Spectral sequences and adiabatic limits

A Taylor series analysis of the Laplacian as the underlying manifold is demormed leads to a Hodge theoretic derivation of the Leray spectral sequence.Partially supported by an NSF postdoctoral fellowship     

Projections of the Aldous chain on binary trees: Intertwining and consistency

Consider the Aldous Markov chain on the space of rooted binary trees with n labeled leaves in which at each transition a uniform random leaf is deleted and reattached to a uniform random edge. Now, fix 1 ≤ k<n and project the leaf mass onto the subtree spanned by the first k leaves. This yields a binary tree with edge weights that we call a “decorated k‐tree with total mass n.” We introduce label swapping dynamics for the Aldous chain so that, when it runs in stationarity, the decorated k‐trees evolve as Markov chains themselves, and are projectively consistent over k. The construction of projectively consistent chains is a crucial step in the construction of the Aldous diffusion on continuum trees by the present authors, which is the n→∞ continuum analog of the Aldous chain and will be taken up elsewhere.     

Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks

We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N-particle cluster to the one for \(N+1\), and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and pre-attachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters.     

Vibronic spectrum of the U2 isoelectronic center in Si: In

The photoluminescence spectrum of Si:In measured at 2 and 4 K using samples from several suppliers has been found to be preparation sensitive. In particular, intensity variations allow us to distinguish a sharp no-phonon line at 1.118 eV, variously referred to as U₂ of P, and its associated vibronic spectrum from the In(NP) lines and their phonon replicas. Whereas the intensity of the latter did not show preparation sensitivity, the former has been observed to change by three orders of magnitude. The U₂ vibronics form a broad-structured spectrum containing density-of-states features. The appearance of phonons other than those conserving crystal momentum demonstrates the exciton is bound to a low symmetry site. In addition, the spectrum includes a peak at 1.109 eV, called R, and a shoulder at 1.107 eV which involves too small an energy loss to be density-of-states related, and these features are most likely modes of the U₂ impurity complex. This complex has been tentatively identified as an isoelectronic center composed of an indium-phosphorus nearest-neighbor substitutional pair.     

Experimental and computational investigation of extinction and autoignition of propane and n-heptane in nonpremixed flows

An experimental and computational investigation is carried out to characterize the influence of reactants on critical conditions for extinction and for autoignition of propane and n-heptane in nonpremixed counterflow configurations. Propane or vaporized n-heptane mixed with nitrogen is transported in one stream while the other stream is made up of air mixed with nitrogen. Measurements of the oxidizer stream temperature needed for autoignition are made at fixed values of the strain rate, either with the fuel mass fraction varied at a fixed oxygen mass fraction or with the oxygen mass fraction varied at a fixed fuel mass fraction. Extinction strain rates for propane are measured as a function of the oxygen mass fraction with room-temperature feed streams and the fuel mass fraction fixed and for n-heptane as a function of the fuel mass fraction with the oxygen mass fraction and feed-stream temperatures fixed. Predictions of critical conditions for extinction and autoignition are made employing detailed kinetic mechanisms. Predictions of critical conditions for extinction are in reasonable agreement with measurements, but there are significant discrepancies for autoignition. Measurements show that increasing the mass fraction of either fuel or oxygen increases the overall reactivity thereby reducing the autoignition temperature. The kinetic models predict the increase in reactivity of the mixing layer with increasing mass fraction of fuel but predict very little change in reactivity of the mixing layer with increasing mass fraction of oxygen, thus failing to predict the influence of oxygen on autoignition. It is concluded that there may exist kinetic pathways responsible for this disagreement that are yet to be discovered, and paths that fail to explain the results are identified.     

A fracture mechanics study of the turbine wheel in the space shuttle auxiliary power unit

A review of fracture mechanics concepts relevant to safe life analysis of fatigue loaded parts was given. For the fracture control on the Shuttle APU turbine wheel, an environmental crack growth test program was conducted on candidate wheel materials exposed to decomposed hydrazine. The decomposed hydrazine was found to be no more severe in causing crack growth than an environment of high temperature air. A fatigue crack growth experimental and analytical study was conducted on the final design of the wheel, and the results indicated that special NDE was required for the wheel to have adequate safe life.     

Bioactive Peptide Brush Polymers via Photoinduced Reversible‐Deactivation Radical Polymerization

Harnessing metal‐free photoinduced reversible‐deactivation radical polymerization (photo‐RDRP) in organic and aqueous phases, we report a synthetic approach to enzyme‐responsive and pro‐apoptotic peptide brush polymers. Thermolysin‐responsive peptide‐based polymeric amphiphiles assembled into spherical micellar nanoparticles that undergo a morphology transition to worm‐like micelles upon enzyme‐triggered cleavage of coronal peptide sidechains. Moreover, pro‐apoptotic polypeptide brushes show enhanced cell uptake over individual peptide chains of the same sequence, resulting in a significant increase in cytotoxicity to cancer cells. Critically, increased grafting density of pro‐apoptotic peptides on brush polymers correlates with increased uptake efficiency and concurrently, cytotoxicity. The mild synthetic conditions afforded by photo‐RDRP, make it possible to access well‐defined peptide‐based polymer bioconjugate structures with tunable bioactivity.