Hierarchical adaptive polynomial chaos expansions

Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be required, which leads to a large polynomial basis whereas usually only a few of the basis functions are in fact significant. Taking into account the sparse structure of the model, advanced techniques such as sparse PCE (SPCE), have been recently proposed to alleviate the computational issue. In this paper, we propose a novel approach to SPCE, which allows one to exploit the model's hierarchical structure. The proposed approach is based on the adaptive enrichment of the polynomial basis using the so-called principle of heredity. As a result, one can reduce the computational burden related to a large pre-defined candidate set while obtaining higher accuracy with the same computational budget

The noncommutative harmonic oscillator in more than one dimensions

The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding two-dimensional harmonic oscillator are solved. The angular momentum operator is derived and its $\star$-genvalue problem is shown to be equivalent to the usual eigenvalue problem. The $\star$-genvalues for the angular momentum are found to depend on the energy difference of the oscillations in each dimension. Furthermore two examples of assymetric noncommutative harmonic oscillator are analysed. The first is the noncommutative two-dimensional Landau problem and the second is the three-dimensional harmonic oscillator with symmetrically noncommuting coordinates and momenta.Comment: 12 page

Mass sensing using an amorphous silicon MEMS resonator

Bilayer micro-bridge resonators of amorphous silicon and titanium were fabricated on a glass substrate at 100°C by surface micromachining using an aluminum sacrificial layer. Au square patterns with sub-micrometer dimensions were patterned on top of the microresonators. These Au squares allowed specific immobilization of thiolated single strand DNA probe oligonucleotides. The frequency response of the electrostatically-actuated resonators was measured optically. The mass loading effect of the Au squares and of the immobilized ssDNA probes were determined by the shift in the resonance frequency of the micro-bridge resonators

A finite difference solution to a mixed boundary value problem for Laplace's equation

Finite difference solution to mixed boundary value problem for Laplace equatio

Juan de Fuca subduction zone from a mixture of tomography and waveform modeling

Seismic tomography images of the upper mantle structures beneath the Pacific Northwestern United States display a maze of high-velocity anomalies, many of which produce distorted waveforms evident in the USArray observations indicative of the Juan de Fuca (JdF) slab. The inferred location of the slab agrees quite well with existing contour lines defining the slab's upper interface. Synthetic waveforms generated from a recent tomography image fit teleseismic travel times quite well and also some of the waveform distortions. Regional earthquake data, however, require substantial changes to the tomographic velocities. By modeling regional waveforms of the 2008 Nevada earthquake, we find that the uppermost mantle of the 1D reference model AK135, the reference velocity model used for most tomographic studies, is too fast for the western United States. Here, we replace AK135 with mT7, a modification of an older Basin-and-Range model T7. We present two hybrid velocity structures satisfying the waveform data based on modified tomographic images and conventional slab wisdom. We derive P and SH velocity structures down to 660 km along two cross sections through the JdF slab. Our results indicate that the JdF slab is subducted to a depth of 250 km beneath the Seattle region, and terminates at a shallower depth beneath Portland region of Oregon to the south. The slab is about 60 km thick and has a P velocity increase of 5% with respect to mT7. In order to fit waveform complexities of teleseismic Gulf of Mexico and South American events, a slab-like high-velocity anomaly with velocity increases of 3% for P and 7% for SH is inferred just above the 660 discontinuity beneath Nevada

Determination of earthquake focal depths and source time functions in central Asia using teleseismic P waveforms

We developed a new method to determine earthquake source time functions and focal depths. It uses theoretical Green's function and a time-domain deconvolution with positivity constraint to estimate the source time function from the teleseismic P waveforms. The earthquake focal depth is also determined in the process by using the time separations of the direct P and depth phases. We applied this method to 606 earthquakes between 1990 and 2005 in Central Asia. The results show that the Centroid Moment Tensor solutions, which are routinely computed for earthquake larger than M5.0 globally using very long period body and surface waves, systematically over-estimated the source depths and durations, especially for shallow events. Away from the subduction zone, most of the 606 earthquakes occurred within the top 20 km of crust. This shallow distribution of earthquakes suggests a high geotherm and a weak ductile lower crust in the region

Upper mantle P velocity structure beneath the Midwestern United States derived from triplicated waveforms

Upper mantle seismic velocity structures in both vertical and horizontal directions are key to understanding the structure and mechanics of tectonic plates. Recent deployment of the USArray Transportable Array (TA) in the Midwestern United States provides an extraordinary regional earthquake data set to investigate such velocity structure beneath the stable North American craton. In this paper, we choose an M_w5.1 Canadian earthquake in the Quebec area, which is recorded by about 400 TA stations, to examine the P wave structures between the depths of 150 km to 800 km. Three smaller Midwestern earthquakes at closer distance to the TA are used to investigate vertical and horizontal variations in P velocity between depths of 40 km to 150 km. We use a grid-search approach to find the best 1-D model, starting with the previously developed S25 regional model. The results support the existence of an 8° discontinuity in P arrivals caused by a negative velocity gradient in the lithosphere between depths of 40 km to 120 km followed by a small (∼1%) jump and then a positive gradient down to 165 km. The P velocity then decreases by 2% from 165 km to 200 km, and we define this zone as the regional lithosphere-asthenosphere boundary (LAB). Beneath northern profiles, waves reflected from the 410 discontinuity (410) are delayed by up to 1 s relative to those turning just below the 410, which we explain by an anomaly just above the discontinuity with P velocity reduced by ∼3%. The 660 discontinuity (660) appears to be composed of two smaller velocity steps with a separation of 16 km. The inferred low-velocity anomaly above 410 may indicate high water concentrations in the transition zone, and the complexity of the 660 may be related to Farallon slab segments that have yet to sink into the deep mantle

Evidence for the Role of Instantons in Hadron Structure from Lattice QCD

Cooling is used as a filter on a set of gluon fields sampling the Wilson action to selectively remove essentially all fluctuations of the gluon field except for the instantons. The close agreement between quenched lattice QCD results with cooled and uncooled configurations for vacuum correlation functions of hadronic currents and for density-density correlation functions in hadronic bound states provides strong evidence for the dominant role of instantons in determining light hadron structure and quark propagation in the QCD vacuum.Comment: 26 pages in REVTeX, plus 10 figures, uuencoded. Submitted to Physical Review D. MIT-CTP-226

Theoretical studies of tone noise from a fan rotor

An analytical study was made of some possible rotor alone noise sources of dipole, quadrapole and monopole characters which generate discrete tone noise. Particular emphasis is given to the tone noise caused by fan inlet flow distortion and turbulence. Analytical models are developed to allow prediction of absolute levels. Experimental data measured on a small scale fan is presented which indicates inlet turbulence interaction with a fan rotor can be a source of tone noise. Predicted and measured tone noise for the small scale rotor are shown to be in reasonable agreement