrate it on two examples. We first show that active particles moving on a surface with no ability to probe its curvature only exhibit steady-state inhomogeneities in the presence of orientational order. We then consider a strongly confined 3D ideal active gas and compute its steady-state density distribution in a box of arbitrary convex shape.
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