0.84 ps Resolution Clock Skew Measurement via Subsampling

An all-digital on-chip clock skew measurement system via subsampling is presented. The clock nodes are sub-sampled with a near-frequency asynchronous sampling clock to result in beat signals which are themselves skewed in the same proportion but on a larger time scale. The beat signals are then suitably masked to extract only the skews of the rising edges of the clock signals. We propose a histogram of the arithmetic difference of the beat signals which decouples the relationship of clock jitter to the minimum measurable skew, and allows skews arbitrarily close to zero to be measured with a precision limited largely by measurement time, unlike the conventional XOR based histogram approach. We also analytically show that the proposed approach leads to an unbiased estimate of skew. The measured results from a 65 nm delay measurement front-end indicate that for an input skew range of +/- 1 fan-out-of-4 (FO4) delay, +/- 3 sigma resolution of 0.84 ps can be obtained with an integral error of 0.65 ps. We also experimentally demonstrate that a frequency modulation on a sampling clock maintains precision, indicating the robustness of the technique to jitter. We also show how FM modulation helps in restoring precision in case of rationally related clocks.

A k-epsilon model for turbulent weld pool convection in gas metal arc welding process

In this paper, we present a modified k - epsilon model capable of addressing turbulent weld-pool convection in a GMAW process, taking into account the morphology of the phase change interface during a Gas Metal Arc Welding (GMAW) process. A three-dimensional turbulence mathematical model has been developed to study the heat transfer and fluid flow within the weld pool by considering the combined effect of three driving forces, viz., buoyancy, Lorentz force and surface tension (Marangoni convection). Mass and energy transports by the droplets are considered through the thermal analysis of the electrode. The falling droplet's heat addition to the molten pool is considered to be a volumetric heat source distributed in an imaginary cylindrical cavity ("cavity model") within the weld pool. This nature of heat source distribution takes into account the momentum and the thermal, energy of the falling droplets. The numerically predicted weld pool dimensions both from turbulence and laminar models are then compared with the experimental post-weld results sectioned across the weld axis. The above comparison enables us to analyze the overall effects of turbulent convection on the nature of heat and fluid flow and hence on the weld pool shape/size during the arc welding processes.

Amine-functionalized multiwall carbon nanotubes impart osteoinductive and bactericidal properties in poly(epsilon-caprolactone) composites

Poly(epsilon-caprolactone) (PCL) is an aliphatic polyester widely used for biomedical applications but lacks the mechanical properties desired for many load-bearing orthopedic applications. The objective of this study was to prepare and characterize PCL composites incorporating multiwall carbon nanotubes (MWNTs) with different surface functional groups. PCL composites were prepared by melt-mixing with three different types of MWNTs: pristine (pMWNT), amine functionalized (aMWNT), and carboxyl functionalized (cMWNT). Melt rheology and scanning electron microscopy indicated good dispersion of the nanotubes in the matrix. Tensile strength and elastic modulus of the polymer was significantly increased by the incorporation of MWNTs and further enhanced by favorable interactions between PCL and aMWNTs. Thermal analysis revealed that MWNTs act as heterogeneous nucleation sites for crystallization of PCL and increase polymer crystallinity. Incorporation of functionalized MWNTs increased the surface water wettability of PCL. Osteoblast proliferation and differentiation was significantly enhanced on functionalized composites. aMWNT composites also exhibited the best bactericidal response. This study demonstrates that surface functionalization of MWNTs profoundly influences the properties of PCL and amine-functionalization offers the optimal combination of mechanical properties, osteogenesis and antimicrobial response. These results have important implications for designing nanocomposites for use in orthopedics.

Small strong epsilon nets

Let P be a set of n points in R-d. A point x is said to be a centerpoint of P if x is contained in every convex object that contains more than dn/d+1 points of P. We call a point x a strong centerpoint for a family of objects C if x is an element of P is contained in every object C is an element of C that contains more than a constant fraction of points of P. A strong centerpoint does not exist even for halfspaces in R-2. We prove that a strong centerpoint exists for axis-parallel boxes in Rd and give exact bounds. We then extend this to small strong epsilon-nets in the plane. Let epsilon(S)(i) represent the smallest real number in 0, 1] such that there exists an epsilon(S)(i)-net of size i with respect to S. We prove upper and lower bounds for epsilon(S)(i) where S is the family of axis-parallel rectangles, halfspaces and disks. (C) 2014 Elsevier B.V. All rights reserved.

epsilon-expansions near three dimensions from conformal field theory

We formally extend the CFT techniques introduced in arXiv: 1505.00963, to phi(2d0/d0-2) theory in d = d(0) dimensions and use it to compute anomalous dimensions near d(0) = 3, 4 in a unified manner. We also do a similar analysis of the O(N) model in three dimensions by developing a recursive combinatorial approach for OPE contractions. Our results match precisely with low loop perturbative computations. Finally, using 3-point correlators in the CFT, we comment on why the phi(3) theory in d(0) = 6 is qualitatively different.

Gamma -> Epsilon Martensite Transformation and Twinning Deformation in fcc Cobalt During Surface Mechanical Attrition Treatment

The deformation microstructure of face-centered cubic cobalt subjected to surface mechanical attrition treatment was studied as a function of strain levels. Strain-induced gamma --> epsilon transformation and twinning deformation were evidenced by transmission electron microscopy and were found to progress continuously in ultrafine and nanocrystalline grains as the strain increased.

Completions of epsilon-dense partial Latin squares

A classical question in combinatorics is the following: given a partial Latin square $P$, when can we complete $P$ to a Latin square $L$? In this paper, we investigate the class of textbf{$epsilon$-dense partial Latin squares}: partial Latin squares in which each symbol, row, and column contains no more than $epsilon n$-many nonblank cells. Based on a conjecture of Nash-Williams, Daykin and H"aggkvist conjectured that all $frac{1}{4}$-dense partial Latin squares are completable. In this paper, we will discuss the proof methods and results used in previous attempts to resolve this conjecture, introduce a novel technique derived from a paper by Jacobson and Matthews on generating random Latin squares, and use this novel technique to study $ epsilon$-dense partial Latin squares that contain no more than $delta n^2$ filled cells in total.

In Chapter 2, we construct completions for all $ epsilon$-dense partial Latin squares containing no more than $delta n^2$ filled cells in total, given that $epsilon < frac{1}{12}, delta < frac{ left(1-12epsilonright)^{2}}{10409}$. In particular, we show that all $9.8 cdot 10^{-5}$-dense partial Latin squares are completable. In Chapter 4, we augment these results by roughly a factor of two using some probabilistic techniques. These results improve prior work by Gustavsson, which required $epsilon = delta leq 10^{-7}$, as well as Chetwynd and H"aggkvist, which required $epsilon = delta = 10^{-5}$, $n$ even and greater than $10^7$.

If we omit the probabilistic techniques noted above, we further show that such completions can always be found in polynomial time. This contrasts a result of Colbourn, which states that completing arbitrary partial Latin squares is an NP-complete task. In Chapter 3, we strengthen Colbourn's result to the claim that completing an arbitrary $left(frac{1}{2} + epsilonright)$-dense partial Latin square is NP-complete, for any $epsilon > 0$.

Colbourn's result hinges heavily on a connection between triangulations of tripartite graphs and Latin squares. Motivated by this, we use our results on Latin squares to prove that any tripartite graph $G = (V_1, V_2, V_3)$ such that begin{itemize} item $|V_1| = |V_2| = |V_3| = n$, item For every vertex $v in V_i$, $deg_+(v) = deg_-(v) geq (1- epsilon)n,$ and item $|E(G)| > (1 - delta)cdot 3n^2$ end{itemize} admits a triangulation, if $epsilon < frac{1}{132}$, $delta < frac{(1 -132epsilon)^2 }{83272}$. In particular, this holds when $epsilon = delta=1.197 cdot 10^{-5}$.

This strengthens results of Gustavsson, which requires $epsilon = delta = 10^{-7}$.

In an unrelated vein, Chapter 6 explores the class of textbf{quasirandom graphs}, a notion first introduced by Chung, Graham and Wilson cite{chung1989quasi} in 1989. Roughly speaking, a sequence of graphs is called "quasirandom"' if it has a number of properties possessed by the random graph, all of which turn out to be equivalent. In this chapter, we study possible extensions of these results to random $k$-edge colorings, and create an analogue of Chung, Graham and Wilson's result for such colorings.

Synthesis and micellization of star-like hyperbranched polymer with poly(ethylene oxide) and Poly(epsilon-caprolactone) arms

Novel star-like hyperbranched polymers with amphiphilic arms were synthesized via three steps. Hyperbranched poly(amido amine)s containing secondary amine and hydroxyl groups were successfully synthesized via Michael addition polymerization of triacrylamide (TT) and 3-amino-1,2-propanediol (APD) with feed molar ratio of 1:2. H-1, C-13, and HSQC NMR techniques were used to clarify polymerization mechanism and the structures of the resultant hyperbranched polymers

Study on the Cell Structure and Compressive Behavior of Biodegradable Poly(epsilon-caprolactone) Foam

Biodegradable poly(e-caprolactone) (PCL) foams with a series of controlled structures were prepared by using chemical foaming method. The cell morphology was detected by scanning electron microscope (SEM). The compressive behavior of the foams was investigated by uniaxial compression test. The effect of density and structural parameters on the foam compressive behavior was analyzed. It was found that the relative compressive modulus has a power law relationship with relative density. Increasing of both the cell wall thickness and the cell density lead to higher compressive modulus of the foam; however, the cell size has no distinct effect on compressive behavior.

Rhythmic Growth-Induced Ring-Banded Spherulites with Radial Periodic Variation of Thicknesses Grown from Poly(epsilon-caprolactone) Solution with Constant Concentration

Birefringent ring-banded spherulites with radial periodic variation of thicknesses were grown from poly(epsilon-caprolactone) (PCL) solutions under conditions for which the Solution concentration was held constant during the whole development of the morphology. The as-grown ring-banded spherulites were investigated by optical (OM) and atomic force (AFM) microscopies, by transmission electron microscopy (TEM) of samples sectioned parallel to the plane of film, and also by electron diffraction (ED) and grazing incidence X-ray diffraction (GIXD) techniques.

Rare-Earth Metal Bis(alkyl)s Supported by a Quinolinyl Anilido-Imine Ligand: Synthesis and Catalysis on Living Polymerization of epsilon-Caprolactone

The tridentate ligand N-(2-((2,6-diisopropylphenylimino)methyl)phenyl)quinolin-8-amine (HL) was prepared. Treatment of HL with 1 equiv of Ln(CH2SiMe3)(3)(THF)(2) afforded the corresponding rare-earth metal bis(alkyl) complexes LLn(CH2SiMe3)(2)(THF)(n) (Ln = Sc, n = 0 (1); Y, n = 1 (2); Lu, n = 0 (3)) in high yields. Variable-temperature H-1 NMR spectral analysis showed that these complexes were fluxional at room temperature. Complexes 1 and 3 were THF-free, where the metal center adopted a square-pyramidal geometry, while in 2 the metal center generated a distorted octahedral geometry owing to the coordination of a THF molecule.