Steklov Approximations of Solutions of Laplacian Boundary Value Problems

Eigenfunction expansion methods have been studied in various ways to study solutions of PDEs. This talk will feature error estimates for approximation of solutions of Laplace’s equation with Dirichlet, Robin or Neumann boundary value conditions using the harmonic Steklov eigenfunctions. Based on the spectral theory of trace spaces the solutions are represented by orthogonal basis from normalized Steklov eigenfuntions. When the region is a rectangle, with explicit formulae for the Steklov eigenfunctions, both theoretical analysis and numerical experiments will introduce the efficiency and accuracy of the Steklov expansion methods in this talk

Steklov Eigenproblems and Approximations of Harmonic Functions

In this work, we provide explicit formulae for harmonic Steklov eigenvalues and associated Steklov eigenfunctions by solving a Steklov eigenproblem on bounded rectangles. This allows the description of all the Steklov eigenvalues and their corresponding Steklov eigenfunctions. Solutions of Laplace's equation subject to inhomogeneous Dirichlet, Neumann, Robin, or other boundary data are approximated by Steklov expansions. These representations involve boundary conditions and explicit spectral approximations are found. In the end, we provide the general formulae for u(0,0) where harmonic functions u(x, y) are solutions of boundary value problems on a rectangle. These harmonic functions are determined precisely in terms of their respective boundary data.Mathematics, Department o

A facile route to the preparation of mixed matrix polyvinylidene fluoride membranes with in-situ generated polyethyleneimine particles

The development of mixed matrix polymeric membranes with embedded functional particles/nanomaterials has been an active area of research during the last two decades. Such membranes are being designed to carry out multiple functions (e.g. retention, sorption and catalysis) with improved properties and performance over those of commercial membranes. Polymeric particles could provide greater flexibility for the preparation of mixed matrix membranes with improved particle–matrix compatibility, particle loading, flux and permselectivity. In this article, we describe a facile and simple route to the preparation of mixed matrix polyvinylidene fluoride (PVDF) membranes embedded with branched polyethylenimine (PEI) particles. The critical step of our novel methodology is the in-situ generation of crosslinked PEI micro/nanoparticles (with diameters ranging from 400 nm to 3 μm) in the membrane casting solution using epichlorohydrin as crosslinker. This eliminates the need to utilize inverse emulsion polymerization techniques to synthesize PEI particles prior to the membrane casting. Using non-solvent induced phase separation (NIPS), we successfully prepared mixed matrix PVDF membranes with uniform particle distribution and PEI particle loadings ranging from 27 to 48 wt%. Our novel membrane preparation route exhibits many advantages including simplicity, scalability and versatility. Preliminary experiments show that our new mixed matrix PVDF membranes with embedded PEI particles can serve as weak-base membrane absorbers for proteins such as bovine serum albumin

Mining Critical Metals and Elements from Seawater: Opportunities and Challenges

The availability and sustainable supply of technology metals and valuable elements is critical to the global economy. There is a growing realization that the development and deployment of the clean energy technologies and sustainable products and manufacturing industries of the 21st century will require large amounts of critical metals and valuable elements including rare-earth elements (REEs), platinum group metals (PGMs), lithium, copper, cobalt, silver, and gold. Advances in industrial ecology, water purification, and resource recovery have established that seawater is an important and largely untapped source of technology metals and valuable elements. This feature article discusses the opportunities and challenges of mining critical metals and elements from seawater. We highlight recent advances and provide an outlook of the future of metal mining and resource recovery from seawater

Real-time monitoring of geosmin and 2-methylisoborneol, representative odor compounds in water pollution using bioelectronic nose with human-like performance

A bioelectronic nose for the real-time assessment of water quality was constructed with human olfactory receptor (hOR) and single-walled carbon nanotube field-effect transistor (swCNT-FET). Geosmin (GSM) and 2-methylisoborneol (MIB), mainly produced by bacteria, are representative odor compounds and also indicators of contamination in the water supply system. For the screening of hORs which respond to these compounds, we performed CRE-luciferase assays of the two odorants in heterologous cell system. Human OR51S1 for GSM and OR3A4 for MIB were selected, and nanovesicles expressing the hORs on surface were produced from HEK-293 cell. Carbon nanotube field-effect transistor was functionalized with the nanovesicles. The bioelectronic nose was able to selectively detect GSM and MIB at concentrations as low as a 10 ng L−1. Furthermore, detection of these compounds from the real samples such as tap water, bottled water and river water was available without any pretreatment processes.OAIID:oai:osos.snu.ac.kr:snu2015-01/102/0000002410/12ADJUST_YN:YEMP_ID:A002014DEPT_CD:458CITE_RATE:6.409DEPT_NM:화학생물공학부SCOPUS_YN:NCONFIRM: