Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent injection rates in a Hele-Shaw cell that is either standard, tapered or rotating can be used to reduce the development of viscous fingering when an inviscid fluid is injected into a viscous fluid over a finite time period. We perform a series of numerical experiments comparing the effectiveness of each strategy to determine how these non-standard Hele-Shaw configurations influence the morphological features of the inviscid-viscous fluid interface. Tapering plates in either converging or diverging directions leads to reduced metrics of viscous fingering at the final time when compared to the standard parallel configuration, especially with carefully chosen injection rates; for the rotating plate case, the effect is even more dramatic, with sufficiently large rotation rates completely stabilising the interface. Next, we illustrate how the number of non-splitting fingers can be controlled by injecting the inviscid fluid at a time-dependent rate while increasing the gap between the plates. Simulations compare well with previous experimental results for various injection rates and geometric configurations. Further, we demonstrate how the fully nonlinear dynamics of the problem affect the number of fingers that emerge and how well this number agrees with predictions from linear stability analysis

MISR stereoscopic image matchers: techniques and results

The Multi-angle Imaging SpectroRadiometer (MISR) instrument, launched in December 1999 on the NASA EOS Terra satellite, produces images in the red band at 275-m resolution, over a swath width of 360 km, for the nine camera angles 70.5/spl deg/, 60/spl deg/, 45.6/spl deg/, and 26.1/spl deg/ forward, nadir, and 26.1/spl deg/, 45.6/spl deg/, 60/spl deg/, and 70.5/spl deg/ aft. A set of accurate and fast algorithms was developed for automated stereo matching of cloud features to obtain cloud-top height and motion over the nominal six-year lifetime of the mission. Accuracy and speed requirements necessitated the use of a combination of area-based and feature-based stereo-matchers with only pixel-level acuity. Feature-based techniques are used for cloud motion retrieval with the off-nadir MISR camera views, and the motion is then used to provide a correction to the disparities used to measure cloud-top heights which are derived from the innermost three cameras. Intercomparison with a previously developed "superstereo" matcher shows that the results are very comparable in accuracy with much greater coverage and at ten times the speed. Intercomparison of feature-based and area-based techniques shows that the feature-based techniques are comparable in accuracy at a factor of eight times the speed. An assessment of the accuracy of the area-based matcher for cloud-free scenes demonstrates the accuracy and completeness of the stereo-matcher. This trade-off has resulted in the loss of a reliable quality metric to predict accuracy and a slightly high blunder rate. Examples are shown of the application of the MISR stereo-matchers on several difficult scenes which demonstrate the efficacy of the matching approach

Saffman-Taylor fingers with kinetic undercooling

The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned in a periodic array. In the streamer context, the relevant regularisation on the interface is not provided by surface tension, but instead has been postulated to involve a mechanism equivalent to kinetic undercooling, which acts to penalise high velocities and prevent blow-up of the unregularised solution. Previous asymptotic results for the Hele-Shaw finger problem with kinetic undercooling suggest that for a given value of the kinetic undercooling parameter, there is a discrete set of possible finger shapes, each analytic at the nose and occupying a different fraction of the channel width. In the limit in which the kinetic undercooling parameter vanishes, the fraction for each family approaches 1/2, suggesting that this 'selection' of 1/2 by kinetic undercooling is qualitatively similar to the well-known analogue with surface tension. We treat the numerical problem of computing these Saffman-Taylor fingers with kinetic undercooling, which turns out to be more subtle than the analogue with surface tension, since kinetic undercooling permits finger shapes which are corner-free but not analytic. We provide numerical evidence for the selection mechanism by setting up a problem with both kinetic undercooling and surface tension, and numerically taking the limit that the surface tension vanishes.Comment: 10 pages, 6 figures, accepted for publication by Physical Review

Maximum likelihood estimation of cloud height from multi-angle satellite imagery

We develop a new estimation technique for recovering depth-of-field from multiple stereo images. Depth-of-field is estimated by determining the shift in image location resulting from different camera viewpoints. When this shift is not divisible by pixel width, the multiple stereo images can be combined to form a super-resolution image. By modeling this super-resolution image as a realization of a random field, one can view the recovery of depth as a likelihood estimation problem. We apply these modeling techniques to the recovery of cloud height from multiple viewing angles provided by the MISR instrument on the Terra Satellite. Our efforts are focused on a two layer cloud ensemble where both layers are relatively planar, the bottom layer is optically thick and textured, and the top layer is optically thin. Our results demonstrate that with relative ease, we get comparable estimates to the M2 stereo matcher which is the same algorithm used in the current MISR standard product (details can be found in [IEEE Transactions on Geoscience and Remote Sensing 40 (2002) 1547--1559]). Moreover, our techniques provide the possibility of modeling all of the MISR data in a unified way for cloud height estimation. Research is underway to extend this framework for fast, quality global estimates of cloud height.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS243 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiangle observations of Arctic clouds from FIRE ACE: June 3, 1998, case study

In May and June 1998 the Airborne Multiangle Imaging Spectroradiometer (AirMISR) participated in the FIRE Arctic Cloud Experiment (ACE). AirMISR is an airborne instrument for obtaining multiangle imagery similar to that of the satellite-borne MISR instrument. This paper presents a detailed analysis of the data collected on June 3, 1998. In particular, AirMISR radiance measurements are compared with measurements made by two other instruments, the Cloud Absorption Radiometer (CAR) and the MODIS airborne simulator (MAS), as well as to plane-parallel radiative transfer simulations. It is found that the AirMISR radiance measurements and albedo estimates compare favorably both with the other instruments and with the radiative transfer simulations. In addition to radiance and albedo, the multiangle AirMISR data can be used to obtain estimates of cloud top height using stereoimaging techniques. Comparison of AirMISR retrieved cloud top height (using the complete MISR-based stereoimaging approach) shows excellent agreement with the measurements from the airborne Cloud Lidar System (CLS) and ground-based millimeterwave cloud radar

Urban Environmental Performance Index: The Quito Pilot Case

In the context of the adoption of the Sustainable Development Goals (SDG) and its indicators, especially Goal 11, the importance of indicators is paramount to the implementation, monitoring and eventual success of the SDG. However, a review of global sustainability indicators reveals major gaps in coverage, including scientific gaps. Indicators are often siloed, meaning at the urban scale where issues often overlap and intersect, existing indicators do not take into consideration cross-sectoral linkages. Finally, many indicators fail to adequately address social equity or inclusion, a high-priority issue identified as central to new definitions of green economy and sustainable development at Rio+20. This research we developed a case study to pilot new indicators based information available for the city of Quito that address these challenges. The development of this pilot indicators has involved the use of several data collection tools and particularly the treatment of data so it could be available for numerical and graphical analysis. The research relied heavily Open Source platforms and tools to perform the analysis. Ultimately, the objective of this research is to scale the study to other cities around the world and other indicators to create an index that is reliable in measuring the environmental performance of the cities, while considering the social distribution of the environmental impacts inside the city

Global Music Perspectives: Music Outside the Western Canon in Local Schools

As a class, we are designing a research project for investigating how music teachers from counties in South-Central Pennsylvania use music from outside the Western canon (i.e. world music ). We are performing a qualitative study by interviewing k-12 music teachers from school districts in South-Central Pennsylvania. Teachers may choose to participate in a focus group interview with other teachers or in one-on-one interviews. The focus group interview will not exceed two hours and the one-on-one interviews will not exceed an hour. The interviews will be guided using a questionnaire (see attached), but the conversation may deviate from these questions at the discretion of the interviewer(s). We will transcribe these interviews to extract common thematic materials and relevant information. We will also compile a literature review of relevant peer-reviewed articles and use the data from said articles to expand upon our gathered information

Modeling the growth of multicellular cancer spheroids in a\ud bioengineered 3D microenvironment and their treatment with an\ud anti-cancer drug

A critical step in the dissemination of ovarian cancer cells is the formation of multicellular spheroids from cells shed from the primary tumor. The objectives of this study were to establish and validate bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer cells in vitro and simultaneously to develop computational models describing the growth of multicellular spheroids in these bioengineered matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and cultured for up to 4 weeks. Immunohistochemistry was used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel.\ud \ud Two computational models were developed. In the first model, each spheroid was treated as an incompressible porous medium, whereas in the second model the concept of morphoelasticity was used to incorporate details about internal stresses and strains. Each model was formulated as a free boundary problem. Functional forms for cell proliferation and apoptosis motivated by the experimental work were applied and the predictions of both models compared with the output from the experiments. Both models simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture time and treatment with paclitaxel. Our mathematical models provide new perspectives on previous experimental results and have informed the design of new 3D studies of multicellular cancer spheroids

Growth of confined cancer spheroids: a combined experimental and mathematical modelling approach

We have integrated a bioengineered three-dimensional platform by generating multicellular cancer spheroids in a controlled microenvironment with a mathematical model to investigate\ud confined tumour growth and to model its impact on cellular processes