Cylinder problem

Dimer problem on the cylinder and torus

Weobtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, andhexagonal lattices)with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on 8.8.4 and hexagonal lattices with toroidal boundary condition by Salinas and Nagle [S.R. Salinas, J.F. Na...

Efficient Algorithms for the Smallest Enclosing Cylinder Problem

Saint-Venant’s Principe of the Problem of the Cylinder

The Statement of Modified Saint-Venant’s Principle is suggested. The axisymmetrical deformation of the infinite circular cylinder loaded by an equilibrium system of forces on its near end is discussed and its formulation of Modified Saint-Venant’s Principle is established. It is evident that finding solutions of boundary-value problems is a precise and pertinent approach to establish Saint-Vena...

Exact solution of a Stefan problem in a nonhomogeneous cylinder

The exact solution is found for the Stefan problem of inwards freezing of a nonhomogeneous cylinder whose specific heat and latent heat depend upon the inverse square of the radial distance. The freezing time for the corresponding annular cylinder is found exactly. The validity of the pseudo-steady-state approximation for the solvable cylinder problem is verified explicitly. It is argued that t...

Variational approach to the Coulomb problem on a cylinder

We evaluate, by means of variational calculations, the bound state energy EB of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential – e / r . The trial wave function involves three variational parameters. EB is obtained as a function of the reduced curvature C = a0 / R , where a0 is the Bohr radius and R is the radius of the cylinder. We find that the energ...