On the applicability of the lognormal distribution in random dynamical systems

This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.

Intracellular demography and the dynamics of Salmonella enterica infections.

An understanding of within-host dynamics of pathogen interactions with eukaryotic cells can shape the development of effective preventive measures and drug regimes. Such investigations have been hampered by the difficulty of identifying and observing directly, within live tissues, the multiple key variables that underlay infection processes. Fluorescence microscopy data on intracellular distributions of Salmonella enterica serovar Typhimurium (S. Typhimurium) show that, while the number of infected cells increases with time, the distribution of bacteria between cells is stationary (though highly skewed). Here, we report a simple model framework for the intensity of intracellular infection that links the quasi-stationary distribution of bacteria to bacterial and cellular demography. This enables us to reject the hypothesis that the skewed distribution is generated by intrinsic cellular heterogeneities, and to derive specific predictions on the within-cell dynamics of Salmonella division and host-cell lysis. For within-cell pathogens in general, we show that within-cell dynamics have implications across pathogen dynamics, evolution, and control, and we develop novel generic guidelines for the design of antibacterial combination therapies and the management of antibiotic resistance.

Intracellular demography and the dynamics of Salmonella enterica infections.

An understanding of within-host dynamics of pathogen interactions with eukaryotic cells can shape the development of effective preventive measures and drug regimes. Such investigations have been hampered by the difficulty of identifying and observing directly, within live tissues, the multiple key variables that underlay infection processes. Fluorescence microscopy data on intracellular distributions of Salmonella enterica serovar Typhimurium (S. Typhimurium) show that, while the number of infected cells increases with time, the distribution of bacteria between cells is stationary (though highly skewed). Here, we report a simple model framework for the intensity of intracellular infection that links the quasi-stationary distribution of bacteria to bacterial and cellular demography. This enables us to reject the hypothesis that the skewed distribution is generated by intrinsic cellular heterogeneities, and to derive specific predictions on the within-cell dynamics of Salmonella division and host-cell lysis. For within-cell pathogens in general, we show that within-cell dynamics have implications across pathogen dynamics, evolution, and control, and we develop novel generic guidelines for the design of antibacterial combination therapies and the management of antibiotic resistance.

Measurement of the magnetic field inside the holes of a drilled bulk high-Tc superconductor

We use macroscopic holes drilled in a bulk YBCO superconductor to probe its magnetic properties in the volume of the sample. The sample is subjected to an AC magnetic flux with a density ranging from 30mT to 130mT and the flux in the superconductor is probed by miniature coils inserted in the holes. In a given hole, three different penetration regimes can be observed: (i) the shielded regime, where no magnetic flux threads the hole; (ii) the gradual penetration regime, where the waveform of the magnetic field has a clipped sine shape whose fundamental component scales with the applied field; and (iii) the flux concentration regime, where the waveform of the magnetic field is nearly a sine wave, with an amplitude exceeding that of the applied field by up to a factor of two. The distribution of the penetration regimes in the holes is compared with that of the magnetic flux density at the top and bottom surfaces of the sample, and is interpreted with the help of optical polarized light micrographs of these surfaces. We show that the measurement of the magnetic field inside the holes can be used as a local characterization of the bulk magnetic properties of the sample.