188 research outputs found
Unbalanced instabilities of rapidly rotating stratified shear flows
The linear stability of a rotating, stratified, inviscid horizontal plane
Couette flow in a channel is studied in the limit of strong rotation and
stratification. An energy argument is used to show that unstable perturbations
must have large wavenumbers. This motivates the use of a WKB-approach which, in
the first instance, provides an approximation for the dispersion relation of
the various waves that can propagate in the flow. These are Kelvin waves,
trapped near the channel walls, and inertia-gravity waves with or without
turning points.
Although, the wave phase speeds are found to be real to all algebraic orders
in the Rossby number, we establish that the flow, whether cyclonic or
anticyclonic, is unconditionally unstable. This is the result of linear
resonances between waves with oppositely signed wave momenta. We derive
asymptotic estimates for the instability growth rates, which are exponentially
small in the Rossby number, and confirm them by numerical computations. Our
results, which extend those of Kushner et al (1998) and Yavneh et al (2001),
highlight the limitations of the so-called balanced models, widely used in
geophysical fluid dynamics, which filter out Kelvin and inertia-gravity waves
and hence predict the stability of the Couette flow. They are also relevant to
the stability of Taylor-Couette flows and of astrophysical accretion discs.Comment: 6 figure
Congregational Honors: A Model for Inclusive Excellence
This essay proposes a conception of honors programs and colleges as sacred communities that acknowledge and embrace the unique human dignity of each of their members. Drawing on Ron Wolfsonâs congregational model articulated in Relational Judaism, McMillan and Chavisâs definition of âsense of community,â and the pedagogy of educators such as Paolo Freire and bell hooks, I argue that to create a true culture of inclusive excellence, an honors program or college should not be constructed as a checklist of âexceptional experiences for exceptional studentsâ but rather as a âcommunity of relationships.â Leading with a student-centered, holistic focus that recognizes and cherishes the specific students served by an institution enables proactive engagement with what Richard Badenhausen has termed the âmonumental demographic shiftsâ in higher education and expands the frequently too narrow conception of who belongs in honors. It also requires grounding our efforts in the data (from the American College Health Association and the U.S. Governmental Affairs Office, among others) reflecting that 55% of U.S. college students reported being diagnosed with or treated for an illness or disability in the past twelve months, more than 88% have felt overwhelmed, 64% report anxiety, and 30% are food insecure, while 51.7% have found academics âtraumatic or very difficult.â The essay concludes by offering concrete strategies for creating authentically relational communities by ensuring that honors programs, advising, and coursework are specifically designed to recognize and welcome the diverse and complex intersectional identities of students and to address the myriad challenges they may face
On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary
Among the many ways to model signals, a recent approach that draws
considerable attention is sparse representation modeling. In this model, the
signal is assumed to be generated as a random linear combination of a few atoms
from a pre-specified dictionary. In this work we analyze two Bayesian denoising
algorithms -- the Maximum-Aposteriori Probability (MAP) and the
Minimum-Mean-Squared-Error (MMSE) estimators, under the assumption that the
dictionary is unitary. It is well known that both these estimators lead to a
scalar shrinkage on the transformed coefficients, albeit with a different
response curve. In this work we start by deriving closed-form expressions for
these shrinkage curves and then analyze their performance. Upper bounds on the
MAP and the MMSE estimation errors are derived. We tie these to the error
obtained by a so-called oracle estimator, where the support is given,
establishing a worst-case gain-factor between the MAP/MMSE estimation errors
and the oracle's performance. These denoising algorithms are demonstrated on
synthetic signals and on true data (images).Comment: 29 pages, 10 figure
Thinking Critically, Acting Justly
In October 2011, just two months after I became Director of the University Honors Program at Loyola New Orleans, my new home town was simultaneously proclaimed both âAmericaâs Best City for Foodiesâ (Forbes) and the countryâs âWorst Food Desertâ (Lammers). The city known for beignets and crawfish, Mardi Gras and jazz, was revealed to have only one supermarket for each 16,000 residents (half the national average), with some residents traveling over fifteen miles from their homes to purchase fresh produce.
In the past six years, the situation has been somewhat ameliorated by multiple farmers markets throughout the city that accept food stamps and by an urban farm movement that has been repurposing land, abandoned and overgrown since Katrina, in the Lower 9th Ward and St. Bernard Parish. Even so, one of six children in New Orleans experiences food insecurity, and food injustice is not the only challenge facing this city of tremendous inequities:
ă» 40% of adults are illiterate;
ă» 39% of New Orleansâ children live in poverty; and
ă» 1 in 14 black males is incarcerated in a city where 60.2% of the population is African American. (Louisiana has the highest incarceration rate in the world.)
I emphasize my cityâs inequities because Loyola, a Jesuit university located in uptown New Orleans, intertwines with its community as both a place of privilege and a point of access. Loyola, a masters-level institution, is far more diverse than Tulane, the much larger, less âartsy,â and more affluent research university next door. In 2017, Loyola was ranked #4 in the region for ethnic diversity by the U.S. News & World Report and, according to The Princeton Review, #13 in the country for race/class interaction (Loyola). Although the Loyola University Honors Program is, like many other honors programs and colleges, somewhat âwhiterâ than the rest of the institution (half of whose undergraduates are students of color), approximately 30% of honors students are people of color, 30% are the first in their families to attend college, and 26% are Pell-eligible. Geographically, 60% of honors students come from outside of Louisiana; some may come for our nationally ranked music industries program, knowing nothing about the cityâs social justice challenges, while others may decide to come after a âVoluntourismâ service or mission trip here in high school. At least 25% of honors students, however, are from the greater New Orleans area and so have experienced in some way the loss and displacement of Katrina regardless of their childhood social and economic backgrounds. More recently, a number of our students lost their homes (some for the second time) or were otherwise affected by the flooding near Baton Rouge in the summer of 2016. Now, as I write this essay, images of devastation from Houston, along with our own cityâs torrential rain and dysfunctional pumps, are bringing up painful memories and raising anxiety. I suspect that my colleagues on the provost council at Loyola have turned our conversations into a virtual drinking game, betting on how quickly I will say the word âhonors.â NCHC board members, in turn, may secretly promise themselves a shot each time I bring up Loyola or New Orleans. I do think my program is special, as each of us does, or at least should, but I am starting my discussion with Loyola because our story crystallizes two essential questions about honors education and social justice: first, how to engage our highestability and most motivated students in questions of justice; and second, how honors can be a place of access, equity, and excellence in higher education
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