Convex approaches to model wavelet sparsity patterns

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees (HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in de-convolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso. © 2011 IEEE.

Shifting atomic patterns: on the origin of the different atomic-scale patterns of graphite as observed using scanning tunnelling microscopy.

We present an in-depth study of the myriad atomically resolved patterns observed on graphite using the scanning tunnelling microscope (STM) over the past three decades. Through the use of highly resolved atomic resolution images, we demonstrate how the interactions between the different graphene layers comprising graphite affect the local surface atomic charge density and its resulting symmetry orientation, with particular emphasis on interactions that are thermodynamically unstable. Moreover, the interlayer graphene coupling is controlled experimentally by varying the tip-surface interaction, leading to associated changes in the atomic patterns. The images are corroborated by first-principles calculations, further validating our claim that surface graphene displacement, coming both from lateral and vertical displacement of the top graphene layer, forms the basis of the rich variety of atomic patterns observed in STM experiments on graphite.

Oscillatory sensitivity patterns for global modes in wakes

Globally unstable wakes with co-flow at intermediate Reynolds numbers are studied, to quantify important spatial regions for the development and control of the global instability. One region of high structural sensitivity is found close to the inlet for all wakes, in agreement with previous findings for cylinder wakes. A second, elongated region of high structural sensitivity is seen downstream of the first one for unconfined wakes at Re = 400. When base flow modifications are considered, a spatially oscillating sensitivity pattern is found inside the downstream high structural sensitivity region. This implies that the same change in the base flow can either destabilize or stabilize the flow, depending on the exact position where it is applied. It is shown that the sensitivity pattern remains unchanged for different choices of streamwise boundary conditions and numerical resolution. Actual base flow modifications are applied in selected configurations, and the linear global modes recomputed. It is confirmed that the linear global eigenvalues move according to the predicted sensitivity pattern for small amplitude base flow modifications, for which the theory applies. We also look at the implications of a small control cylinder on the flow. Only the upstream high sensitivity region proves to be robust in terms of control, but one should be careful not to disturb the flow in the downstream high sensitivity region, in order to achieve control. The findings can have direct implications on the numerical resolution requirements for wakes at higher Reynolds numbers. Furthermore, they provide one more possible explanation to why confined wakes have a more narrow frequency spectrum than unconfined wakes.

Visual retrieval of concrete crack properties for automated post-earthquake structural safety evaluation

The safety of post-earthquake structures is evaluated manually through inspecting the visible damage inflicted on structural elements. This process is time-consuming and costly. In order to automate this type of assessment, several crack detection methods have been created. However, they focus on locating crack points. The next step, retrieving useful properties (e.g. crack width, length, and orientation) from the crack points, has not yet been adequately investigated. This paper presents a novel method of retrieving crack properties. In the method, crack points are first located through state-of-the-art crack detection techniques. Then, the skeleton configurations of the points are identified using image thinning. The configurations are integrated into the distance field of crack points calculated through a distance transform. This way, crack width, length, and orientation can be automatically retrieved. The method was implemented using Microsoft Visual Studio and its effectiveness was tested on real crack images collected from Haiti.

Microfabrication of electrode patterns for high-frequency ultrasound transducer arrays.

High-frequency ultrasound is needed for medical imaging with high spatial resolution. A key issue in the development of ultrasound imaging arrays to operate at high frequencies (≥30 MHz) is the need for photolithographic patterning of array electrodes. To achieve this directly on 1-3 piezocomposite, the material requires not only planar, parallel, and smooth surfaces, but also an epoxy composite filler that is resistant to chemicals, heat, and vacuum. This paper reports, first, on the surface finishing of 1-3 piezocomposite materials by lapping and polishing. Excellent surface flatness has been obtained, with an average surface roughness of materials as low as 3 nm and step heights between ceramic/polymer of ∼80 nm. Subsequently, high-frequency array elements were patterned directly on top of these surfaces using a photolithography process. A 30-MHz linear array electrode pattern with 50-μm element pitch has been patterned on the lapped and polished surface of a high-frequency 1-3 piezocomposite. Excellent electrode edge definition and electrical contact to the composite were obtained. The composite has been lapped to a final thickness of ∼55 μm. Good adhesion of electrodes on the piezocomposite has been achieved and electrical impedance measurements have demonstrated their basic functionality. The array was then packaged, and acoustic pulse-echo measurements were performed. These results demonstrate that direct patterning of electrodes by photolithography on 1-3 piezocomposite is feasible for fabrication of high-frequency ultrasound arrays. Furthermore, this method is more conducive to mass production than other reported array fabrication techniques.

Modeling fatigue crack growth in crystalline solids with discrete dislocation plasticity

Analyses of crack growth under cyclic loading conditions are discussed where plastic flow arises from the motion of large numbers of discrete dislocations and the fracture properties are embedded in a cohesive surface constitutive relation. The formulation is the same as used to analyse crack growth under monotonic loading conditions, differing only in the remote loading being a cyclic function of time. Fatigue, i.e. crack growth in cyclic loading at a driving force for which the crack would have arrested under monotonic loading, emerges in the simulations as a consequence of the evolution of internal stresses associated with the irreversibility of the dislocation motion. A fatigue threshold, Paris law behaviour, striations, the accelerated growth of short cracks and the scaling with material properties are outcomes of the calculations. Results for single crystals and polycrystals will be discussed.

Continuous Diffraction Patterns from Circular Arrays of Carbon Nanotubes

We report the remarkable diffraction effects produced from circular patterned arrays of multiwalled carbon nanotubes (MWCNTs). Highly ordered circular arrays of multiwalled carbon nanotubes (with inter-nanotube spacings of 633 nm) display optical dispersion effects similar to compact discs. These arrays display remarkable diffraction patterns in the far field which are spatially continuous. High quality diffraction patterns were obtained experimentally which are in excellent agreement with the theoretical calculations. The achieved continuous diffraction patterns pave the way towards the utilization of engineered carbon nanotube arrays in applications like three dimensional holograms.

Effects of exhaust inlet size on the fluid flow patterns created by an Aaberg exhaust hood

The aim of this paper is to investigate the effects of the size of the exhaust inlet on the fluid flow patterns created by an Aaberg exhaust hood. Streamlines and lines of constant speed modelling those created by an Aaberg hood are used to examine the effect of the inlet size on the size and profile of the hood's effective suction area. © 1992.

A flexural crack model for damage detection in reinforced concrete structures

The use of changes in vibration data for damage detection of reinforced concrete structures faces many challenges that obstruct its transition from a research topic to field applications. Among these is the lack of appropriate damage models that can be deployed in the damage detection methods. In this paper, a model of a simply supported reinforced concrete beam with multiple cracks is developed to examine its use for damage detection and structural health monitoring. The cracks are simulated by a model that accounts for crack formation, propagation and closure. The beam model is studied under different dynamic excitations, including sine sweep and single excitation frequency, for various damage levels. The changes in resonant frequency with increasing loads are examined along with the nonlinear vibration characteristics. The model demonstrates that the resonant frequency reduces by about 10% at the application of 30% of the ultimate load and then drops gradually by about 25% at 70% of the ultimate load. The model also illustrates some nonlinearity in the dynamic response of damaged beams. The appearance of super-harmonics shows that the nonlinearity is higher when the damage level is about 35% and then decreases with increasing damage. The restoring force-displacement relationship predicted the reduction in the overall stiffness of the damaged beam. The model quantitatively predicts the experimental vibration behaviour of damaged RC beams and also shows the damage dependency of nonlinear vibration behaviour. © 2011 Published under licence by IOP Publishing Ltd.

Alternating spatial patterns for coordinated group motion

Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude and average but different phases, move together in alternating spatial patterns, taking turns being towards the front, sides and back of the group. We propose a model and control laws to investigate the connections between these spatial dynamics, communication when sensing is range or direction limited, and convergence of coordinated group motions. ©2007 IEEE.