Korea Institute for Advanced Study

Order–Disorder Tricriticality in Symmetric A n B n Star Polymer Melts

Abstract Tricriticality usually requires tuning an additional thermodynamic parameter. Here, we show that, in symmetric AnBn star polymer melts, the arm number n itself plays this role and drives the order–disorder transition (ODT) from second order to first order. By developing...

Boundedness of polarized log Calabi–Yau fibrations with bounded bases

We investigate the boundedness problem for log Calabi–Yau fibrations whose bases and general fibers are bounded. We prove that the total spaces of log Calabi–Yau fibrations are bounded in codimension one after fixing some natural invariants, which confirms a conjecture of Birkar...

Murmurations, Mestre–Nagao sums, and convolutional neural networks for elliptic curves

Abstract We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over $$\mathbb {Q}$$ Q and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki–Vlah, Bujanović–Kazalicki–Novak, and Pozdnyakov...

Precipitate phase selection and grain boundary morphology in Cu-Ni-Si-Mn alloys: A machine-learning interatomic potential study

Alloys inevitably contain interphase boundaries, whose energetics govern nucleation processes and precipitate morphology. In Cu-Ni-Si alloys, Mn addition markedly changes grain boundary (GB) precipitation behavior. While GB precipitation of stable Ni 2 Si in Mn-free alloys is ass...

Trend to Equilibrium and Diffusion Limit for the Inertial Kuramoto–Sakaguchi Equation

Abstract. In this paper, we study the inertial Kuramoto–Sakaguchi equation for interacting oscillatory systems. On the one hand, we prove the convergence toward corresponding phase-homogeneous stationary states in weighted Lebesgue norm sense when the coupling strength is small e...

Towards A Universal Analytical Model of Population III Star Formation: A Bridge Between Cosmological Scales and Protostars

Abstract We construct an analytical model of Population III star formation that connects the cosmological radiation background to sub-AU protostellar disk fragmentation, a dynamic range inaccessible to any single simulation. Our approach is based on combining separate models of t...

ODIN: Confirmation and 3D Reconstruction of Six Massive Protoclusters at Cosmic Noon

Abstract Protoclusters represent sites of accelerated galaxy formation and extreme astrophysical activity characteristic of dense environments. Identifying massive protoclusters and mapping their spatial structures are therefore crucial for understanding how large-scale environme...

Remarks on Symplectic Geometry

The relatively new subject, symplectic geometry, has been studied the past five decades. Symplectic geometry is the mathematical subject studying the geometry of symplectic manifolds. A symplectic manifold is an even-dimensional smooth manifold equipped with a closed non-degenera...

Minimum Partition of Polygons under Width and Cut Constraints

We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in a fixed set of directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width constraint for a set of directions if the lengt...