Generalized principal eigenvalues for heterogeneous road-field systems

This paper develops the notion and properties of the generalized principal eigenvalue for an elliptic system coupling an equation in a plane with one on a line in this plane, together with boundary conditions that express exchanges taking place between the plane and the line. This study is motivated by the reaction-diffusion model introduced by Berestycki, Roquejoffre and Rossi [The influence of a line with fast diffusion on Fisher-KPP propagation, J. Math. Biol. 66(4-5) (2013) 743-766] to describe the effect on biological invasions of networks with fast diffusion imbedded in a field. Here we study the eigenvalue associated with heterogeneous generalizations of this model. In a forthcoming work [Influence of a line with fast diffusion on an ecological niche, preprint (2018)] we show that persistence or extinction of the associated nonlinear evolution equation is fully accounted for by this generalized eigenvalue. A key element in the proofs is a new Harnack inequality that we establish for these systems and which is of independent interest

Influence of a road on a population in an ecological niche facing climate change

We introduce a model designed to account for the influence of a line with fast diffusion–such as a road or another transport network–on the dynamics of a population in an ecological niche.This model consists of a system of coupled reaction-diffusion equations set on domains with different dimensions (line / plane). We first show that, in a stationary climate, the presence of the line is always deleterious and can even lead the population to extinction. Next, we consider the case where the niche is subject to a displacement, representing the effect of a climate change. We find that in such case the line with fast diffusion can help the population to persist. We also study several qualitative properties of this system. The analysis is based on a notion of generalized principal eigenvalue developed and studied by the authors (2019)

From image to technology: a multidisciplinary approach for improving the quality of organic bread.

This study is part of a research programme devoted to improving the quality of organic bread. It aims to identify and test prototypes of breads approved by consumers. This is achieved by analysing consumer representations and preferences and placing them within the framework of technological, sensory and nutritional dimensions of the products. The multidisciplinary approach implements an original qualitative approach that combines three consumer focus groups made up of both loyal and occasional consumers, and confrontation sessions with the programme scientific partners. Four prototypes of organic breads have thus been formalised and subsequently tested on a sample of 120 consumers from two sites (Angers and Strasbourg). From an operational point of view, proposals for organic breads approved by consumers are formulated. In terms of methodology, the contributions of a multidisciplinary study are discussed

Insulator-Metal Transition in One Dimension Induced by Long-Range Electronic Interactions

The effects of a long range electronic potential on a one dimensional commensurate Charge Density Wave (CDW) state are investigated. Using numerical techniques it is shown that a transition to a metallic ground state is reached as the range of the electron-electron repulsion increases. In this metallic state, the optical conductivity exhibits a large Drude weight. Possible interpretations of our results are discussed.Comment: 5 pages, Revtex, minor misprints corrected and a reference to earlier work by V. Emery and C. Noguera adde

Antiferromagnetic Phases of One-Dimensional Quarter-Filled Organic Conductors

The magnetic structure of antiferromagnetically ordered phases of quasi-one-dimensional organic conductors is studied theoretically at absolute zero based on the mean field approximation to the quarter-filled band with on-site and nearest-neighbor Coulomb interaction. The differences in magnetic properties between the antiferromagnetic phase of (TMTTF)$_2$X and the spin density wave phase in (TMTSF)$_2$X are seen to be due to a varying degrees of roles played by the on-site Coulomb interaction. The nearest-neighbor Coulomb interaction introduces charge disproportionation, which has the same spatial periodicity as the Wigner crystal, accompanied by a modified antiferromagnetic phase. This is in accordance with the results of experiments on (TMTTF)$_2$Br and (TMTTF)$_2$SCN. Moreover, the antiferromagnetic phase of (DI-DCNQI)$_2$Ag is predicted to have a similar antiferromagnetic spin structure.Comment: 8 pages, LaTeX, 4 figures, uses jpsj.sty, to be published in J. Phys. Soc. Jpn. 66 No. 5 (1997

Modular Moose: A new generation software reverse engineering environment

Advanced reverse engineering tools are required to cope with the complexity of software systems and the specific requirements of numerous different tasks (re-architecturing, migration, evolution). Consequently, reverse engineering tools should adapt to a wide range of situations. Yet, because they require a large infrastructure investment, being able to reuse these tools is key. Moose is a reverse engineering environment answering these requirements. While Moose started as a research project 20 years ago, it is also used in industrial projects, exposing itself to all these difficulties. In this paper we present ModMoose, the new version of Moose. ModMoose revolves around a new meta-model, modular and extensible; a new toolset of generic tools (query module, visualization engine, ...); and an open architecture supporting the synchronization and interaction of tools per task. With ModMoose, tool developers can develop specific meta-models by reusing existing elementary concepts, and dedicated reverse engineering tools that can interact with the existing ones

Competition of Dimerization and Charge Ordering in the Spin-Peierls State of Organic Conductors

The effect of the charge ordering on the spin-Peierls (SP) state has been examined by using a Peierls-Hubbard model at quarter-filling with dimerization, on-site and nearest-neighbor repulsive interactions. By taking account of the presence of dimerization, a bond distortion is calculated variationally with the renormalization group method based on bosonization. When the charge ordering appears at V=V_c with increasing the nearest-neighbor interaction (V), the distortion exhibits a maximum due to competition between the dimerization and the charge ordering. It is shown that the second-order phase transition occurs from the SP state with the bond alternation to a mixed state with an additional component of the site alternationat V = V_c.Comment: 11 pages, 13 figures, to be published in J. Phys. Soc. Jpn. 72 No.6 (2003

Charge gap in the one--dimensional dimerized Hubbard model at quarter-filling

We propose a quantitative estimate of the charge gap that opens in the one-dimensional dimerized Hubbard model at quarter-filling due to dimerization, which makes the system effectively half--filled, and to repulsion, which induces umklapp scattering processes. Our estimate is expected to be valid for any value of the repulsion and of the parameter describing the dimerization. It is based on analytical results obtained in various limits (weak coupling, strong coupling, large dimerization) and on numerical results obtained by exact diagonalization of small clusters. We consider two models of dimerization: alternating hopping integrals and alternating on--site energies. The former should be appropriate for the Bechgaard salts, the latter for compounds where the stacks are made of alternating $TMTSF$ and $TMTTF$ molecules. % $(TMTSF)_2 X$ and $(TMTTF)_2 X$ ($X$ denotes $ClO_4$, $PF_6$, $Br$...).Comment: 33 pages, RevTeX 3.0, figures on reques

Deducing correlation parameters from optical conductivity in the Bechgaard salts

Numerical calculations of the kinetic energy of various extensions of the one-dimensional Hubbard model including dimerization and repulsion between nearest neighbours are reported. Using the sum rule that relates the kinetic energy to the integral of the optical conductivity, one can determine which parameters are consistent with the reduction of the infrared oscillator strength that has been observed in the Bechgaard salts. This leads to improved estimates of the correlation parameters for both the TMTSF and TMTTF series.Comment: 12 pages, latex, figures available from the author

Coexistent State of Charge Density Wave and Spin Density Wave in One-Dimensional Quarter Filled Band Systems under Magnetic Fields

We theoretically study how the coexistent state of the charge density wave and the spin density wave in the one-dimensional quarter filled band is enhanced by magnetic fields. We found that when the correlation between electrons is strong the spin density wave state is suppressed under high magnetic fields, whereas the charge density wave state still remains. This will be observed in experiments such as the X-ray measurement.Comment: 7 pages, 15 figure