Tautologies, models and theories--can we find "laws" of manufacturing?

"This is a revised version of Little (1992) in Manufacturing Systems: Foundations of World-Class Practice, J.A. Heim and W.D. Compton, eds."Are there "laws" of manufacturing? If so, what do they look like? If not, what other forms of knowledge might comprise intellectual foundations for a discipline of manufacturing? We differentiate among mathematical tautologies, laws, models, and theories, giving examples of each. Laws closely analogous to those of nineteenth century physics appear to be unlikely but empirical models offer the prospect of building new understanding of manufacturing, even if they may lack the precision of their classical counterparts. Descriptive models serving scientific goals tend to differ from prescriptive models for problem-solving. The latter must be complete enough to solve the practical problem at hand and yet be selective in their detail so as not to paralyze problem-solving with irrelevant complication. A growing collection of parsimonious models and theories can form a basis for the design, analysis and control of complex manufacturing systems

Assumptions for a Market Share Theorem

Many marketing models use variants of the relationship: market share equals marketing effort divided by total marketing effort. Usually, share is defined within a customer group presumed to be reasonably homogeneous and overall share is obtained by weighting for the number in the group. Although the basic relationship can be assumed directly, certain insight is gained by deriving it from more fundamental assumptions as follows: For the given customer group, each competitive seller has a real-valued "attraction" with the following properties: (1) attraction is non-negative; (2) the attraction of a set of sellers is the sum of the attractions of the individual sellers; and (3) if the attractions of two sets of sellers are equal, the sellers have equal market shares in the customer groups. It is shown that, if the relation between share and attraction satisfies the above assumptions, is a continuous function, and is required to hold for arbitrary values of attraction and sets of sellers, then the relation is: Share equals attraction divided by total attraction. Insofar as various factors can be assembled into an attraction function that satisfies the assumptions of the theorem, the method for calculating share follows directly

Variable sediment oxygen uptake in response to dynamic forcing

Seiche-induced turbulence and the vertical distribution of dissolved oxygen above and within the sediment were analyzed to evaluate the sediment oxygen uptake rate (JO2), diffusive boundary layer thickness (δDBL), and sediment oxic zone depth (zmax) in situ. High temporal-resolution microprofiles across the sediment-water interface and current velocity data within the bottom boundary layer in a medium-sized mesotrophic lake were obtained during a 12-h field study. We resolved the dynamic forcing of a full 8-h seiche cycle and evaluated JO2 from both sides of the sediment-water interface. Turbulence (characterized by the energy dissipation rate, ε), the vertical distribution of dissolved oxygen across the sediment-water interface (characterized by δDBL and zmax), JO2, and the sediment oxygen consumption rate (RO2) are all strongly correlated in our freshwater system. Seiche-induced turbulence shifted from relatively active (ε = 1.2 × 10-8 W kg-1) to inactive (ε = 7.8 × 10-12 W kg-1). In response to this dynamic forcing, δDBL increased from 1.0 mm to the point of becoming undefined, zmax decreased from 2.2 to 0.3 mm as oxygen was depleted from the sediment, and JO2 decreased from 7.0 to 1.1 mmol m-2 d-1 over a time span of hours. JO2 and oxygen consumption were found to be almost equivalent (within ~ 5% and thus close to steady state), with RO2 adjusting rapidly to changes in JO2. Our results reveal the transient nature of sediment oxygen uptake and the importance of accurately characterizing turbulence when estimating JO2

Response of sediment microbial community structure in a freshwater reservoir to manipulations in oxygen availability

Hypolimnetic oxygenation systems (HOx) are being increasingly used in freshwater reservoirs to elevate dissolved oxygen levels in the hypolimnion and suppress sediment-water fluxes of soluble metals (e.g. Fe and Mn) which are often microbially mediated. We assessed changes in sediment microbial community structure and corresponding biogeochemical cycling on a reservoir-wide scale as a function of HOx operations. Sediment microbial biomass as quantified by DNA concentration was increased in regions most influenced by the HOx. Following an initial decrease in biomass in the upper sediment while oxygen concentrations were low, biomass typically increased at all depths as the 4-month-long oxygenation season progressed. A distinct shift in microbial community structure was only observed at the end of the season in the upper sediment near the HOx. While this shift was correlated to HOx-enhanced oxygen availability, increased TOC levels and precipitation of Fe- and Mn-oxides, abiotic controls on Fe and Mn cycling, and/or the adaptability of many bacteria to variations in prevailing electron acceptors may explain the delayed response and the comparatively limited changes at other locations. While the sediment microbial community proved remarkably resistant to relatively short-term changes in HOx operations, HOx-induced variation in microbial structure, biomass, and activity was observed after a full season of oxygenatio

Rapidly Reconfigurable Optically Induced Photonic Crystals in Hot Rubidium Vapor

Through periodic index modulation, we create two different types of photonic structures in a heated rubidium vapor for controlled reflection, transmission, and diffraction of light. The modulation is achieved through the use of the ac Stark effect resulting from a standing-wave control field. The periodic intensity structures create translationally invariant index profiles analogous to photonic crystals in spectral regions of steep dispersion. Experimental results are consistent with modeling

Polyhedra in loop quantum gravity

Interwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in Euclidean space: a polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: we give formulas for the edge lengths, the volume and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner with the state of a quantum polyhedron, thus generalizing the notion of quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spinfoams with non-simplicial graphs.Comment: 32 pages, many figures. v2 minor correction

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j3j Symbols, and Character Localization

In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic formulae for the character $\chi^J(g)$ of an SU(2) group element and for Wigner's $3j$ symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is in fact exact. This result provides a non trivial example of a Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure