arXiv subjects

Junho Lee

Publications and source records attributed to Junho Lee.

50 records · Page 3Linked to original sources

arXiv2017

Microstructure and elevated-temperature mechanical properties of refractory AlMo0.5NbTa0.5TiZr High Entropy Alloy fabricated by powder metallurgy

New approaches for the design of alloy systems with multiprincipal elements is recently researched in refractory materials field. However, most research aimed at arc melting process with weakness of coarsening of grains and inhomogeneous microstructure of segregation of elements during the cooling. This study aims to design and fabricate high-entropy alloy with powder metallurgy. In this study, a refractory high entropy alloys with composition near AlMo0.5NbTa0.5TiZr were produced by powder metallurgy. The alloy consists of two body-centered cubic (BCC) phases. One phase was disordered BCC enriched with Mo, Nb and Ta and the other phase was ordered BCC enriched with Al and Zr. The AlMo0.5NbTa0.5TiZr alloy had a density of 7.46g/cm3 and Vickers microhardness of 678HV. Its compressive yield strength was 2466MPa at 298K and 964MPa at 1273K. The properties of the alloy and the beneficial effects from powder metallurgy on the microstructure and properties were outlined.

cond-mat.mtrl-sci↗

arXiv2013

Shedding new light on the mystery of wetting on soft solids

One of the most questionable issues in wetting is the vertical force balance that is excluded in Young's law. On soft deformable solids, such as biotic materials and synthetic polymers, the vertical force of liquid leads to a microscopic protrusion of the contact line, i.e. a "wetting ridge". The wetting principle that determines the geometry of the ridge-tip is at the heart of the issues over the past half century. Here, we reveal a universal wetting principle by directly visualizing ridge-tips with high spatio-temporal resolution using x-ray microscopy. We find that the tip-geometry is asymmetric and bent, and invariant during ridge growth or by surface softness. This singular geometry is explained by linking the macroscopic and microscopic contact angles to Young's and Neumann's laws, respectively. Our dual-scale model would be applicable to a general framework in wetting and give new clues to various issues in cell-substrate interaction and elasto-capillary problems.

cond-mat.soft↗

arXiv2012

Recursion Formulas for Spin Hurwitz Numbers

The classical Hurwitz numbers which count coverings of a complex curve have an analog when the curve is endowed with a theta characteristic. These "spin Hurwitz numbers", recently studied by Eskin, Okounkov and Pandharipande, are interesting in their own right. By the authors' previous work, they are also related to the Gromov-Witten invariants of Kahler surfaces. We prove a recursive formula for spin Hurwitz numbers, which then gives the dimension zero GW invariants of Kahler surfaces with positive geometric genus. The proof uses a degeneration of spin curves, an invariant defined by the spectral flow of certain anti-linear deformations of the d-bar operator, and an interesting localization phenomenon for eigenfunctions that shows that maps with even ramification points cancel in pairs.

math.SG↗

arXiv2012

Degree three spin Hurwitz numbers

Recently, Gunningham \cite{G} calculated all spin Hurwitz numbers in terms of combinatorics of Sergeev algebra. In this paper, we use a spin curve degeneration to obtain a recursion formula for degree three spin Hurwitz numbers.

math.SG↗

arXiv2012

Sum Formulas for Local Gromov-Witten Invariants of Spin Curves

Holomorphic 2-forms on Kähler surfaces lead to "Local Gromov-Witten invariants" of spin curves. This paper shows how to derive sum formulas for such local GW invariants from the sum formula for GW invariants of certain ruled surfaces. These sum formulas also verify the Maulik-Pandharipande formulas that were recently proved by Kiem and Li.

math.SG↗

arXiv2012

Local GW Invariants of Elliptic Multiple Fibers

We use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with $p_g>0$.

math.SG↗

arXiv2009

An obstruction bundle relating Gromov-Witten invariants of curves and Kahler surfaces

In [LP] the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kahler surface X with p_g>0 are a sum of such local GW invariants. This paper describes how the local GW invariants arise from an obstruction bundle (in the sense of Taubes) over the space of stable maps into curves. Together with the results of [LP], this reduces the calculation of the GW invariants of complex surfaces to computations in the GW theory of curves.

math.SG↗

arXiv2006

Holomorphic 2-forms and Vanishing Theorems for Gromov-Witten Invariants

On a compact Kähler manifold $X$ with a holomorphic 2-form $\a$, there is an almost complex structure associated with $\a$. We show how this implies vanishing theorems for the Gromov-Witten invariants of $X$. This extends the approach, used in \cite{lp} for Kähler surfaces, to higher dimensions.

math.SG↗

arXiv2006

A Structure Theorem for the Gromov-Witten Invariants of Kahler Surfaces

We prove a structure theorem for the Gromov-Witten invariants of compact Kahler surfaces with geometric genus $p_g>0$. Under the technical assumption that there is a canonical divisor that is a disjoint union of smooth components, the theorem shows that the GW invariants are universal functions determined by the genus of this canonical divisor components and the holomorphic Euler characteristic of the surface. We compute special cases of these universal functions.

math.SG↗

arXiv2005

Yau-Zaslow formula on K3 surfaces for non-primitive classes

We compute the genus zero family Gromov-Witten invariants for K3 surfaces using the topological recursion formula and the symplectic sum formula for a degeneration of elliptic K3 surfaces. In particular we verify the Yau-Zaslow formula for non-primitive classes of index two.

math.SG↗

arXiv2005

Symplectic Gluing and Family Gromov-Witten Invariants

This article describes the use of symplectic cut-and-paste methods to compute Gromov-Witten invariants. Our focus is on recent advances extending these methods to Kahler surfaces with geometric genus p_g>0, for which the usual GW invariants vanish for most homology classes. This involves extending the Splitting Formula and the Symplectic Sum Formula to the family GW invariants introduced by the first author. We present applications to the invariants of elliptic surfaces and to the Yau-Zaslow Conjecture. In both cases the results agree with the conjectures of algebraic geometers and yield a proof, to appear in [LL1], of previously unproved cases of the Yau-Zaslow Conjecture.

math.AG↗

arXiv2004

Counting Elliptic Curves in K3 Surfaces

We compute the genus one family Gromov-Witten invariants of K3 surfaces for non-primitive classes. These calculations verify Gottsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two topological recursion formula and the symplectic sum formula to establish relationships among various generating functions.

math.SG↗

arXiv2003

Family Gromov-Witten Invariants for Kahler Surfaces

The usual Gromov-Witten invariants are zero for Kähler surfaces with $p_g\geq 1$. In this paper we use analytic methods to define Family Gromov-Witten Invariants for Kähler surfaces. We prove that these are well-defined invariants of the deformation class of the Kähler structure.

math.SG↗

arXiv2003

Counting Curves in Elliptic Surfaces by Symplectic Methods

We explicitly compute family GW invariants of elliptic surfaces for primitive classes. That involves establishing a TRR formula and a symplectic sum formula for elliptic surfaces and then determining the GW invariants using an argument from \cite{ip3}. In particular, as in \cite{bl1}, these calculations also confirm the well-known Yau-Zaslow Conjecture \cite{yz} for primitive classes in $K3$ surfaces.

math.SG↗