Solid rocket motor nozzles

The steps in the nozzle design process are examined. The nozzle designer's role in defining design requirements and constraints is included along with discussions of each of the three basic phases of the nozzle design process itself: (1) aerodynamic design, in which the gas-contacting surfaces are configured to produce the required performance within the envelope limits; (2) thermal design, in which termal liners and thermal insulators are selected and configured to maintain the surfaces as closely as practical against effects of erosion and to limit the structure temperature to acceptable levels; and (3) structural design, in which materials are selected and configured to support the thermal components and to sustain the predicted loads. Analytical techniques that are used to establish thermal and structural design integrity and to predict nozzle performance are discussed along with methods for nozzle quality assurance. Emphasis is placed on nozzle design and materials for modern high-temperature aluminized propellants. Recurring nozzle design problems of graphite cracking and ejection, differential erosion at material interfaces, lack of sufficient proven nondestructive testing (NDT) techniques, the uncertainty of adhesive bonding, and inadequate definition of material properties, particularly at high temperatures are considered

Arrays of Josephson junctions in an environment with vanishing impedance

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunnelling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalisation of the Hamiltonian operator is used in order to reliably parametrise the effects due to inhomogeneity in the array and non-ideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.Comment: 13 pages, 9 figures, uses RevTeX and epsfig, Revised version, Better readability and some new result

Juntas in the ℓ1\ell^{1}-grid and Lipschitz maps between discrete tori

We show that if $A \subset [k]^n$, then $A$ is $\epsilon$-close to a junta depending upon at most $\exp(O(|\partial A|/(k^{n-1}\epsilon)))$ coordinates, where $\partial A$ denotes the edge-boundary of $A$ in the $\ell^1$-grid. This is sharp up to the value of the absolute constant in the exponent. This result can be seen as a generalisation of the Junta theorem for the discrete cube, from [E. Friedgut, Boolean functions with low average sensitivity depend on few coordinates, Combinatorica 18 (1998), 27-35], or as a characterization of large subsets of the $\ell^1$-grid whose edge-boundary is small. We use it to prove a result on the structure of Lipschitz functions between two discrete tori; this can be seen as a discrete, quantitative analogue of a recent result of Austin [T. Austin, On the failure of concentration for the $\ell^{\infty}$-ball, preprint]. We also prove a refined version of our junta theorem, which is sharp in a wider range of cases.Comment: 29 pages. A mistake in Example 2 (pointed out by an anonymous referee) has now been correcte

The implications of contractual terms of employment for women and leadership: an autoethnographic study in UK higher education

This article is concerned with the implications of casual, non-permanent forms of employment that have become a common cultural practice in higher education. It proposes that contractual terms of employment have important implications for women and leadership in higher education, since to pursue leadership, usually one must first gain permanency in an organization, in contractual terms. Based on an autoethnographic study by a female academic in a UK higher education institution, the article illustrates that temporary forms of employment, should they be protracted, can stifle leadership aspirations due to lack of career progression opportunities and lead to a sense of alienation from the target community of practice, and even to personal difficulties, such as feelings of isolation and poor self-esteem. The article discusses theoretical and practical implications for women’s leadership arising from the findings and makes recommendations for improvements in practice in the higher education sector. The findings and recommendations from this study will also be relevant to other organizational contexts where casual or temporary, fixed term, zero-hours non-permanent forms of employment are common

Problems Encountered With Control Networks in Highly-Restructurable Digital Systems

This paper discusses problems encountered with control networks in highly restructurable digital systems. In particular the treatment of implementation errors is covered with emphasis on concurrent processing. The implementation of concurrent processing networks may result in errors which will be quite complex to detect and systematic methods are warranted. Four meta control elements are employed in obtaining convenient concurrent structures. We analyze several error detecting schemes and conclude that the arc-node method with node partitioning appears to be the most realistic approach at this time

On a biased edge isoperimetric inequality for the discrete cube

The `full' edge isoperimetric inequality for the discrete cube (due to Harper, Bernstein, Lindsay and Hart) specifies the minimum size of the edge boundary $\partial A$ of a set $A \subset \{0,1\}^n$, as a function of $|A|$. A weaker (but more widely-used) lower bound is $|\partial A| \geq |A| \log_2(2^n/|A|)$, where equality holds iff $A$ is a subcube. In 2011, the first author obtained a sharp `stability' version of the latter result, proving that if $|\partial A| \leq |A| (\log(2^n/|A|)+\epsilon)$, then there exists a subcube $C$ such that $|A \Delta C|/|A| = O(\epsilon /\log(1/\epsilon))$. The `weak' version of the edge isoperimetric inequality has the following well-known generalization for the `$p$-biased' measure $\mu_p$ on the discrete cube: if $p \leq 1/2$, or if $0 < p < 1$ and $A$ is monotone increasing, then $p\mu_p(\partial A) \geq \mu_p(A) \log_p(\mu_p(A))$. In this paper, we prove a sharp stability version of the latter result, which generalizes the aforementioned result of the first author. Namely, we prove that if $p\mu_p(\partial A) \leq \mu_p(A) (\log_p(\mu_p(A))+\epsilon)$, then there exists a subcube $C$ such that $\mu_p(A \Delta C)/\mu_p(A) = O(\epsilon' /\log(1/\epsilon'))$, where $\epsilon' =\epsilon \ln (1/p)$. This result is a central component in recent work of the authors proving sharp stability versions of a number of Erd\H{o}s-Ko-Rado type theorems in extremal combinatorics, including the seminal `complete intersection theorem' of Ahlswede and Khachatrian. In addition, we prove a biased-measure analogue of the `full' edge isoperimetric inequality, for monotone increasing sets, and we observe that such an analogue does not hold for arbitrary sets, hence answering a question of Kalai. We use this result to give a new proof of the `full' edge isoperimetric inequality, one relying on the Kruskal-Katona theorem.Comment: 36 pages. More explanations added, and minor corrections made, in response to referee comment

On the Structure of Subsets of the Discrete Cube with Small Edge Boundary

Abstract. The edge isoperimetric inequality in the discrete cube specifies, for each pair of integers m and n, the minimum size gn(m) of the edge boundary of n an m-element subset of {0, 1} ; the extremal families (up to automorphisms of n the discrete cube) are initial segments of the lexicographic ordering on {0, 1} . n We show that for any m-element subset F ⊂ {0, 1} and any integer l, if the edge boundary of F has size at most gn(m) + l, then there exists an extremal n family G ⊂ {0, 1} such that |F∆G| ≤ Cl, where C is an absolute constant. This is best-possible, up to the value of C. Our result can be seen as a ‘stability’ version of the edge isoperimetric inequality in the discrete cube, and as a discrete analogue of the seminal stability result of Fusco, Maggi and Pratelli [15] for the isoperimetric inequality in Euclidean space

Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond

We study the infrared behaviour of tree-level QCD amplitudes and we derive infrared-factorization formulae that are valid at any perturbative order. We explicitly compute all the universal infrared factors that control the singularities in the various soft and/or collinear limits at O(as^2).Comment: latex, 38 pages, 11 eps figure

Jizz and the joy of pattern recognition:virtuosity, discipline and the agency of insight in UK naturalists’ arts of seeing

Approaches to visual skilling from anthropology and STS have tended to highlight the forces of discipline and control in understanding how shared visual accounts of the world are created in the face of potential differences brought about by multi-sensorial perception. Drawing upon a range of observational and interview material from an immersion in naturalist training and biological recording activities between 2003 and 2009, I focus upon jizz, a distinct form of gestalt perception much coveted by naturalist communities in the UK. Jizz is described as a tacit and embodied way of seeing that instantaneously reveals the identity of a species, relying upon but simultaneously suspending the arduous and meticulous study of an organism’s diagnostic characteristics. I explore the potential and limitations of jizz to allow for both visual precision and an enchanted and varied form of encounter with nature. In so doing, I explore how the specific characteristics of wild, intangible and irreverent virtuoso performance work closely together with disciplining taxonomic standards. As such, discipline and irreverence work together, are mutually enabling, and allow for an accommodation rather than a segregation of potential difference brought about by perceptual variety