Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate

We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space is the largest one in which we can expect convergence to the steady size distribution. Although this convergence is known to occur under fairly general conditions on the coefficients of the equation, we prove that it does not happen uniformly with respect to the initial data when the fragmentation rate in bounded. First we get the result for fragmentation kernels which do not form arbitrarily small fragments by taking advantage of the Dyson-Phillips series. Then we extend it to general kernels by using the notion of quasi-compactness and the fact that it is a topological invariant

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

Physicians' Multitasking and Incentives: Empirical Evidence from a Natural Experiment

We analyse how physicians respond to contractual changes and incentives within a multitasking environment. In 1999 the Quebec government (Canada) introduced an optional mixed compensation system, combining a fixed per diem with a discounted (relative to the traditional fee-for-service system) fee for services provided. We combine panel survey and administrative data on Quebec physicians to evaluate the impact of this change in incentives on their practice choices. We highlight the differentiated impact of incentives on various dimensions of physician behaviour by considering a wide range of labour supply variables: time spent on seeing patients, time devoted to teaching, administrative tasks or research, as well as the volume of clinical services and average time per clinical service. Our results show that, on average, the reform induced physicians who changed from FFS to MC to reduce their volume of (billable) services by 6.15% and to reduce their hours of work spent on seeing patients by 2.57%. Their average time spent per service increased by 3.58%, suggesting a potential quality-quantity substitution. Also the reform induced these physicians to increase their time spent on teaching and administrative duties (tasks not remunerated under the fee-for-service system) by 7.9%.Physician payment mechanisms, multitasking, mixed-payment systems, incentive contracts, labour supply, self-selection, panel estimation

On the exponential decay to equilibrium of the degenerate linear Boltzmann equation

In this paper we study the decay to the equilibrium state for the solution of the linear Boltzmann equation in the torus \T^d=\bR^d/\bZ^{d}, $d \in \N$, by allowing that the non-negative cross section $\sigma$ can vanish in a subregion X:=\{ x \in \T^d\, \vert \, \sigma(x)=0\} of the domain with $\text{meas}(X)\geq 0$ with respect to the Lebesgue measure. We show that the geometrical characterization of $X$ is the key property to produce exponential decay to equilibrium

Homogenization of the linear Boltzmann equation in a domain with a periodic distribution of holes

Consider a linear Boltzmann equation posed on the Euclidian plane with a periodic system of circular holes and for particles moving at speed 1. Assuming that the holes are absorbing -- i.e. that particles falling in a hole remain trapped there forever, we discuss the homogenization limit of that equation in the case where the reciprocal number of holes per unit surface and the length of the circumference of each hole are asymptotically equivalent small quantities. We show that the mass loss rate due to particles falling into the holes is governed by a renewal equation that involves the distribution of free-path lengths for the periodic Lorentz gas. In particular, it is proved that the total mass of the particle system at time t decays exponentially fast as t tends to infinity. This is at variance with the collisionless case discussed in [Caglioti, E., Golse, F., Commun. Math. Phys. 236 (2003), pp. 199--221], where the total mass decays as Const./t as the time variable t tends to infinity.Comment: 29 pages, 1 figure, submitted; figure 1 corrected in new versio

Violation of Kirchhoff's Laws for a Coherent RC Circuit

What is the complex impedance of a fully coherent quantum resistance-capacitance (RC) circuit at GHz frequencies in which a resistor and a capacitor are connected in series? While Kirchhoff's laws predict addition of capacitor and resistor impedances, we report on observation of a different behavior. The resistance, here associated with charge relaxation, differs from the usual transport resistance given by the Landauer formula. In particular, for a single mode conductor, the charge relaxation resistance is half the resistance quantum, regardless of the transmission of the mode. The new mesoscopic effect reported here is relevant for the dynamical regime of all quantum devices

The relaxation time of a chiral quantum R-L circuit

We report on the GHz complex admittance of a chiral one dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission-independent. This shows that the relaxation time of a chiral R-L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the c cuit

Analysis of the meiotic segregation in intergeneric hybrids of tilapias

Tilapia species exhibit a large ecological diversity and an important propensity to interspecific hybridisation. This has been shown in the wild and used in aquaculture. However, despite its important evolutionary implications, few studies have focused on the analysis of hybrid genomes and their meiotic segregation. Intergeneric hybrids between Oreochromis niloticus and Sarotherodon melanotheron, two species highly differentiated genetically, ecologically, and behaviourally, were produced experimentally. The meiotic segregation of these hybrids was analysed in reciprocal second generation hybrid (F2) and backcross families and compared to the meiosis of both parental species, using a panel of 30 microsatellite markers. Hybrid meioses showed segregation in accordance to Mendelian expectations, independent from sex and the direction of crosses. In addition, we observed a conservation of linkage associations between markers, which suggests a relatively similar genome structure between the two parental species and the apparent lack of postzygotic incompatibility, despite their important divergence. These results provide genomics insights into the relative ease of hybridisation within cichlid species when prezygotic barriers are disrupted. Overall our results support the hypothesis that hybridisation may have played an important role in the evolution and diversification of cichlids