Some comments on the inverse problem of pure point diffraction

In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible extensions, we present, in a non-technical manner, some examples of homometric structures.Comment: 6 pages, contribution to Aperiodic 201

Scaling of the turbulence transition threshold in a pipe

We report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in $Re$. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as $O(Re^{-1})$.Comment: 4 pages, RevTex (submitted to Phys. Rev. Lett.

Hadwiger number of graphs with small chordality

The Hadwiger number of a graph G is the largest integer h such that G has the complete graph K_h as a minor. We show that the problem of determining the Hadwiger number of a graph is NP-hard on co-bipartite graphs, but can be solved in polynomial time on cographs and on bipartite permutation graphs. We also consider a natural generalization of this problem that asks for the largest integer h such that G has a minor with h vertices and diameter at most $s$. We show that this problem can be solved in polynomial time on AT-free graphs when s>=2, but is NP-hard on chordal graphs for every fixed s>=2

Adaptive colour change and background choice behaviour in peppered moth caterpillars is mediated by extraocular photoreception

Light sensing by tissues distinct from the eye occurs in diverse animal groups, enabling circadian control and phototactic behaviour. Extraocular photoreceptors may also facilitate rapid colour change in cephalopods and lizards, but little is known about the sensory system that mediates slow colour change in arthropods. We previously reported that slow colour change in twig-mimicking caterpillars of the peppered moth (Biston betularia) is a response to achromatic and chromatic visual cues. Here we show that the perception of these cues, and the resulting phenotypic responses, does not require ocular vision. Caterpillars with completely obscured ocelli remained capable of enhancing their crypsis by changing colour and choosing to rest on colour-matching twigs. A suite of visual genes, expressed across the larval integument, likely plays a key role in the mechanism. To our knowledge, this is the first evidence that extraocular colour sensing can mediate pigment-based colour change and behaviour in an arthropod

POTENTIAL PITFALLS IN RENEWABLE RESOURCE DECISION MAKING THAT UTILIZES CONVEX COMBINATIONS OF DISCRETE ALTERNATIVES

Decision makers in renewable resource planning are often unable to specify their objective function a priori, and are presented with a discrete set of alternatives reflecting a range of options that are actually much more continuous. It is common for the decision maker to be interested in some other alternative than those originally developed. An iterative process thus often takes place between decision maker an analyst as they search for a satisfactory alternative. This paper analyzes the economic tenability of simply interpolating (taking convex combinations of) initial alternatives to generate new alternatives in this process. It is shown that convex combinations of outputs will be producible (feasible) with the interpolated input levels, under very common conditions. In fact, the cost estimate resulting from interpolating the cost of two (or more) alternatives will generally be an overestimate. The magnitude of this overestimate is investigated in a test case. It is concluded that this cost overestimate can be rather large, and is not systematically predictable. Only when the output sets in the original alternatives are very similar are the interpolated cost estimates fairly accurate.Resource /Energy Economics and Policy,

Dynamic photoconductive gain effect in shallow-etched AlGaAs/GaAs quantum wires

We report on a dynamic photoconductive gain effect in quantum wires which are lithographically fabricated in an AlGaAs/GaAs quantum well via a shallow-etch technique. The effect allows resolving the one-dimensional subbands of the quantum wires as maxima in the photoresponse across the quantum wires. We interpret the results by optically induced holes in the valence band of the quantum well which shift the chemical potential of the quantum wire. The non-linear current-voltage characteristics of the quantum wires also allow detecting the photoresponse effect of excess charge carriers in the conduction band of the quantum well. The dynamics of the photoconductive gain are limited by the recombination time of both electrons and holes

Diffractive point sets with entropy

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor addition