Generalization of the fractal Einstein law relating conduction and diffusion on networks

We settle a long-standing controversy about the exactness of the fractal Einstein and Alexander-Orbach laws by showing that the properties of a class of fractal trees violate both laws. A new formula is derived which unifies the two classical results by showing that if one holds, then so must the other, and resolves a puzzling discrepancy in the properties of Eden trees and diffusion-limited aggregates. We also conjecture that the result holds for networks which have no fractal dimension. The failure of the classical laws is attributed to anisotropic exploration of the network by a random walker. The occurrence of this newly revealed behavior means that the conventional laws must be checked if they, or numerous results which depend on them, are to be applied accuratel

Morphology and thermal conductivity of model organic aerogels

The intersection volume of two independent 2-level cut Gaussian random fields is proposed to model the open-cell microstructure of organic aerogels. The experimentally measured X-ray scattering intensity, surface area and solid thermal conductivity of both polymeric and colloidal organic aerogels can be accounted for by the model.Comment: 5 pages. RevTex with 4 encapsulated figures. Higher resolution figures have been submitted for publication. To be published in Phys. Rev. E (Rapid Comm.). email, [email protected]

Brief communication: Dentists' reproducibility in scoring the Plaque Index using a fluorescent colouring agent

Statement of the problem: Fluorescein is a plaque detection agent, which fluoresces yellow-green when excited with blue light (dental light curing lamp). Little is known about the reproducibility of scoring with the Silness-Löe plaque index (1964) when using this agent. Purpose of the study: To evaluate the level of agreement of the plaque index measurements using a fluorescent colouring agent among eight dentists. Materials and methods: Eight dentists in Cork were recruited as examiners for a randomised clinical study investigating the impact of a personalised caries prevention approach. They were trained and calibrated in the use of the plaque index using Plaque Test (Ivoclar Vivadent, Liechtenstein) in the Oral Health Services Research Centre and School of Dental Hygiene, University College Cork. For inter-examiner and intra-examiner reproducibility, a previously calibrated ‘gold standard’ examiner and seven dentists examined 10 to 12 subjects each, while one dentist examined four subjects only for inter-examiner reproducibility. The adult subjects were recruited at the Cork University Dental School and Hospital. To evaluate inter-examiner and intra-examiner reproducibility at site level, squared weighted kappa statistics were calculated. Results: The weighted kappa statistics varied from 0.31 to 0.54 for inter-examiner reproducibility under the acceptable level (kappa statistics = 0.60) for research purposes and from 0.43 to 0.65 for intra-examiner reproducibility. Conclusions: The levels of agreement were fair to good. Further studies are needed, preferably including a qualitative study to analyse feedback from dentists to determine the cause of such variation. This study re-emphasises the importance of clinician calibration ahead of clinical studies

A Hilbertian projection method for constrained level set-based topology optimisation

We present an extension of the projection method proposed by Challis et al ($\textit{Int J Solids Struct}$. Volume $\textbf{45}$(14-15) (2008) 4130-4146) for constrained level set-based topology optimisation that harnesses the Hilbertian velocity extension-regularisation framework. Our $\textit{Hilbertian projection method}$ chooses a normal velocity for the level set function as a linear combination of: 1) an orthogonal projection operator applied to the extended optimisation objective shape sensitivity; and 2) a weighted sum of orthogonal basis functions for the extended constraint shape sensitivities. This combination aims for the best possible first-order improvement of the optimisation objective in addition to first-order improvement of the constraints. Our formulation utilising basis orthogonalisation naturally handles linearly dependent constraint shape sensitivities. Furthermore, use of the Hilbertian extension-regularisation framework ensures that the resulting normal velocity is extended away from the boundary and enriched with additional regularity. Our approach is generally applicable to any topology optimisation problem to be solved in the level set framework. We consider several benchmark constrained microstructure optimisation problems and demonstrate that our method is effective with little-to-no parameter tuning. We also find that our method performs well when compared to a Hilbertian sequential linear programming method.Comment: 23 pages, 8 figure

Diffusion on asymmetric fractal networks

We derive a renormalization method to calculate the spectral dimension $\bar{d}$ of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of microstructural details to be quantitatively investigated. In addition to providing new models for physical networks, the results allow precise tests of theories of diffusive transport. For example, the properties of a class of non-recurrent trees ($\bar{d}>2$) with asymmetric elements and branching violate the Alexander Orbach scaling law

Transport and Elastic Properties of Fractal Media

We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and mass fractal materials. Variational bounds on the conductivity, diffusivity and elastic moduli of the materials are evaluated. We find that a fractally rough interface has a relatively strong influence on the properties of composites. In contrast a fractal volume (mass) has little effect on material properties.Comment: 10 pages, 6 figure

Partner choice, relationship satisfaction, and oral contraception: the congruency hypothesis

Hormonal fluctuation across the menstrual cycle explains temporal variation in women’s judgment of the attractiveness of members of the opposite sex. Use of hormonal contraceptives could therefore influence both initial partner choice and, if contraceptive use subsequently changes, intrapair dynamics. Associations between hormonal contraceptive use and relationship satisfaction may thus be best understood by considering whether current use is congruent with use when relationships formed, rather than by considering current use alone. In the study reported here, we tested this congruency hypothesis in a survey of 365 couples. Controlling for potential confounds (including relationship duration, age, parenthood, and income), we found that congruency in current and previous hormonal contraceptive use, but not current use alone, predicted women’s sexual satisfaction with their partners. Congruency was not associated with women’s nonsexual satisfaction or with the satisfaction of their male partners. Our results provide empirical support for the congruency hypothesis and suggest that women’s sexual satisfaction is influenced by changes in partner preference associated with change in hormonal contraceptive use

The Effects of Age and Lifetime Flight Behavior on Flight Capacity in Drosophila Melanogaster

The Effects of Flight Behavior on Physiology and Senescence May Be Profound in Insects Because of the Extremely High Metabolic Costs of Flight. Flight Capacity in Insects Decreases with Age; in Contrast, Limiting Flight Behavior Extends Lifespan and Slows the Age-Related Loss of Antioxidant Capacity and Accumulation of Oxidative Damage in Flight Muscles. in This Study, We Tested the Effects of Age and Lifetime Flight Behavior on Flight Capacity by Measuring Wingbeat Frequency, the Ability to Fly in a Hypo-Dense Gas Mixture, and Metabolic Rate in Drosophila Melanogaster. Specifically, 5-Day-Old Adult Flies Were Separated into Three Life-Long Treatments: (1) Those Not Allowed to Fly (No Flight), (2) Those Allowed - But Not Forced - to Fly (Voluntary Flight) and (3) Those Mechanically Stimulated to Fly (Induced Flight). Flight Capacity Senesced Earliest in Flies from the No-Flight Treatment, Followed by the Induced-Flight Group and Then the Voluntary Flight Group. Wingbeat Frequency Senesced with Age in All Treatment Groups, But Was Most Apparent in the Voluntary- and Induced-Flight Groups. Metabolic Rate during Agitated Flight Senesced Earliest and Most Rapidly in the Induced Flight Group, and Was Low and Uniform throughout Age in the No-Flight Group. Early Senescence in the Induced-Flight Group Was Likely Due to the Acceleration of Deleterious Aging Phenomena Such as the Rapid Accumulation of Damage at the Cellular Level, While the Early Loss of Flight Capacity and Low Metabolic Rates in the No-Flight Group Demonstrate that Disuse Effects Can Also Significantly Alter Senescence Patterns of Whole-Insect Performance

Contact inhibition of locomotion and mechanical cross-talk between cell-cell and cell-substrate adhesion determines the pattern of junctional tension in epithelial cell aggregates

We generated a computational approach to analyze the biomechanics of epithelial cell aggregates, either island or stripes or entire monolayers, that combines both vertex and contact-inhibition-of-locomotion models to include both cell-cell and cell-substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces and apical aspect ratios that decreased when moving from the edge to the island center. Our in silico analysis also showed that tension on cell-cell junctions and apical stress is not homogeneous across the island. Instead, these parameters are higher at the island center and scales up with island size, which we confirmed experimentally using laser ablation assays and immunofluorescence. Without formally being a 3-dimensional model, our approach has the minimal elements necessary to reproduce the distribution of cellular forces and mechanical crosstalk as well as distribution of principal stress in cells within epithelial cell aggregates. By making experimental testable predictions, our approach would benefit the mechanical analysis of epithelial tissues, especially when local changes in cell-cell and/or cell-substrate adhesion drive collective cell behavior.Comment: 39 pages, 8 Figures. Supplementary Information is include