Optimal phenotypic plasticity in a stochastic environment minimizes the cost/benefit ratio

This paper addresses the question of optimal phenotypic plasticity as a response to environmental fluctuations while optimizing the cost/benefit ratio, where the cost is energetic expense of plasticity, and benefit is fitness. The dispersion matrix \Sigma of the genes' response (H = ln|\Sigma|) is used: (i) in a numerical model as a metric of the phenotypic variance reduction in the course of fitness optimization, then (ii) in an analytical model, in order to optimize parameters under the constraint of limited energy availability. Results lead to speculate that such optimized organisms should maximize their exergy and thus the direct/indirect work they exert on the habitat. It is shown that the optimal cost/benefit ratio belongs to an interval in which differences between individuals should not substantially modify their fitness. Consequently, even in the case of an ideal population, close to the optimal plasticity, a certain level of genetic diversity should be long conserved, and a part, still to be determined, of intra-populations genetic diversity probably stem from environment fluctuations. Species confronted to monotonous factors should be less plastic than vicariant species experiencing heterogeneous environments. Analogies with the MaxEnt algorithm of E.T. Jaynes (1957) are discussed, leading to the conjecture that this method may be applied even in case of multivariate but non multinormal distributions of the responses

Water and the WTO: Don’t kill the messenger.

It is widely recognized that forecasting future climate shocks at a regional level̶which regions will be flooded, which ones will be under water stress on a year by year basis̶is largely out of reach. In such circumstances, trade gets back a role that has faded away during the last sixty years of relatively stable climatic, economic and political conditions. It is to be the ultimate insurer. Regions under sudden water stress will need to import food products in exceptional quantities, and trade happens to be a cheap (efficient) insurance scheme to face a sudden instability in water resources in some parts of the world. There are thus good reasons to look at whether the world trade regime could provide a strong and sound framework to the international water regime. Not many papers have looked at this issue. They generally see the WTO as a source of problems rather than of solutions. Hence, they argue for specific international agreements on water. But, the climate community experience of the COP15 (the 2009 Copenhagen Summit on Climate Change) is a strong warning signal showing how difficult it is to build a “specific” international regime. In contrast, this paper argues that the basic principles on which the world trade regime is built would be equally useful for the international water regime, and that the WTO rules are flexible enough to address the specific problems raised by water management in a international context. It also argues that, if current international trade mirrors domestic distortions, limiting such trade will cost a lot in terms of water use. Killing the messenger (trade) does not solve the problems (domestic markets).

Cosmic-ray acceleration in young protostars

The main signature of the interaction between cosmic rays and molecular clouds is the high ionisation degree. This decreases towards the densest parts of a cloud, where star formation is expected, because of energy losses and magnetic effects. However recent observations hint to high levels of ionisation in protostellar systems, therefore leading to an apparent contradiction that could be explained by the presence of energetic particles accelerated within young protostars. Our modelling consists of a set of conditions that has to be satisfied in order to have an efficient particle acceleration through the diffusive shock acceleration mechanism. We find that jet shocks can be strong accelerators of protons which can be boosted up to relativistic energies. Another possibly efficient acceleration site is located at protostellar surfaces, where shocks caused by impacting material during the collapse phase are strong enough to accelerate protons. Our results demonstrate the possibility of accelerating particles during the early phase of a proto-Solar-like system and can be used as an argument to support available observations. The existence of an internal source of energetic particles can have a strong and unforeseen impact on the star and planet formation process as well as on the formation of pre-biotic molecules.Comment: Accepted by Astronomy and Astrophysic

New patterns in high-speed granular flows

We report on new patterns in high-speed flows of granular materials obtained by means of extensive numerical simulations. These patterns emerge from the destabilization of unidirectional flows upon increase of mass holdup and inclination angle, and are characterized by complex internal structures including secondary flows, heterogeneous particle volume fraction, symmetry breaking and dynamically maintained order. In particular, we evidenced steady and fully developed "supported" flows, which consist of a dense core surrounded by a highly energetic granular gas. Interestingly, despite their overall diversity, these regimes are shown to obey a scaling law for the mass flow rate as a function of the mass holdup. This unique set of 3D flow regimes raises new challenges for extending the scope of current granular rheological models

K-mouflage gravity models that pass Solar System and cosmological constraints

We show that Solar System tests can place very strong constraints on K-mouflage models of gravity, which are coupled scalar field models with nontrivial kinetic terms that screen the fifth force in regions of large gravitational acceleration. In particular, the bounds on the anomalous perihelion of the Moon imposes stringent restrictions on the K-mouflage Lagrangian density, which can be met when the contributions of higher-order operators in the static regime are sufficiently small. The bound on the rate of change of the gravitational strength in the Solar System constrains the coupling strength $\beta$ to be smaller than $0.1$. These two bounds impose tighter constraints than the results from the Cassini satellite and Big Bang Nucleosynthesis. Despite the Solar System restrictions, we show that it is possible to construct viable models with interesting cosmological predictions. In particular, relative to $\Lambda$-CDM, such models predict percent-level deviations for the clustering of matter and the number density of dark matter haloes. This makes these models predictive and testable by forthcoming observational missions.Comment: 15 page

The formulation of dynamical contact problems with friction in the case of systems of rigid bodies and general discrete mechanical systems—Painlevé and Kane paradoxes revisited

International audienceThe dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modelling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase of kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative, that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this formulation. Mathematics Subject Classification (2010). 70F35, 70F40