Physics-driven proper orthogonal decomposition: A simulation methodology for partial differential equations.

A simulation methodology derived from a learning algorithm based on Proper Orthogonal Decomposition (POD) is presented to solve partial differential equations (PDEs) for physical problems of interest. Using the developed methodology, a physical problem of interest is projected onto a functional space described by a set of basis functions (or POD modes) that are trained via the POD by solution data collected from direct numerical simulations (DNSs) of the PDE. The Galerkin projection of the PDE is then performed to account for physical principles guided by the PDE.

Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures.

Multi-dimensional direct numerical simulation (DNS) of the Schrödinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices, etc. In large-scale nanostructures, extensive computational effort needed in DNS may become prohibitive due to the high degrees of freedom (DoF). This study employs a physics-based reduced-order learning algorithm, enabled by the first principles, for simulation of the Schrödinger equation to achieve high accuracy and efficiency.

Electrical transport properties of graphene nanoribbons produced from sonicating graphite in solution.

A simple one-stage solution-based method was developed to produce graphene nanoribbons by sonicating graphite powder in organic solutions with polymer surfactant. The graphene nanoribbons were deposited on a silicon substrate, and characterized by Raman spectroscopy and atomic force microscopy. Single-layer and few-layer graphene nanoribbons with a width ranging from sub-10 nm to tens of nanometers and lengths ranging from hundreds of nanometers to 1 µm were routinely observed.

Physicochemically modified silicon as a substrate for protein microarrays.

Reverse phase protein microarrays (RPMA) enable high throughput screening of posttranslational modifications of important signaling proteins within diseased cells. One limitation of protein-based molecular profiling is the lack of a PCR-like intrinsic amplification system for proteins. Enhancement of protein microarray sensitivities is an important goal, especially because many molecular targets within patient tissues are of low abundance.

Nanoporous surfaces as harvesting agents for mass spectrometric analysis of peptides in human plasma.

Silica-based nanoporous surfaces have been developed in order to capture low molecular weight peptides from human plasma. Harvested peptides were subjected to mass spectrometric analysis by using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) as a means of detecting and assessing the bound molecules. Peptide profiles consisting of about 70 peaks in the range 800-10,000 m/z were generated.