Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions

In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledge

Daytime is money

Based on real-time trade data from the Swiss franc overnight interbank repo market and SIX Interbank Clearing (SIC) - the Swiss real-time gross settlement (RTGS) system - we are able to gain valuable insights on the daytime value of money and its determinants: First, an implicit hourly interbank interest rate can be derived from the intraday term structure of the overnight rate. We thereby provide evidence that an implicit intraday money market exists. Second, we show that after the introduction of the foreign exchange settlement system CLS the value of intraday liquidity has increased during the hours of the CLS settlement cycle. Third, the turnover as well as the liquidity in SIC influence the intraday rate correspondingly. These facts provide evidence for the cost of immediacy. Features like RTGS, delivery-versus-payment and payment-versus-payment substitute credit risk with liquidity risk which in turn increases the value of intraday liquidity. The analysis is central bank policy relevant insofar as different designs of intraday liquidity facilities and different collateral policies result in different intraday term structures for the overnight money market.interbank money market, intraday credit, term structure

The yielding dynamics of a colloidal gel

Attractive colloidal gels display a solid-to-fluid transition as shear stresses above the yield stress are applied. This shear-induced transition is involved in virtually any application of colloidal gels. It is also crucial for controlling material properties. Still, in spite of its ubiquity, the yielding transition is far from understood, mainly because rheological measurements are spatially averaged over the whole sample. Here, the instrumentation of creep and oscillatory shear experiments with high-frequency ultrasound opens new routes to observing the local dynamics of opaque attractive colloidal gels. The transition proceeds from the cell walls and heterogeneously fluidizes the whole sample with a characteristic time whose variations with applied stress suggest the existence of an energy barrier linked to the gelation process. The present results provide new test grounds for computer simulations and theoretical calculations in the attempt to better understand the yielding transition. The versatility of the technique should also allow extensive mesoscopic studies of rupture mechanisms in soft solids ranging from crystals to glassy materials.Comment: 8 pages, 5 figure

Quantum-like models cannot account for the conjunction fallacy

Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities—this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed

Vote Trading With and Without Party Leaders

Two groups of voters of known sizes disagree over a single binary decision to be taken by simple majority. Individuals have different, privately observed intensities of preferences and before voting can buy or sell votes among themselves for money. We study the implication of such trading for outcomes and welfare when trades are coordinated by the two group leaders and when they take place anonymously in a competitive market. The theory has strong predictions. In both cases, trading falls short of full efficiency, but for opposite reasons: with group leaders, the minority wins too rarely; with market trades, the minority wins too often. As a result, with group leaders, vote trading improves over no-trade; with market trades, vote trading can be welfare reducing. All predictions are strongly supported by experimental results.

Shear-induced fragmentation of Laponite suspensions

Simultaneous rheological and velocity profile measurements are performed in a smooth Couette geometry on Laponite suspensions seeded with glass microspheres and undergoing the shear-induced solid-to-fluid (or yielding) transition. Under these slippery boundary conditions, a rich temporal behaviour is uncovered, in which shear localization is observed at short times, that rapidly gives way to a highly heterogeneous flow characterized by intermittent switching from plug-like flow to linear velocity profiles. Such a temporal behaviour is linked to the fragmentation of the initially solid sample into blocks separated by fluidized regions. These solid pieces get progressively eroded over time scales ranging from a few minutes to several hours depending on the applied shear rate $\dot{\gamma}$. The steady-state is characterized by a homogeneous flow with almost negligible wall slip. The characteristic time scale for erosion is shown to diverge below some critical shear rate $\dot{\gamma}^\star$ and to scale as $(\dot{\gamma}-\dot{\gamma}^\star)^{-n}$ with $n\simeq 2$ above $\dot{\gamma}^\star$. A tentative model for erosion is discussed together with open questions raised by the present results.Comment: 19 pages, 13 figures, submitted to Soft Matte

Local Oscillatory Rheology from Echography

Local Oscillatory Rheology from Echography (LORE) consists in a traditional rheology experiment synchronized with high-frequency ultrasonic imaging which gives access to the local material response to oscillatory shear. Besides classical global rheological quantities, this method provides quantitative time-resolved information on the local displacement across the entire gap of the rheometer. From the local displacement response, we compute and decompose the local strain in its Fourier components and measure the spatially-resolved viscoelastic moduli. After benchmarking our method on homogeneous Newtonian fluids and soft solids, we demonstrate that this technique is well suited to characterize spatially heterogeneous samples, wall slip, and the emergence of nonlinearity under large amplitude oscillatory stress in soft materials.Comment: 10 pages, 5 figures, submitted to Phys. Rev. Applie

Real-Time Nearfield Acoustic Holography: Implementation of the Direct and Inverse Impulse Responses in the Time-Wavenumber Domain

The aim of the study is to demonstrate that some methods are more relevant for implementing the Real-Time Nearfield Acoustic Holography than others. First by focusing on the forward propagation problem, different approaches are compared to build the impulse response to be used. One of them in particular is computed by an inverse Fourier transform applied to the theoretical transfer function for propagation in the frequency-wavenumber domain. Others are obtained by directly sampling an analytical impulse response in the time-wavenumber domain or by additional low-pass filtering. To estimate the performance of each impulse response, a simulation test involving several monopoles excited by non stationary signals is presented and some features are proposed to assess the accuracy of the temporal signals resulting from reconstruction processing on a forward plane. Then several inverse impulse responses used to solve the inverse problem, which consists in back propagating the acoustic signals acquired by the microphone array, are built directly from a transfer function or by using Wiener inverse filtering from the direct impulse responses obtained for the direct problem. Another simulation test is performed to compare the signals reconstructed on the source plane. The same indicators as for the propagation study are used to highlight the differences between the methods tested for solving the Holography inverse problem.Comment: 15 th International Congress on Sound and Vibration, Daejeon : Cor\'ee, R\'epublique de (2008