Differential quadrature method for space-fractional diffusion equations on 2D irregular domains

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature (DQ) methods for solving the 2D space-fractional diffusion equations on irregular domains. The methods in presence reduce the original equation into a set of ordinary differential equations (ODEs) by introducing valid DQ formulations to fractional directional derivatives based on the functional values at scattered nodal points on problem domain. The required weighted coefficients are calculated by using radial basis functions (RBFs) as trial functions, and the resultant ODEs are discretized by the Crank-Nicolson scheme. The main advantages of our methods lie in their flexibility and applicability to arbitrary domains. A series of illustrated examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table

Gold Nanoparticles and Its Potential Applications in Cancer Research

2009 Spring Meeting of the NANOFANS Forum. Presented on May 1, 2009 from 11 am-2 pm in the Marcus Nanotechnology Building (Rooms 1116-1118) on the Georgia Tech campus.Cancer Nanotechnology: New Opportunities in Engineering and Medicine / Shuming Nie, Director, Center of Cancer Nanotechnology Excellence, Emory and Georgia Tech -- Magnetic Nanoparticles and Ovarian Cancer: A Potential New Direction in Therapeutic Intervention / John McDonald, Director, Ovarian Cancer Institute and Chair of the School of Biology at Georgia Tech -- Gold Nanoparticles and Its Potential Applications in Cancer Research / Mostafa El-Sayed, Director, Laser Dynamics Laboratory at the School of Chemistry & Biochemistry at Georgia Tech.Shuming Nie is the Wallace H. Coulter Distinguished Chair Professor in Biomedical Engineering at Emory University and the Georgia Institute of Technology. His research interest is broadly in biomolecular engineering and nanotechnology. John McDonald is taking an integrated systems approach to the study of cancer. This means that he views cancer not as a defect in any particular gene or protein, but as a de-regulated cellular/ inter-cellular process. Mostafa El-Sayed is the Julius Brown Chair and Regents Professor in the School of Chemistry and Biochemistry at Georgia Tech. He researches Nanoscience and also investigates how Nanoparticles can be used in Nanomedicine, Nano Catalysis, and Nanophotonics

Quantum state engineering with flux-biased Josephson phase qubits by Stark-chirped rapid adiabatic passages

In this paper, the scheme of quantum computing based on Stark chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei et al., Phys. Rev. Lett. 100, 113601 (2008)] is extensively applied to implement the quantum-state manipulations in the flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark-shifts. Then, assisted by various transition pulses universal quantum logic gates as well as arbitrary quantum-state preparations could be implemented. Compared with the usual PI-pulses operations widely used in the experiments, the adiabatic population passage proposed here is insensitive the details of the applied pulses and thus the desirable population transfers could be satisfyingly implemented. The experimental feasibility of the proposal is also discussed.Comment: 9 pages, 4 figure

Unsupervised Feature Selection with Adaptive Structure Learning

The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are estimated using all the input features of data. However, the estimated intrinsic structures are unreliable/inaccurate when the redundant and noisy features are not removed. Therefore, we face a dilemma here: one need the true structures of data to identify the informative features, and one need the informative features to accurately estimate the true structures of data. To address this, we propose a unified learning framework which performs structure learning and feature selection simultaneously. The structures are adaptively learned from the results of feature selection, and the informative features are reselected to preserve the refined structures of data. By leveraging the interactions between these two essential tasks, we are able to capture accurate structures and select more informative features. Experimental results on many benchmark data sets demonstrate that the proposed method outperforms many state of the art unsupervised feature selection methods

Relaying systems with reciprocity mismatch : impact analysis and calibration

Cooperative beamforming can provide significant performance improvement for relaying systems with the help of the channel state information (CSI). In time-division duplexing (TDD) mode, the estimated CSI will deteriorate due to the reciprocity mismatch. In this work, we examine the impact and the calibration of the reciprocity mismatch in relaying systems. To evaluate the impact of the reciprocity mismatch for all devices, the closed-form expression of the achievable rate is first derived. Then, we analyze the performance loss caused by the reciprocity mismatch at sources, relays, and destinations respectively to show that the mismatch at relays dominates the impact. To compensate the performance loss, a two-stage calibration scheme is proposed for relays. Specifically, relays perform the intra-calibration based on circuits independently. Further, the inter-calibration based on the discrete Fourier transform (DFT) codebook is operated to improve the calibration performance by cooperation transmission, which has never been considered in previous work. Finally, we derive the achievable rate after relays perform the proposed reciprocity calibration scheme and investigate the impact of estimation errors on the system performance. Simulation results are presented to verify the analytical results and to show the performance of the proposed calibration approach

Origin of the Mosaicity in Graphene Grown on Cu(111)

We use low-energy electron microscopy to investigate how graphene grows on Cu(111). Graphene islands first nucleate at substrate defects such as step bunches and impurities. A considerable fraction of these islands can be rotationally misaligned with the substrate, generating grain boundaries upon interisland impingement. New rotational boundaries are also generated as graphene grows across substrate step bunches. Thus, rougher substrates lead to higher degrees of mosaicity than do flatter substrates. Increasing the growth temperature improves crystallographic alignment. We demonstrate that graphene growth on Cu(111) is surface diffusion limited by comparing simulations of the time evolution of island shapes with experiments. Islands are dendritic with distinct lobes, but unlike the polycrystalline, four-lobed islands observed on (100)-textured Cu foils, each island can be a single crystal. Thus, epitaxial graphene on smooth, clean Cu(111) has fewer structural defects than it does on Cu(100).Comment: Article revised following reviewer comment

In-plane orientation effects on the electronic structure, stability and Raman scattering of monolayer graphene on Ir(111)

We employ angle-resolved photoemission spectroscopy (ARPES) to investigate the electronic structures of two rotational variants of epitaxial, single-layer graphene on Ir(111). As grown, the more-abundant R0 variant is nearly charge-neutral, with strong hybridization between graphene and Ir bands near the Fermi level. The graphene Fermi surface and its replicas exactly coincide with Van Hove singularities in the Ir Fermi surface. Sublattice symmetry breaking introduces a small gap-inducing potential at the Dirac crossing, which is revealed by n-doping the graphene using K atoms. The energy gaps between main and replica bands (originating from the moir\'e interference pattern between graphene and Ir lattices) is shown to be non-uniform along the mini- zone boundary due to hybridization with Ir bands. An electronically mediated interaction is proposed to account for the stability of the R0 variant. The variant rotated 30{\deg} in-plane, R30, is p-doped as grown and K doping reveals no band gap at the Dirac crossing. No replica bands are found in ARPES measurements. Raman spectra from the R30 variant exhibit the characteristic phonon modes of graphene, while R0 spectra are featureless. These results show that the film/substrate interaction changes from chemisorption (R0) to physisorption (R30) with in-plane orientation. Finally, graphene-covered Ir has a work function lower than the clean substrate but higher than graphite.Comment: Manuscript plus 7 figure

Stable equivariant abelianization, its properties, and applications

AbstractLet G be a finite group. For a based G-space X and a Mackey functor M, a topological Mackey functor X⊗˜M is constructed, which will be called the stable equivariant abelianization of X with coefficients in M. When X is a based G-CW complex, X⊗˜M is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold–Thom theorem. Applying a variant of Elmendorf's construction, we get a model for the Eilenberg–Mac Lane spectrum HM. The proof uses a structure theorem for Mackey functors and our previous results