Designing risk messages in response to human-caused disasters

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A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows

In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting some inf-convolution structure of the metric we show convergence of the whole process for the standard class of energy functionals under suitable compactness assumptions, and investigate in details the case of internal energies. The interest is double: On the one hand we prove existence of weak solutions for a certain class of reaction-advection-diffusion equations, and on the other hand this process is constructive and well adapted to available numerical solvers.Comment: Final version, to appear in SIAM SIM

Timing mirror structures observed by Cluster with a magnetosheath flow model

The evolution of structures associated with mirror modes during their flow in the Earth's magnetosheath is studied. The fact that the related magnetic fluctuations can take distinct shapes, from deep holes to high peaks, has been assessed in previous works on the observational, modeling and numerical points of view. In this paper we present an analytical model for the flow lines and velocity magnitude inside the magnetosheath. This model is used to interpret almost 10 years of Cluster observations of mirror structures: by back tracking each isolated observation to the shock, the "age", or flow time, of these structures is determined together with the geometry of the shock. Using this flow time the evolutionary path of the structures may be studied with respect to different quantities: the distance to mirror threshold, the amplitude of mirror fluctuations and the skewness of the magnetic amplitude distribution as a marker of the shape of the structures. These behaviours are confronted to numerical simulations which confirm the dynamical perspective gained from the association of the statistical analysis and the analytical model: magnetic peaks are mostly formed just behind the shock and are quickly overwhelmed by magnetic holes as the plasma conditions get more mirror stable. The amplitude of the fluctuations are found to saturate before the skewness vanishes, i.e. when both structures quantitatively balance each other, which typically occurs after a flow time of 100–200 s in the Earth's magnetosheath. Comparison with other astrophysical contexts is discussed

Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers

We investigate properties of the scale dependence and cross-scale transfer of kinetic energy in compressible three-dimensional hydrodynamic turbulence, by means of two direct numerical simulations of decaying turbulence with initial Mach numbers M = 1/3 and M = 1, and with moderate Reynolds numbers, R_lambda ~ 100. The turbulent dynamics is analyzed using compressible and incompressible versions of the dynamic spectral transfer (ST) and the Karman-Howarth-Monin (KHM) equations. We find that the nonlinear coupling leads to a flux of the kinetic energy to small scales where it is dissipated; at the same time, the reversible pressure-dilatation mechanism causes oscillatory exchanges between the kinetic and internal energies with an average zero net energy transfer. While the incompressible KHM and ST equations are not generally valid in the simulations, their compressible counterparts are well satisfied and describe, in a quantitatively similar way, the decay of the kinetic energy on large scales, the cross-scale energy transfer/cascade, the pressure dilatation, and the dissipation. There exists a simple relationship between the KHM and ST results through the inverse proportionality between the wave vector k and the spatial separation length l as k l ~ 3^1/2. For a given time the dissipation and pressure-dilatation terms are strong on large scales in the KHM approach whereas the ST terms become dominant on small scales; this is owing to the complementary cumulative behavior of the two methods. The effect of pressure dilatation is weak when averaged over a period of its oscillations and may lead to a transfer of the kinetic energy from large to small scales without a net exchange between the kinetic and internal energies. Our results suggest that for large-enough systems there exists an inertial range for the kinetic energy cascade ...Comment: 14 pages, 10 figure

Recent Decisions

CHOICE OF LAW--WRONGFUL DEATH--GOVERNMENTAL-INTEREST ANALYSIS DETERMINES LAW APPLICABLE TO MEASURE OF DAMAGES IN CLAIMS ARISING FROM FOREIGN Air CRASH John Edison Drake =============== EUROPEAN COMMUNITIES--FREE MOVEMENT OF WORKERS--COURT OF JUSTICE SETS GUIDELINES FOR USE BY MEMBER STATES OF THE PUBLIC POLICY EXCEPTION IN ARTICLE 48 Heidi A. Rohrbach ================ TAX TREATIES--UNITED STATES MAY USE THE INTERNAL REVENUE CODE SUMMONING AUTHORITY TO OBTAIN DOMESTIC INFORMATION SOLELY TO AID A FOREIGN DOMESTIC TAX INVESTIGATION PURSUANT TO A TAX TREATY John R. Hellinger ============== TREATY INTERPRETATION--WARSAW CONVENTION-- PASSENGERS UNDERGOING SEARCH PREREQUISITE TO BOARDING ARE ENGAGED IN OPERATIONS OF EMBARKING Elizabeth Graeme Brownin

Magnetic field turbulence in the solar wind at sub-ion scales: in situ observations and numerical simulations

We investigate the transition of the solar wind turbulent cascade from MHD to sub-ion range by means of a detail comparison between in situ observations and hybrid numerical simulations. In particular we focus on the properties of the magnetic field and its component anisotropy in Cluster measurements and hybrid 2D simulations. First, we address the angular distribution of wave-vectors in the kinetic range between ion and electron scales by studying the variance anisotropy of the magnetic field components. When taking into account the single-direction sampling performed by spacecraft in the solar wind, the main properties of the fluctuations observed in situ are also recovered in our numerical description. This result confirms that solar wind turbulence in the sub-ion range is characterized by a quasi-2D gyrotropic distribution of k-vectors around the mean field. We then consider the magnetic compressibility associated with the turbulent cascade and its evolution from large-MHD to sub-ion scales. The ratio of field-aligned to perpendicular fluctuations, typically low in the MHD inertial range, increases significantly when crossing ion scales and its value in the sub-ion range is a function of the total plasma beta only, as expected from theoretical predictions, with higher magnetic compressibility for higher beta. Moreover, we observe that this increase has a gradual trend from low to high beta values in the in situ data; this behaviour is well captured by the numerical simulations. The level of magnetic field compressibility that is observed in situ and in the simulations is in fairly good agreement with theoretical predictions, especially at high beta, suggesting that in the kinetic range explored the turbulence is supported by low-frequency and highly-oblique fluctuations in pressure balance, like kinetic Alfv\'en waves or other slowly evolving coherent structures.Comment: Manuscript submitted to Frontiers Astronomy and Space Sciences, Research Topic: Improving the Understanding of Kinetic Processes in Solar Wind and Magnetosphere: From CLUSTER to MM

Nonlinear theory of mirror instability near threshold

An asymptotic model based on a reductive perturbative expansion of the drift kinetic and the Maxwell equations is used to demonstrate that, near the instability threshold, the nonlinear dynamics of mirror modes in a magnetized plasma with anisotropic ion temperatures involves a subcritical bifurcation,leading to the formation of small-scale structures with amplitudes comparable with the ambient magnetic field

On the irredundant part of the first Piola-Kirchhoff stress tensor

Let us assume a given medium moves and deforms in an ambient smooth and oriented Riemannian manifold N with metric (, ). This medium at hand is supposed to maintain the shape of a compact smooth orientable and connected manifold M with boundary. Clearly dim M ≤ dim N. By a configuration j of the medium we mean a smooth embedding of M into N. The configuration space is E(M, N), the collection of all smooth embeddings of M into N endowed with the C∞-topology. [...] The main purpose of this notes is to exhibit (in absence of exterior force densities) the irredundant part of a(j) that determines the force densities mentioned and the virtual work caused by any infinitesimal distortion at j.[...

Statistics of magnetic reconnection and turbulence in Hall-MHD and hybrid-PIC simulations

Properties of decaying Alfvenic plasma turbulence are investigated by means of two-dimensional Hall-magnetohydrodynamic and hybrid particle-in-cell numerical simulations. In most cases, spectral properties of turbulent fluctuations find good agreement in both the numerical models. The power spectra of the magnetic field exhibit a double power-law with spectral index -5/3 at large, fluid scales and -3 at sub-ion scales, while for velocity fluctuations the spectral index at fluid scales is -3/2. In both models, the development of a turbulent cascade is concurrently characterized by magnetic reconnection events that are fast, with inverse reconnection rates much smaller than the characteristic large-eddy turnover times. Moreover, these reconnection events trigger a direct energy transfer from large to sub-ion scales. This supports the existence of a reconnection-mediated turbulent regime at sub-ion scales. We conclude that the Hall-MHD fluid description captures to a large extent the transition of the turbulent cascade between the fluid and sub-ion scales

A detailed analysis of a multi-agent diverse team

In an open system we can have many different kinds of agents. However, it is a challenge to decide which agents to pick when forming multi-agent teams. In some scenarios, agents coordinate by voting continuously. When forming such teams, should we focus on the diversity of the team or on the strength of each member? Can a team of diverse (and weak) agents outperform a uniform team of strong agents? We propose a new model to address these questions. Our key contributions include: (i) we show that a diverse team can overcome a uniform team and we give the necessary conditions for it to happen; (ii) we present optimal voting rules for a diverse team; (iii) we perform synthetic experiments that demonstrate that both diversity and strength contribute to the performance of a team; (iv) we show experiments that demonstrate the usefulness of our model in one of the most difficult challenges for Artificial Intelligence: Computer Go