Drell-Hearn-Gerasimov Sum Rule for the Nucleon in the Large-N_c Limit

We show that the Drell-Hearn-Gerasimov sum rule for the nucleon is entirely saturated by the \Delta resonance in the limit of a large number of colors, N_c \to \infty. Corrections are at relative order 1/N_c^2.Comment: 6 pages, latex, no figure

Microfluidic multipoles: theory and applications

Microfluidic multipoles (MFMs) have been realized experimentally and hold promise for "open-space" biological and chemical surface processing. Whereas convective flow can readily be predicted using hydraulic-electrical analogies, the design of advanced MFMs is constrained by the lack of simple, accurate models to predict mass transport within them. In this work, we introduce the first exact solutions to mass transport in multipolar microfluidics based on the iterative conformal mapping of 2D advection-diffusion around a simple edge into dipoles and multipolar geometries, revealing a rich landscape of transport modes. The models were validated experimentally with a library of 3D printed MFM devices and found in excellent agreement. Following a theory-guided design approach, we further ideated and fabricated two new classes of spatiotemporally reconfigurable MFM devices that are used for processing surfaces with time-varying reagent streams, and to realize a multistep automated immunoassay. Overall, the results set the foundations for exploring, developing, and applying open-space MFMs.Comment: 16 pages, 5 figure

Nucleon-Nucleon Scattering Observables in Large-NcN_c QCD

Nucleon-nucleon scattering observables are considered in the context of the large $N_c$ limit of QCD for initial states with moderately high momenta ($p \sim N_c$). The scattering is studied in the framework of the time-dependent mean-field approximation. We focus on the dependence of those observables on the spin and isospin of the initial state which may be computed using time-dependent mean-field theory. We show that, up to corrections, all such observables must be invariant under simultaneous spin and isospin flips ({\it i.e.} rotations through $\pi/2$ in both spin and isospin) acting on either particle. All observables of this class obtained from spin unpolarized measurements must be isospin independent up to $1/N_c$ corrections. Moreover, it can be shown that the leading correction is of relative order $1/N_c^2$ rather than $1/N_c$.Comment: 4 page

Mass transfer and structural analysis of microfluidic sensors

Thesis (Ph. D.)--Massachusetts Institute of Technology, Biological Engineering Division, February 2006.Includes bibliographical references (leaves 181-191).Surface-based sensors take advantage of the natural high surface-to-volume ratios in microfluidic devices, low reagent consumption and high potential for integration in more complex micro total analysis systems (microTAS or pTAS). This thesis studies the fundamental limits of on-chip integrated microfluidic sensors. More specifically, it focuses on detection methods involving surface interaction in channels with thicknesses on the order of a few microns or less. Through mass transfer analysis, we demonstrate that, for thin enough channels, sample detection is limited by the convective transport of analytes, and neither by diffusion nor reaction. The results provided extend the validity of transport models to include transport in the absence of mass transfer boundary layer. All existing analytic solutions to the Graetz problem are described and compiled. The analysis, complemented by finite element simulations, successfully predicts experimental observations made for on-chip immunoassays in micron-thick fluidic channels. Subsequently, our study of on chip detection systems is carried on with emphasis on resonating cantilever sensors. In order to interpret the output signal from these devices, we develop a dynamic cantilever model to link spatially and temporally dependent mass adsorption with resonance frequency change.(cont.) The mass adsorption is then directly related to the sensors' operating conditions via the mass transfer models previously developed. We then develop a 2D finite-element model capable of predicting the devices response and of extracting bimolecular rate constants. Finally, since hydraulic resistance severely increases as channels get shallower, we provide a structural analysis of polymer-based microsystems. Through scaling and numerical simulations we demonstrate the effect of channel deformation on the flow conditions inside the device and vice versa. Finally, channel deformation is experimentally quantified using optical methods and compared with the models developed. Throughout this thesis, the approach to physical modeling has been to use mathematical and numerical analysis as predictive tools in the design of integrated lab-on-a-chip systems. Whenever possible, scaling and analytic solutions are developed, since they provide a direct relationship between experimental observations, geometry and the multiple dependent variables in the system, and can be readily used as design criteria by the experimentalist.by Thomas Gervais.Ph.D

Excited Heavy Baryons and Their Symmetries I: Formalism

This is the first of two papers to study a new emergent symmetry which connects orbitally excited heavy baryons to the ground states in the combined heavy quark and large $N_c$ limit. The existence of this symmetry is shown in a model-independent way, and different possible realizations of the symmetry are discussed. It is also proved that this emergent symmetry commutes with the large $N_c$ spin-flavor symmetry.Comment: 20 pages in REVTe

Matching language and accent in virtual assistant responses

Traditionally a voice-controlled virtual assistant interacts with a user in a neutral, accent-free way. A virtual assistant that matches the language and accent of the user can be more appealing. This disclosure uses machine-learning models to match the language and accent of a virtual assistant to that of the user who commands it