Models of stress fluctuations in granular media

We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model is equivalent to a diffusion equation (where the r\^ole of time is played by the vertical coordinate) plus a randomly varying convection term. We calculate the response and correlation function of this model, and discuss several properties, in particular related to the stress distribution function. We then turn to the tensorial model, where the basic starting point is a wave equation which, in the absence of disorder, leads to a ray-like propagation of stress. In the presence of disorder, the rays acquire a diffusive width and the angle of propagation is shifted. A striking feature is that the response function becomes negative, which suggests that the contact network is mechanically unstable to very weak perturbations. The stress correlation function reveals characteristic features related to the ray-like propagation, which are absent in the scalar description. Our analytical calculations are confirmed and extended by a numerical analysis of the stochastic wave equation.Comment: 32 pages, latex, 18 figures and 6 diagram

Control of field- and current-driven magnetic domain wall motion by exchange bias in Cr2 O3/Co/Pt trilayers

We investigate the motion of magnetic domain walls driven by magnetic fields and current-driven spin-orbit torques in an exchange-biased system with perpendicular magnetization. We consider Cr2O3/Co/Pt trilayers as a model system, in which the magnetization of the Co layer can be exchanged biased out-of-plane or in-plane depending on the field-cooling direction. In field-driven experiments, the in-plane exchange bias favors the propagation of the domain walls with internal magnetization parallel to the exchange-bias field. In current-driven experiments, the domain walls propagate along the current direction, but the domain wall velocity increases and decreases symmetrically (antisymmetrically) for both current polarities when the exchange bias is parallel (perpendicular) to the current line. At zero external field, the exchange bias modifies the velocity of current-driven domain wall motion by a factor of 10. We also find that the exchange bias remains stable under external fields up to 15 kOe and nanosecond-long current pulses with current density up to 3.5 × 1012 A/m. Our results demonstrate versatile control of the domain wall motion by exchange bias, which is relevant to achieve field-free switching of the magnetization in perpendicular systems and current-driven manipulation of domain walls velocity in spintronic device

No arbitrage and closure results for trading cones with transaction costs

In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for ${\mathcal{A}}$ , the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment, ${\tilde{ {\mathcal{A}}}}$ , does obey the fundamental theorem of asset pricing and, secondly, if ${\tilde{ {\mathcal{A}}}}$ is arbitrage-free then it is the closure of ${\mathcal{A}}$ . We then conclude by showing how to represent claims

Tournaments and Even Graphs are Equinumerous

A graph is called \emph{odd} if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and \emph{even} otherwise. Pontus von Br\"omssen (n\'e Andersson) showed that the existence of such an automorphism is independent of the orientation, and considered the question of counting pairwise non-isomorphic even graphs. Based on computational evidence, he made the rather surprising conjecture that the number of pairwise non-isomorphic \emph{even graphs} on $n$ vertices is equal to the number of pairwise non-isomorphic \emph{tournaments} on $n$ vertices. We prove this conjecture using a counting argument with several applications of the Cauchy-Frobenius Theorem

K-corrections and Extinction Corrections for Type Ia Supernovae

The measurement of the cosmological parameters from Type Ia supernovae hinges on our ability to compare nearby and distant supernovae accurately. Here we present an advance on a method for performing generalized K-corrections for Type Ia supernovae which allows us to compare these objects from the UV to near-IR over the redshift range 0<z<2. We discuss the errors currently associated with this method and how future data can improve upon it significantly. We also examine the effects of reddening on the K-corrections and the light curves of Type Ia supernovae. Finally, we provide a few examples of how these techniques affect our current understanding of a sample of both nearby and distant supernovae.Comment: Accepted for the August issue of PASP. 39 pages, 15 figure

Salmonella Paratyphi A Outer Membrane Vesicles Displaying Vi Polysaccharide as a Multivalent Vaccine against Enteric Fever.

Typhoid and paratyphoid fevers have a high incidence worldwide and coexist in many geographical areas, especially in low-middle-income countries (LMIC) in South and Southeast Asia. There is extensive consensus on the urgent need for better and affordable vaccines against systemic Salmonella infections. Generalized modules for membrane antigens (GMMA), outer membrane exosomes shed by Salmonella bacteria genetically manipulated to increase blebbing, resemble the bacterial surface where protective antigens are displayed in their native environment. Here, we engineered S Paratyphi A using the pDC5-viaB plasmid to generate GMMA displaying the heterologous S Typhi Vi antigen together with the homologous O:2 O antigen. The presence of both Vi and O:2 was confirmed by flow cytometry on bacterial cells, and their amount was quantified on the resulting vesicles through a panel of analytical methods. When tested in mice, such GMMA induced a strong antibody response against both Vi and O:2, and these antibodies were functional in a serum bactericidal assay. Our approach yielded a bivalent vaccine candidate able to induce immune responses against different Salmonella serovars, which could benefit LMIC residents and travelers.BactiVac catalyst Grant in collaboration with GSK

High frequency longitudinal and transverse dynamics in water

High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S(Q,\omega) of liquid water have been performed for wave vectors Q between 4 and 30 nm^-1 in distinctly different thermodynamic conditions (T= 263 - 420 K ; at, or close to, ambient pressure and at P = 2 kbar). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost non-dispersive) is confirmed. The study of their temperature- and Q-dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q-dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes the complete transition from the adiabatic sound velocity (c_0) (viscous limit) to the infinite frequency sound velocity (c_\infinity) (elastic limit). On decreasing Q, as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in the S(Q,\omega) as soon as the purely viscous regime is left.Comment: 28 pages, 12 figure

Lower Critical Dimension of Ising Spin Glasses

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be investigated. We study domain walls induced by two rather different types of boundary-condition changes, and, in each case, analyze the system-size dependence of an appropriately defined ``defect energy'', which we denote by DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with \theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition changes. These results are in reasonable agreement with each other, allowing for small systematic effects. They also agree well with earlier work on smaller sizes. The negative value indicates that two dimensions is below the lower critical dimension d_c. For the +-J model, we obtain a different result, namely the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta = 0, indicating that the lower critical dimension for the +-J model exactly d_c=2.Comment: 4 pages, 4 figures, 1 table, revte