612 research outputs found
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
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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
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