Eddy-mean flow interactions in western boundary current jets

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2009.This thesis examines the nature of eddy-mean flow interactions in western boundary current jets and recirculation gyre dynamics from both theoretical and observational perspectives. It includes theoretical studies of eddy-mean flow interactions in idealized configurations relevant to western boundary current jet systems, namely (i) a study of the mechanism by which eddies generated from a localized forcing drive mean recirculation gyres through the process of nonlinear rectification; and (ii) a study of the role of eddies in the downstream evolution of a baroclinic jet subject to mixed instabilities. It also includes an observational analysis to characterize eddy-mean flow interactions in the Kuroshio Extension using data from the downstream location of maximum eddy kinetic energy in the jet. New insights are presented into a rectification mechanism by which eddies drive the recirculation gyres observed in western boundary current systems. Via this mechanism, eddies drive the recirculations by an up-gradient eddy potential vorticity flux inside a localized region of eddy activity. The effectiveness of the process depends on the properties of the energy radiation from the region, which in turn depends on the population of waves excited. In the zonally-evolving western boundary current jet, eddies also act to stabilize the unstable jet through down-gradient potential vorticity fluxes. In this configuration, the role of eddies depends critically on their downstream location relative to where the unstable time-mean jet first becomes stabilized by the eddy activity. The zonal advection of eddy activity from upstream of this location is fundamental to the mechanism permitting the eddies to drive the mean flows. Observational results are presented that provide the first clear evidence of a northern recirculation gyre in the Kuroshio Extension, as well as support for the hypothesis that the recirculations are, at least partially, eddy-driven. Support for the idealized studies’ relevance to the oceanic regime is provided both by indications that various model simplifications are appropriate to the observed system, as well as by demonstrated consistencies between model predictions and observational results in the downstream development of time-mean and eddy properties.Funding was for this research and my education was provided by the MIT Presidential Fellowship and NSF grants OCE-0220161 and OCE-0825550. The financial assistance of the Houghton Fund, the MIT Student Assistance Fund, and WHOI Academic Programs is also gratefully acknowledged

Exact solution of the Bernoulli matching model of sequence alignment

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths $X,Y$. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.Comment: 13 pages, 4 figure

Insertion of Benzylisocyanide into a Zr-P bond and Rearrangement. Atom-Economical Synthesis of a Phosphaalkene

Reaction of (N3N)ZrPHPh (1, N3N = N(CH2CH2NSiMe3)33−) with PhCH2NC affords the 1,1-insertion product (N3N)Zr[C(PHPh)NCH2Ph] (2), which thermally rearranges to the phosphaalkene-containing complex, (N3N)Zr[N(CH2Ph)C(H)PPh] (3)

An O(n^3)-Time Algorithm for Tree Edit Distance

The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case $O(n^3)$-time algorithm for this problem, improving the previous best $O(n^3\log n)$-time algorithm~\cite{Klein}. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems (which is interesting in its own right), together with a deeper understanding of the previous algorithms for the problem. We also prove the optimality of our algorithm among the family of \emph{decomposition strategy} algorithms--which also includes the previous fastest algorithms--by tightening the known lower bound of $\Omega(n^2\log^2 n)$~\cite{Touzet} to $\Omega(n^3)$, matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of $\Theta(n m^2 (1 + \log \frac{n}{m}))$ when the two trees have different sizes $m$ and~$n$, where $m < n$.Comment: 10 pages, 5 figures, 5 .tex files where TED.tex is the main on

Exact Asymptotic Results for a Model of Sequence Alignment

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model in the large c limit. We show that in the BM model, for all c, the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble. In particular, in the large c limit, this provides an exact expression for the asymptotic length distribution in the original LCS problem.Comment: 4 pages Revtex, 2 .eps figures include

Simulated herbivory : the key to disentangling plant defence responses

Plants are subjected to a multitude of stimuli during insect herbivory, resulting in a complex and cumulative defence response. Breaking down the components of herbivory into specific stimuli and identifying the mechanisms of defence associated with them has thus far been challenging. Advances in our understanding of responses to inconspicuous stimuli, such as those induced by microbial symbionts in herbivore secretions and mechanical stimulation caused by insects, have illuminated the intricacies of herbivory. Here, we provide a synthesis of the interacting impacts of herbivory on plants and the consequential complexities associated with uncoupling defence responses. We propose that simulated herbivory should be used to complement true herbivory to decipher the mechanisms of insect herbivore-induced plant defence responses