Confinement induced instability of thin elastic film

A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical peel geometry, undulations appear along the contact line below a critical film thickness or below a critical curvature of the plate. Perturbation analysis of the stress equilibrium equations shows that for a critically confined film the total excess energy indeed attains a minima for a finite amplitude of the perturbations which grow with further increase in the confinement.Comment: 11 pages, 6 figure

Friction and abrasion of elastomeric materials

An abrasion apparatus is described. Experimental measurements are reported for four representative elastomeric materials, including a typical high-quality tire tread material and a possible replacement material for aircraft tire treads based on transpolypentenamer (TPPR). Measurements are carried out at different levels of frictional work input, corresponding to different severities of wear, and at both ambient temperature and at 100 C. Results indicate the marked superiority in abrasion resistance of the material based on TPPR, especially at 100 C, in comparison with the other materials examined

Unfolding the Sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.Comment: Main text with supporting appendix. Revised to agree with published version. New result in the Supplementary Informatio

Magic angles and cross-hatching instability in hydrogel fracture

The full 2D analysis of roughness profiles of fracture surfaces resulting from quasi-static crack propagation in gelatin gels reveals an original behavior characterized by (i) strong anisotropy with maximum roughness at $V$-independent symmetry-preserving angles, (ii) a sub-critical instability leading, below a critical velocity, to a cross-hatched regime due to straight macrosteps drifting at the same magic angles and nucleated on crack-pinning network inhomogeneities. Step height values are determined by the width of the strain-hardened zone, governed by the elastic crack blunting characteristic of soft solids with breaking stresses much larger that low strain moduli

A pearl on SAT solving in Prolog

A succinct SAT solver is presented that exploits the control provided by delay declarations to implement watched literals and unit propagation. Despite its brevity the solver is surprisingly powerful and its elegant use of Prolog constructs is presented as a programming pearl

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

New scaling for the alpha effect in slowly rotating turbulence

Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers. Thus, the contribution of density stratification is less important than that of turbulent velocity. The alpha effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence) we find that the contribution of density stratification might be even less important than suggested by the analytic theory.Comment: 10 pages, 9 figures, revised version, Astrophys. J., in pres

Polonium-210 poisoning: a first-hand account

Background: Polonium-210 (210Po) gained widespread notoriety after the poisoning and subsequent death of Mr Alexander Litvinenko in London, UK, in 2006. Exposure to 210Po resulted initially in a clinical course that was indistinguishable from infection or exposure to chemical toxins, such as thallium. Methods: A 43-year-old man presented to his local hospital with acute abdominal pain, diarrhoea, and vomiting, and was admitted to the hospital because of dehydration and persistent gastrointestinal symptoms. He was initially diagnosed with gastroenteritis and treated with antibiotics. Clostridium difficile toxin was subsequently detected in his stools, which is when he first raised the possibility of being poisoned and revealed his background and former identity, having been admitted under a new identity with which he had been provided on being granted asylum in the UK. Within 6 days, the patient had developed thrombocytopenia and neutropenia, which was initially thought to be drug induced. By 2 weeks, in addition to bone marrow failure, he had evidence of alopecia and mucositis. Thallium poisoning was suspected and investigated but ultimately dismissed because blood levels of thallium, although raised, were lower than toxic concentrations. The patient continued to deteriorate and within 3 weeks had developed multiple organ failure requiring ventilation, haemofiltration, and cardiac support, associated with a drop in consciousness. On the 23rd day after he first became ill, he suffered a pulseless electrical activity cardiorespiratory arrest from which he could not be resuscitated and was pronounced dead. Findings: Urine analysis using gamma-ray spectroscopy on day 22 showed a characteristic 803 keV photon emission, raising the possibility of 210Po poisoning. Results of confirmatory analysis that became available after the patient's death established the presence of 210Po at concentrations about 109-times higher than normal background levels. Post-mortem tissue analyses showed autolysis and retention of 210Po at lethal doses in several organs. On the basis of the measured amounts and tissue distribution of 210Po, it was estimated that the patient had ingested several 1000 million becquerels (a few GBq), probably as a soluble salt (eg, chloride), which delivered very high and fatal radiation doses over a period of a few days. Interpretation: Early symptoms of 210Po poisoning are indistinguishable from those of a wide range of chemical toxins. Hence, the diagnosis can be delayed and even missed without a high degree of suspicion. Although body surface scanning with a standard Geiger counter was unable to detect the radiation emitted by 210Po, an atypical clinical course prompted active consideration of poisoning with radioactive material, with the diagnosis ultimately being made with gamma-ray spectroscopy of a urine sample

Phase transition for cutting-plane approach to vertex-cover problem

We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g, for the ER ensemble at connectivity c=e=2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, also the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, change close to this phase transition from "easy" to "hard". In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach, hence the algorithm operates in a space OUTSIDE the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an "easy-hard" transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.Comment: 4 pages, 3 figure

Optimization by Quantum Annealing: Lessons from hard 3-SAT cases

The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the Traveling Salesman Problem, in the present case the linear-schedule Quantum Annealing performance is definitely worse than Classical Annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.Comment: 10 pages, 6 figures, submitted to PR