Related papers: Dimer problem on a spherical surface
Forming an interface between immiscible fluids incurs a free-energy cost that usually favors minimizing the interfacial area. An emulsion droplet of fixed volume therefore tends to form a sphere, and pairs of droplets tend to coalesce.…
The dynamic behavior of a partially wetting polymer droplet driven over a nanostructured interface is studied using molecular dynamics simulations. We consider the bead-spring model to represent a polymeric liquid that partially wets a…
Circular-Beams were introduced as a very general solution of the paraxial wave equation carrying Orbital Angular Momentum. Here we study their properties, by looking at their normalization and their expansion in terms of Laguerre-Gauss…
The work presents the detailed analysis of the water dimer properties. Their parameters are investigated on the basis of a multipole interaction potential extended up to the quadrupole--quadrupole and dipole--octupole terms. All main…
For a particle that is constrained on an ($N-1$)-dimensional ($N\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface,…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
We provide a general formulation of the spin-orbit coupling on a 2D curved surface. Considering the wide applicability of spin-orbit effect in spinor-based condensed matter physics, a general spin-orbit formulation could aid the study of…
In this contribution to the proceedings of the 11th Mathematical Society of Japan (MSJ) Seasonal Institute (July 2018) we give an overview of some recent work on a mathematical model for small deformations of a spherical membrane. The idea…
We investigate the properties of forced inertial modes of a rotating fluid inside a spherical shell. Our forcing is tidal like, but its main property is that it is on the large scales. Our solutions first confirm some analytical results…
The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this…
Using high resolution DM simulations we study the shape of dark matter halos. Halos become more spherical with decreasing mass. This trend is even more pronounced for the inner part of the halo. Angular momentum and shape are correlated.…
A new type of quasi-two-dimensional complex plasma system was observed which consisted of monodisperse microspheres and their binary agglomerations (dimers). The particles and their dimers levitated in a plasma sheath at slightly different…
In the search for appropriate discretizations of surface theory it is crucial to preserve such fundamental properties of surfaces as their invariance with respect to transformation groups. We discuss discretizations based on M\"obius…
We address ring-shaped surface waves supported by defocusing thermal media with circular cross-section. Such waves exist because of the balance between repulsion from the interface and deflection of light from the bulk medium due to…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
The Willmore energy plays a central role in the conformal geometry of surfaces in the conformal 3-sphere \(S^3\). It also arises as the leading term in variational problems ranging from black holes, to elasticity, and cell biology. In the…
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are…
Thermo-responsive hydrogels are a promising material for creating controllable actuators for use in micro-scale devices, since they expand and contract significantly (absorbing or expelling fluid) in response to relatively small temperature…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…