Joongul Lee

An explicit formula for the A-polynomial of the knot with Conway’s notation C(2n,3)

An explicit formula for the

Particle condensation in pair exclusion process

A

Явные формулы для инвариантов Черна - Саймонса орбиобразий скрученных узлов и реберные многочлены скрученных узлов@@@Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

-polynomial of the knot with Conways notation

On the steady-state probability distribution of nonequilibrium stochastic systems

C(2n,3)

On the volume and Chern–Simons invariant for 2-bridge knot orbifolds

is obtained from the explicit Riley-Mednykh polynomial of it.

The volume of hyperbolic cone-manifolds of the knot with Conway’s notation C(2n,3)

Condensation is characterized with a single macroscopic condensate whose mass is proportional to a system size N . We demonstrate how important particle interactions are in condensation phenomena. We study a modified version of the zero-range process by including a pair exclusion. Each particle is associated with its own partner and particles of a pair are forbidden to stay at the same site. The pair exclusion is weak in that a particle interacts with only a single one among all others. It turns out that such a weak interaction changes the nature of condensation drastically. There appear a number of mesoscopic condensates: the mass of a condensate scales as m con ∼ N 1/2 and the number of condensates scales as N con ∼ N 1/2 with a logarithmic correction. These results are derived analytically through a mapping to a solvable model under a certain assumption and confirmed numerically.

Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

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Explicit formulae for Chern–Simons invariants of the hyperbolic orbifolds of the knot with Conway’s notation C(2n, 3)

A driven stochastic system in a constant temperature heat bath relaxes into a steady state that is characterized by the steady-state probability distribution. We investigate the relationship between the driving force and the steady-state probability distribution. We adopt the force decomposition method in which the force is decomposed as the sum of a gradient of a steady-state potential and the remaining part. The decomposition method allows one to find a set of force fields each of which is compatible with a given steady state. Such a knowledge provides useful insight into stochastic systems, especially those in a nonequilibrium situation. We demonstrate the decomposition method in stochastic systems under overdamped and underdamped dynamics and discuss the connection between them.

Effects of strain and interface roughness between an AlN buffer layer and a ZnO film grown by using radio-frequency magnetron sputtering

This paper extends the work by Mednykh and Rasskazov presented in [On the structure of the canonical fundamental set for the 2-bridge link orbifolds, Universitat Bielefeld, Sonderforschungsbereich 343, Discrete Structuren in der Mathematik, Preprint (1988), pp. 98–062, www.mathematik.uni-bielefeld.de/sfb343/preprints/pr98062.ps.gz]. By using their approach, we derive the Riley–Mednykh polynomial for a family of 2-bridge knot orbifolds. As a result, we obtain explicit formulae for the volumes and Chern–Simons invariants of orbifolds and cone-manifolds on the knot with Conway’s notation C(2n, 4).