72 citations · 601 across the 34 of their papers we have counts for
35 papers
A log-log upper bound on blow-up rates for the mass-critical half-wave equation
Taegyu Kim, Soonsik Kwon, Jeongheon Park
We study finite-time blow-up for the one-dimensional focusing mass-critical half-wave equation \begin{equation*} i\partial_tu=|D|u-|u|^2u. \end{equation*} For even initial data wit…
Blow-up construction and instability for mass-critical half-wave equation with slightly superthreshold mass
Taegyu Kim, Soonsik Kwon, Jeongheon Park
We study the blow-up dynamics for the -critical focusing half-wave equation on the real line, a nonlocal dispersive PDE arising in various physical models. As in other mass-cr…
Melting and freezing rates of the radial interior Stefan problem in two dimension
Jeongheon Park
We consider the interior Stefan problem under radial symmetry in two dimension. A water ball surrounded by ice undergoes melting or freezing. We construct a discrete family of glob…
Modularity Enhances the Rate of Evolution in a Rugged Fitness Landscape
Jeong-Man Park, Man Chen, Dong Wang +1
Biological systems are modular, and this modularity affects the evolution of biological systems over time and in different environments. We here develop a theory for the dynamics o…
On the Universality of the Energy Response Function in the Long-Range Spin Glass Model with Sparse, Modular Couplings
Jeong-Man Park, Michael W. Deem
We consider energy relaxation of the long-range spin glass model with sparse couplings, the so-called dilute Sherrington-Kirkpatrick (SK) model, starting from a random initial stat…
Quasispecies Theory for Evolution of Modularity
Jeong-Man Park, Liang Ren Niestemski, Michael W. Deem
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological s…