Competing orders II: the doped quantum dimer model

We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `slave' particle U(1) and SU(2) gauge theories. We account for the non-perturbative effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper (L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1 excitations and their coupling to superflow and density wave fluctuations.Comment: 22 pages, 10 figures; part I is cond-mat/0408329; (v2) changed title and added clarification

Modeling Complex Material Systems Using Stochastic Reconstruction and Lattice Particle Simulation

abstract: In this dissertation, three complex material systems including a novel class of hyperuniform composite materials, cellularized collagen gel and low melting point alloy (LMPA) composite are investigated, using statistical pattern characterization, stochastic microstructure reconstruction and micromechanical analysis. In Chapter 1, an introduction of this report is provided, in which a brief review is made about these three material systems. In Chapter 2, detailed discussion of the statistical morphological descriptors and a stochastic optimization approach for microstructure reconstruction is presented. In Chapter 3, the lattice particle method for micromechanical analysis of complex heterogeneous materials is introduced. In Chapter 4, a new class of hyperuniform heterogeneous material with superior mechanical properties is investigated. In Chapter 5, a bio-material system, i.e., cellularized collagen gel is modeled using correlation functions and stochastic reconstruction to study the collective dynamic behavior of the embed tumor cells. In chapter 6, LMPA soft robotic system is generated by generalizing the correlation functions and the rigidity tunability of this smart composite is discussed. In Chapter 7, a future work plan is presented.Dissertation/ThesisDoctoral Dissertation Materials Science and Engineering 201

Relative stereociliary motion in a hair bundle opposes amplification at distortion frequencies

Direct gating of mechanoelectrical-transduction channels by mechanical force is a basic feature of hair cells that assures fast transduction and underpins the mechanical amplification of acoustic inputs. But the associated nonlinearity - the gating compliance - inevitably distorts signals. Because reducing distortion would make the ear a better detector, we sought mechanisms with that effect. Mimicking in vivo stimulation, we used stiff probes to displace individual hair bundles at physiological amplitudes and measured the coherence and phase of the relative stereociliary motions with a dual-beam differential interferometer. Although stereocilia moved coherently and in phase at the stimulus frequencies, large phase lags at the frequencies of the internally generated distortion products indicated dissipative relative motions. Tip links engaged these relative modes and decreased the coherence in both stimulated and free hair bundles. These results show that a hair bundle breaks into a highly dissipative serial arrangement of stereocilia at distortion frequencies, precluding their amplification.Comment: 33 pages in total, including the main article with one table and three figures, as well as the supplemental information that itself contains two figure

Stirring up trouble: Multi-scale mixing measures for steady scalar sources

The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence of stirring. These variances can be weighted at various spatial scales, leading to a family of multi-scale mixing measures and efficiencies. We derive a priori estimates on these efficiencies from the advection--diffusion partial differential equation, focusing on a broad class of statistically homogeneous and isotropic incompressible flows. The analysis produces bounds on the mixing efficiencies in terms of the Peclet number, a measure the strength of the stirring relative to molecular diffusion. We show by example that the estimates are sharp for particular source, sink and flow combinations. In general the high-Peclet number behavior of the bounds (scaling exponents as well as prefactors) depends on the structure and smoothness properties of, and length scales in, the scalar source and sink distribution. The fundamental model of the stirring of a monochromatic source/sink combination by the random sine flow is investigated in detail via direct numerical simulation and analysis. The large-scale mixing efficiency follows the upper bound scaling (within a logarithm) at high Peclet number but the intermediate and small-scale efficiencies are qualitatively less than optimal. The Peclet number scaling exponents of the efficiencies observed in the simulations are deduced theoretically from the asymptotic solution of an internal layer problem arising in a quasi-static model.Comment: 37 pages, 7 figures. Latex with RevTeX4. Corrigendum to published version added as appendix

Radar Signal Processing for Interference Mitigation

It is necessary for radars to suppress interferences to near the noise level to achieve the best performance in target detection and measurements. In this dissertation work, innovative signal processing approaches are proposed to effectively mitigate two of the most common types of interferences: jammers and clutter. Two types of radar systems are considered for developing new signal processing algorithms: phased-array radar and multiple-input multiple-output (MIMO) radar. For phased-array radar, an innovative target-clutter feature-based recognition approach termed as Beam-Doppler Image Feature Recognition (BDIFR) is proposed to detect moving targets in inhomogeneous clutter. Moreover, a new ground moving target detection algorithm is proposed for airborne radar. The essence of this algorithm is to compensate for the ground clutter Doppler shift caused by the moving platform and then to cancel the Doppler-compensated clutter using MTI filters that are commonly used in ground-based radar systems. Without the need of clutter estimation, the new algorithms outperform the conventional Space-Time Adaptive Processing (STAP) algorithm in ground moving target detection in inhomogeneous clutter. For MIMO radar, a time-efficient reduced-dimensional clutter suppression algorithm termed as Reduced-dimension Space-time Adaptive Processing (RSTAP) is proposed to minimize the number of the training samples required for clutter estimation. To deal with highly heterogeneous clutter more effectively, we also proposed a robust deterministic STAP algorithm operating on snapshot-to-snapshot basis. For cancelling jammers in the radar mainlobe direction, an innovative jamming elimination approach is proposed based on coherent MIMO radar adaptive beamforming. When combined with mutual information (MI) based cognitive radar transmit waveform design, this new approach can be used to enable spectrum sharing effectively between radar and wireless communication systems. The proposed interference mitigation approaches are validated by carrying out simulations for typical radar operation scenarios. The advantages of the proposed interference mitigation methods over the existing signal processing techniques are demonstrated both analytically and empirically

Multimodal Image Fusion and Its Applications.

Image fusion integrates different modality images to provide comprehensive information of the image content, increasing interpretation capabilities and producing more reliable results. There are several advantages of combining multi-modal images, including improving geometric corrections, complementing data for improved classification, and enhancing features for analysis...etc. This thesis develops the image fusion idea in the context of two domains: material microscopy and biomedical imaging. The proposed methods include image modeling, image indexing, image segmentation, and image registration. The common theme behind all proposed methods is the use of complementary information from multi-modal images to achieve better registration, feature extraction, and detection performances. In material microscopy, we propose an anomaly-driven image fusion framework to perform the task of material microscopy image analysis and anomaly detection. This framework is based on a probabilistic model that enables us to index, process and characterize the data with systematic and well-developed statistical tools. In biomedical imaging, we focus on the multi-modal registration problem for functional MRI (fMRI) brain images which improves the performance of brain activation detection.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120701/1/yuhuic_1.pd