Measuring nonlinear stresses generated by defects in 3D colloidal crystals

The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening, yield, and fatigue.Comment: in Nature Materials (2016

Morphology and processing of aligned carbon nanotube carbon matrix nanocomposites

Intrinsic and scale-dependent properties of carbon nanotubes (CNTs) have led aligned CNT architectures to emerge as promising candidates for next-generation multifunctional applications. Enhanced operating regimes motivate the study of CNT-based aligned nanofiber carbon matrix nanocomposites (CNT A-CMNCs). However, in order to tailor the material properties of CNT A-CMNCs, porosity control of the carbon matrix is required. Such control is usually achieved via multiple liquid precursor infusions and pyrolyzations. Here we report a model that allows the quantitative prediction of the CNT A-CMNC density and matrix porosity as a function of number of processing steps. The experimental results indicate that the matrix porosity of A-CMNCs comprised of ∼1% aligned CNTs decreased from ∼61% to ∼55% after a second polymer infusion and pyrolyzation. The model predicts that diminishing returns for porosity reduction will occur after 4 processing steps (matrix porosity of ∼51%), and that >10 processing steps are required for matrix porosity <50%. Using this model, prediction of the processing necessary for the fabrication of liquid precursor derived A-CMNC architectures, with possible application to other nanowire/nanofiber systems, is enabled for a variety of high value applications.National Science Foundation (U.S.) (Grant CMMI-1130437

On Online Labeling with Polynomially Many Labels

In the online labeling problem with parameters n and m we are presented with a sequence of n keys from a totally ordered universe U and must assign each arriving key a label from the label set {1,2,...,m} so that the order of labels (strictly) respects the ordering on U. As new keys arrive it may be necessary to change the labels of some items; such changes may be done at any time at unit cost for each change. The goal is to minimize the total cost. An alternative formulation of this problem is the file maintenance problem, in which the items, instead of being labeled, are maintained in sorted order in an array of length m, and we pay unit cost for moving an item. For the case m=cn for constant c>1, there are known algorithms that use at most O(n log(n)^2) relabelings in total [Itai, Konheim, Rodeh, 1981], and it was shown recently that this is asymptotically optimal [Bul\'anek, Kouck\'y, Saks, 2012]. For the case of m={\Theta}(n^C) for C>1, algorithms are known that use O(n log n) relabelings. A matching lower bound was claimed in [Dietz, Seiferas, Zhang, 2004]. That proof involved two distinct steps: a lower bound for a problem they call prefix bucketing and a reduction from prefix bucketing to online labeling. The reduction seems to be incorrect, leaving a (seemingly significant) gap in the proof. In this paper we close the gap by presenting a correct reduction to prefix bucketing. Furthermore we give a simplified and improved analysis of the prefix bucketing lower bound. This improvement allows us to extend the lower bounds for online labeling to the case where the number m of labels is superpolynomial in n. In particular, for superpolynomial m we get an asymptotically optimal lower bound {\Omega}((n log n) / (log log m - log log n)).Comment: 15 pages, Presented at European Symposium on Algorithms 201

Spacings and pair correlations for finite Bernoulli convolutions

We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure $\nu_r$, as $N$ tends to infinity. Numerical evidence suggests that for a generic $r$, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some partial results in this direction; for instance, we show that, on average, the pair correlations do not exhibit attraction or repulsion in the limit. On the other hand, for certain algebraic $r$ the behavior is totally different.Comment: 17 pages, 6 figure

Aligned carbon nanotube carbon matrix nanocomposites

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 129-141).Materials comprising carbon nanotube (CNT) aligned nanowire (NW) polymer nanocomposites (A-PNCs) have emerged as promising architectures for next-generation multifunctional applications. Enhanced operating regimes, such as operating temperatures, motivate the study of CNT aligned NW ceramic matrix nanocomposites (A-CMNCs). Here we report the synthesis of CNT A-CMNCs through the pyrolysis of CNT A-PNC precursors, creating carbon matrix CNT A-CMNCs. The CNT A-CMNC processing parameters were evaluated using an apparent density measurement, polymer re-infusion modeling, and CNT quality analysis, which elucidate the limitations of the processing parameters currently used to fabricate CNT A-CMNCs. Theoretical tools developed to help quantify and analyze the morphology of the CNTs in the A-CMNCs, and NWs in general, show that morphological parameters, such as NW outer diameter and inter-wire spacing, that are usually overlooked may have significant effects on the physical properties of NW architectures. Mechanical characterization of the CNT A-CMNCs illustrates that the presence of aligned CNTs can lead to an enhancement of > 60% in microhardness, meaning that the fabrication of high strength, high temperature, lightweight next-generation material architectures may be possible using the presented method. Finally, factors that influence the physical properties of CNT A-CMNCs, such as CNT waviness and the porosity of the carbon matrix, are identified, and since their effects cannot be modeled using existing theory, future paths of study that could enable their quantification are recommended.by Itai Y. Stein.S.M