Persistence of a pinch in a pipe

The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology. Here we provide a particularly surprising consequence of this confluence of geometry and physics in tubular structures: the anomalously large persistence of a localized pinch in an elastic pipe whose effect decays very slowly as an oscillatory exponential with a persistence length that diverges as the thickness of the tube vanishes, which we confirm experimentally. The result is more a consequence of geometry than material properties, and is thus equally applicable to carbon nanotubes as it is to oil pipelines.Comment: 6 pages, 3 figure

A mean field description of jamming in non-cohesive frictionless particulate systems

A theory for kinetic arrest in isotropic systems of repulsive, radially-interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with simulations, including the non-trivial shear exponent. Both statics and dynamics are treated in a simplified, one-particle level description, and coupled via the assumption that kinetic arrest occurs on the boundary between mechanically stable and unstable regions of the static parameter diagram. This suggests the arrested states observed in simulations are at (or near) an elastic buckling transition. Some additional numerical evidence to confirm the scaling of microscopic quantities is also provided.Comment: 9 pages, 3 figs; additional clarification of different elastic moduli exponents, plus typo fix. To appear in PR

Assessing Value in Product Networks

Traditionally, the value of a product has been assessed according to the direct revenues the product creates. However, products do not exist in isolation but rather influence one another's sales. Such influence is especially evident in eCommerce environments, where products are often presented as a collection of webpages linked by recommendation hyperlinks, creating a largescale product network. Here we present the first attempt to use a systematic approach to estimate products' true value to a firm in such a product network. Our approach, which is in the spirit of the PageRank algorithm, uses easily available data from large-scale electronic commerce sites and separates a product’s value into its own intrinsic value, the value it receives from the network, and the value it contributes to the network. We apply this approach to data collected from Amazon.com and from BarnesAndNoble.com. Focusing on one domain of interest, we find that if products are evaluated according to their direct revenue alone, without taking their network value into account, the true value of the "long tail" of electronic commerce may be underestimated, whereas that of bestsellers might be overestimated1

Marketing Percolation

A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or difference equations similar to the logistic equation (Bass 1969). This mean field approach is contrasted with the discrete percolation on a lattice, with simulations of "social percolation" (Solomon et al 2000) in two to five dimensions giving power laws instead of exponential growth, and strong fluctuations right at the percolation threshold.Comment: to appear in Physica

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by non-linear quasi-static simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a non-uniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, mexican hat, and so on. This master curve is parameterised by a dimensionless measure of the non-uniformity of the shell. We also speculate on how overlapping timescales for gelation and deformation may alter our findings.Comment: 8 pages, 7 figs. Some extra clarification of a few points, and minor corrections. To appear in Phys. Rev.

Volume-controlled buckling of thin elastic shells: Application to crusts formed on evaporating partially-wetted droplets

Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and the substrate. This volume constraint mimics the incompressibility of the unevaporated solvent. Discontinuous buckling is found to occur for sufficiently thin and/or large contact angle shells, and robustly takes the form of a single circular region near the boundary that `snaps' to an inverted shape, in contrast to externally pressurised shells. Scaling theory for shallow shells is shown to well approximate the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force.Comment: 7 pages in J. Phys. Cond. Mat. spec; 4 figs (2 low-quality to reach LANL's over-restrictive size limits; ask for high-detailed versions if required

Studies of Optical and Electronic Properties of Nanoparticles for Solar Energy Conversion

The higher energy needs for today\u27s technological society requires sustainable and renewable energy source, such as solar energy. This study focuses on using semiconducting quantum dots and fluorescent dyes as light absorbers for solar energy conversion devices such as solar cells. Quantum dots are small nanocrystals (usually 2-10 nm in diameter) with tunable absorbing properties. The smaller the dot, the shorter the wavelength being absorbed. Quantum dots are extremely efficient light absorbers and emitters. Fluorescent dyes have a high quantum yield. In order to examine the energy conversion, cadmium selenide (CdSe) quantum dots and Rhodamine 6G (R6G) dye were spin coated onto graphene (two dimensional nanomaterial). The Kish graphene is mechanically exfoliated to produce graphene. The graphene is then placed onto SiO2/Si substrate. The number of graphene layers present was estimated through a fluorescence microscope. Lifetime measurements were carried out through time resolved photoluminescence. Trials were conducted with rhodamine 6G both with and without the presence of graphene flakes. Lifetime was found to decrease when rhodamine 6G was placed over the graphene flakes, which is indicative of energy transfer. Lifetime studies of cadmium selenide quantum dot films were also conducted. Tests will continue to determine the effects of cadmium selenide quantum dots placed on top of graphene. Comparisons and analyzation will between the lifetimes of these two materials on graphene will then be determined. These studies will contribute to the ongoing research towards the understanding of energy conversion

The Effects of Attrition on the Growth and Equity of Competitive Services

The growth of a new service is similar to a leaking bucket: There is an influx of new customers and, concurrently, an outflow of customers who either switch to competitors or leave the category. This attrition is a major concern for service providers and significantly affects long-range profits. In this study, the authors investigate the influence of attrition on the growth of service markets. They develop a model of a multifirm growing market, where a firm may acquire customers from the pool of nonusers (which can include new customers as well as customers who disadopted the category in the past) and also acquire customers who switched from competitors. Alternatively, the firm may lose customers who switch or “churn” to a competitor or leave the category entirely. By capturing the complex dynamics of customer acquisition and retention, this model enables an in-depth analysis of the growth of services. The authors use the model to explore the influence of attrition on the service category and on a particular brand. For service categories, they show that ignoring attrition biases the diffusion parameters and hence affects management diagnostics. For the individual brand, they present a brand-level growth model and use it to capture the effect of attrition on the firm’s customer equity: they calculate the customer equity of a growing service and evaluate service firms that operate in competitive industries, including Amazon.com, Barnes&Noble.com, E*Trade, Mobistar, and SK Telecom. For four of the five firms, the results are close to the stock market valuations, which may indicate the role of customer equity in the valuation of growing service firms. The services growth model adds to the customer equity approach not only by explicitly incorporating customer attrition into market growth, but also by allowing for inter-firm churn dynamics to be included in the estimation. Hence, it is especially well suited to dealing with cases where interfirm customer churn is an integral part of the growth process