Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts

We study the asymptotic behaviour of the following linear growth-fragmentation equation$$\dfrac{\partial}{\partial t} u(t,x) + \dfrac{\partial}{\partial x} \big(x u(t,x)\big) + B(x) u(t,x) =4 B(2x)u(t,2x),$$ and prove that under fairly general assumptions on the division rate $B(x),$ its solution converges towards an oscillatory function,explicitely given by the projection of the initial state on the space generated by the countable set of the dominant eigenvectors of the operator. Despite the lack of hypo-coercivity of the operator, the proof relies on a general relative entropy argument in a convenient weighted $L^2$ space, where well-posedness is obtained via semigroup analysis. We also propose a non-dissipative numerical scheme, able to capture the oscillations

A 2D model for hydrodynamics and biology coupling applied to algae growth simulations

Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint-Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.Comment: 27 pages, 11 figure

Creep behaviour of as received, aged and cold worked INCONEL 617 at 850 °C and 950 °C

The effect of initial microstructure on alloy 617 creep behaviour has been investigated at 850 °C and 950 °C. The solution treated material shows non-classical creep behaviour at both temperatures with a strain rate drop at the beginning of the tests followed by a creep rate increase to a plateau before the onset of the tertiary creep. The intragranular secondary carbides which precipitate early at test temperature are responsible of the strong initial hardening effect by pinning the dislocations. This effect is overpassed during the thermo mechanical ageing of the alloy which induces growth of these carbides. Prior 1000 h thermal ageing at the temperature test totally removes the strain rate drop and reduces the lifetime. The intragranular microstructure has evolved thanks to the prior thermal ageing before the creep tests. Microstructural examinations also show the presence of grain boundary migration and recrystallization in the material during creep tests of the as received and aged materials. Preliminary cold work treatment highly reduces the strain rate of Inconel 617 and enhances the lifetime at 850 °C while the opposite is observed at 950 °C

Understanding interface effects in perovskite thin films

The control of matter properties (transport, magnetic, dielectric,...) using synthesis as thin films is strongly hindered by the lack of reliable theories, able to guide the design of new systems, through the understanding of the interface effects and of the way the substrate constraints are imposed to the material. The present paper analyses the energetic contributions at the interfaces, and proposes a model describing the microscopic mechanisms governing the interactions at an epitaxial interface between a manganite and another transition metal oxide in perovskite structure (as for instance $\rm SrTiO_3$). The model is checked against experimental results and literature analysis

Layer-averaged Euler and Navier-Stokes equations

In this paper we propose a strategy to approximate incompressible hydrostatic free surface Euler and Navier-Stokes models. The main advantage of the proposed models is that the water depth is a dynamical variable of the system and hence the model is formulated over a fixed domain.The proposed strategy extends previous works approximating the Euler and Navier-Stokes systems using a multilayer description. Here, the needed closure relations are obtained using an energy-based optimality criterion instead of an asymptotic expansion. Moreover, the layer-averaged description is successfully applied to the Navier-Stokes system with a general form of the Cauchy stress tensor

An Analytical Expression for the Hubble diagram of supernovae and gamma-ray bursts

A recent paper by Harmut Traunm\"uller shows that the most adequate equation to interpret the observations on magnitude and redshift from 892 type 1a supernovae would be mu = 5 log[(1+z) ln(1+z)] + const. We discuss this result which is exacly the one we have obtained few years ago when postulating a relation between the speed of light and the expansion of the universe. We also compare our analytical result to the conclusion of Marosi who studied 280 supernovae and gamma-ray bursts in the range 0.1014 < z < 8.1. The difference between his results and ours is at worst of 0.3 %.Comment: 7 pages, 1 figur

Semantic and pragmatic motivations for constructional preferences: a corpus-based study of provide, supply, and present

A select group of transfer verbs can enter into four different constructions: the ditransitive construction (He provided John the money), the prepositional-dative construction (He provided the money to John), a construction with a prepositional theme (He provided John with the money), and a construction with a recipient realized by a for-phrase (He provided the money for John). In this article, we take a close look at three such verbs: provide, supply, and present. Corpus analysis shows that these three verbs display different structural preferences with respect to the for-, to-, and with-patterns. To explain these preferences, the study investigates pragmatic principles (following Mukherjee 2001 on provide) and the role played by semantic factors. An examination of the semantics of the verbs and the lexically motivated constructional semantics of the to, for, and with-patterns shows (i) that the three constructions are not interchangeable, and (ii) that the preferential differences between the three verbs find an explanation in the compatibility between lexical and constructional semantics. The description is mainly based on data from the British National Corpus

Tax Evasion and Social Interactions

The paper extends the standard tax evasion model by allowing for social interactions. In Manski's (1993) nomenclature, our model takes into account social conformity effects (i.e., endogenous interactions), fairness effects (i.e., exogenous interactions) and sorting effects (i.e., correlated effects). Our model is tested using experimental data. Participants must decide how much income to report given their tax rate and audit probability, and given those faced by the other members of their group as well as their mean reported income. The estimation is based on a two-limit simultaneous tobit with fixed group effects. A unique social equilibrium exists when the model satisfies coherency conditions. In line with Brock and Durlauf (2001b), the intrinsic nonlinearity between individual and group responses is sufficient to identify the model without imposing any exclusion restrictions. Our results are consistent with fairness effects but reject social conformity and correlated effects.social interactions; tax evasion; simultaneous tobit; laboratory experiments

Tax Evasion and Social Interactions

The paper extends the standard tax evasion model by allowing for social interactions. In Manski's (1993) nomenclature, our model takes into account social conformity effects (i.e., endogenous interactions), fairness effects (i.e., exogenous interactions) and sorting effects (i.e., correlated effects). Our model is tested using experimental data. Participants must decide how much income to report given their tax rate and audit probability, and given those faced by the other members of their group as well as their mean reported income. The estimation is based on a two-limit simultaneous tobit with fixed group effects. A unique social equilibrium exists when the model satisfies coherency conditions. In line with Brock and Durlauf (2001b), the intrinsic nonlinearity between individual and group responses is sufficient to identify the model without imposing any exclusion restrictions. Our results are consistent with fairness effects but reject social conformity and correlated effects.laboratory experiments; simultaneous Tobit; social interactions; tax evasion

Tax Evasion and Social Interactions

The paper extends the standard tax evasion model by allowing for social interactions. In Manski's (1993) nomenclature, our model takes into account social conformity effects (i.e., endogenous interactions), fairness effects (i.e., exogenous interactions) and sorting effects (i.e., correlated effects). Our model is tested using experimental data. Participants must decide how much income to report given their tax rate and audit probability, and given those faced by the other members of their group as well as their mean reported income. The estimation is based on a two-limit simultaneous tobit with fixed group effects. A unique social equilibrium exists when the model satisfies coherency conditions. In line with Brock and Durlauf (2001b), the intrinsic nonlinearity between individual and group responses is sufficient to identify the model without imposing any exclusion restrictions. Our results are consistent with fairness effects but reject social conformity and correlated effects.Social interactions, tax evasion, simultaneous tobit, laboratory experiments