Mokwon Lee

Nanocrack-regulated self-humidifying membranes

The regulation of water content in polymeric membranes is important in a number of applications, such as reverse electrodialysis and proton-exchange fuel-cell membranes. External thermal and water management systems add both mass and size to systems, and so intrinsic mechanisms of retaining water and maintaining ionic transport in such membranes are particularly important for applications where small system size is important. For example, in proton-exchange membrane fuel cells, where water retention in the membrane is crucial for efficient transport of hydrated ions, by operating the cells at higher temperatures without external humidification, the membrane is self-humidified with water generated by electrochemical reactions. Here we report an alternative solution that does not rely on external regulation of water supply or high temperatures. Water content in hydrocarbon polymer membranes is regulated through nanometre-scale cracks (‘nanocracks’) in a hydrophobic surface coating. These cracks work as nanoscale valves to retard water desorption and to maintain ion conductivity in the membrane on dehumidification. Hydrocarbon fuel-cell membranes with surface nanocrack coatings operated at intermediate temperatures show improved electrochemical performance, and coated reverse-electrodialysis membranes show enhanced ionic selectivity with low bulk resistance.

BetaSCPWeb: side-chain prediction for protein structures using Voronoi diagrams and geometry prioritization

Many applications, such as protein design, homology modeling, flexible docking, etc. require the prediction of a proteins optimal side-chain conformations from just its amino acid sequence and backbone structure. Side-chain prediction (SCP) is an NP-hard energy minimization problem. Here, we present BetaSCPWeb which efficiently computes a conformation close to optimal using a geometry-prioritization method based on the Voronoi diagram of spherical atoms. Its outputs are visual, textual and PDB file format. The web server is free and open to all users at http://voronoi.hanyang.ac.kr/betascpweb with no login requirement.

BetaCavityWeb: a webserver for molecular voids and channels

Molecular cavities, which include voids and channels, are critical for molecular function. We present a webserver, BetaCavityWeb, which computes these cavities for a given molecular structure and a given spherical probe, and reports their geometrical properties: volume, boundary area, buried area, etc. The servers algorithms are based on the Voronoi diagram of atoms and its derivative construct: the beta-complex. The correctness of the computed result and computational efficiency are both mathematically guaranteed. BetaCavityWeb is freely accessible at the Voronoi Diagram Research Center (VDRC) (http://voronoi.hanyang.ac.kr/betacavityweb).

Support-free hollowing for 3D printing via Voronoi diagram of ellipses

Recent work has demonstrated that the interior material layout of a 3D model can be designed to make a fabricated replica satisfy application-specific demands on its physical properties such as resistance to external loads. A widely used practice to fabricate such models is by layer-based additive manufacturing (AM) or 3D printing, which however suffers from the problem of adding and removing interior supporting structures. In this paper, we present a novel method for generating support-free elliptic hollowing for 3D shapes which can entirely avoid additional supporting structures. To achieve this, we perform the ellipse hollowing in the polygons on parallel section planes and protrude the ellipses of one plane to its neighboring planes. To pack the ellipses in a polygon, we construct the Voronoi diagram of ellipses to efficiently reason the free-space around the ellipses and other geometric features by taking advantage of the available algorithm for the efficient and robust construction of the Voronoi diagram of circles. We demonstrate the effectiveness and feasibility of our proposed method by generating interior designs for and printing various 3D shapes.

Topology-Oriented Incremental Algorithm for the Robust Construction of the Voronoi Diagrams of Disks

Voronoi diagrams are useful for spatial reasoning, and the robust and efficient construction of the ordinary Voronoi diagram of points is well known. However, its counterpart for circular disks in R2 and spherical balls in R3 remains a challenge. In this article, we propose a topology-oriented incremental algorithm which robustly and efficiently computes a Voronoi diagram by incrementing a new disk generator to an existing one. The key idea is to enforce the convexity of the Voronoi cell corresponding to the incrementing disk so that a simple variation of the algorithm for points proposed by Sugihara in 1992 can be applied. A benchmark using both random and degenerate disks shows that the proposed algorithm is superior to CGAL in both computational efficiency and algorithmic robustness.

BetaSCP2: A Program for the Optimal Prediction of Side-Chains in Proteins

The side-chain prediction problem (SCP-problem), is a computational problem to predict the optimal structure of proteins by finding the optimal dihedral angles. The SCP-problem is one of key computational cornerstones for many important problems such as protein design, flexible docking of proteins, homology modeling, etc. The SCP-problem can be formulated as a minimization problem of an integer linear program which is NP-hard thus inevitably invites heuristic approach to find the solution. In this paper, we report a heuristic algorithm, called BetaSCP2, which quickly finds an excellent solution of the SCP-problem. The solution process of the BetaSCP2 is facilitated by the Voronoi diagram and its dual structure called the quasi-triangulation. The BetaSCP2 is entirely implemented using the Molecular Geometry engine called BULL! which has been developed by Voronoi Diagram Research Center (VDRC) in C++ programming language. The benchmark test of the BetaSCP2 with other programs is also provided. The BetaSCP2 program is available as both a stand-alone and a web server program from VDRC.

BULL! - The Molecular Geometry Engine Based on Voronoi Diagram, Quasi-Triangulation, and Beta-Complex

Libraries are available for the power diagram and the ordinary Voronoi diagram of points upon which application programs can be easily built. However, its counterpart for the Voronoi diagram of spheres does not exist despite of enormous applications, particularly those in molecular worlds. In this paper, we present the BULL! library which abbreviates “Beta Universe Library Liberandam!” for computing the Voronoi diagram of spheres, transforming it to the quasi-triangulation, and extracting the beta-complex. Being an engine library implemented in the standard C++, application programmers can simply call API-functions of BULL! to build application programs correctly, efficiently, and easily. The BULL! engine is designed so that the application programs developed by embedding API-functions are completely independent of the future modifications of the engine.

Robust Construction of the Additively-Weighted Voronoi Diagram via Topology-Oriented Incremental Algorithm

Voronoi diagrams tessellate the space where each cell corresponds to an associated generator under an a priori defined distance and have been extensively used to solve geometric problems of various disciplines. Additively-weighted Voronoi diagrams, also called the Voronoi diagram of disks and spheres, have many critical applications and a few algorithms are known. However, algorithmic robustness remains a major hurdle to use these Voronoi diagrams in practice. There are two important yet different approaches to design robust algorithms: the exact-computation and topology-oriented approaches. The former uses high-precision arithmetic and guarantees the correctness mathematically with the cost of a significant use of computational resources. The latter focuses on topological properties to keep consistency using logical computation rather than numerical computation. In this paper, we present a robust and efficient algorithm for computing the Voronoi diagram of disks using a topology-oriented incremental method. The algorithm is rather simple as it primarily checks topological changes only during each disk is incrementally inserted into a previously constructed Voronoi diagram of some other disks.

BetaConcept: A Program for Voronoi Diagrams, Dual Structures, and Complexes in the Plane

Voronoi diagrams are powerful for solving spatial problems among particles with different sizes. In particular, the Voronoi diagram of spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capability for solving molecular biology/material science problems in an unified framework. Beta-complex is a generalization of (weighted) alpha-complex and they share similarities and dissimilarities. This paper presents the Beta Concept program which facilitates easy understanding of the powerful capability of the Voronoi diagram, its dual structure, and the beta-complex in the plane. Beta Concept is a Windows program with a graphic user interface written in the standard C++ language and is freely available at the Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).