Blocking and invasion for reaction–diffusion equations in periodic media

We investigate the large time behavior of solutions of reaction–diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade the domain. In particular, we relate such solutions with front-like solutions such as pulsating traveling fronts. Next, we focus on the homogeneous bistable equation set in a domain with periodic holes, and specifically on the cases where fronts are not known to exist. We show how the geometry of the domain can block or allow invasion. We finally exhibit a periodic domain on which the propagation takes place in an asymmetric fashion, in the sense that the invasion occurs in a direction but is blocked in the opposite one

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)

Augmented Reality for People with Visual Impairments: Designing and Creating Audio-Tactile Content from Existing Objects

ISBN: 978-3-319-94273-5International audienceTactile maps and diagrams are widely used as accessible graphical media for people with visual impairments, in particular in the context of education. They can be made interactive by augmenting them with audio feedback. It is however complicated to create audio-tactile graphics that have rich and realistic tactile textures. To overcome these limitations, we propose a new augmented reality approach allowing novices to easily and quickly augment real objects with audio feedback. In our user study, six teachers created their own audio-augmentation of objects, such as a botanical atlas, within 30 minutes or less. Teachers found the tool easy to use and were confident about re-using it. The resulting augmented objects allow two modes: exploration mode provides feedback on demand about an element, while quiz mode provides questions and answers. We evaluated the resulting audio-tactile material with five visually impaired children. Participants found the resulting interactive graphics exciting to use independently of their mental imagery skills

Density Matrix Renormalization Group Applied to the Ground State of the XY-Spin-Peierls System

We use the density matrix renormalization group (DMRG) to map out the ground state of a XY-spin chain coupled to dispersionless phonons of frequency $\omega$. We confirm the existence of a critical spin-phonon coupling $_c\propto \omega ^{0.7}$ for the onset of the spin gap bearing the signature of a Kosterlitz-Thouless transition. We also observe a classical-quantum crossover when the spin-Peierls gap $\Delta$ is of order $$. In the classical regime, $\Delta >\omega$, the mean-field parameters are strongly renormalized by non-adiabatic corrections. This is the first application of the DMRG to phonons.Comment: 10 pages, 5 figures. To be published in PR

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

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

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

Competition between Pauli and orbital effects in a charge-density wave system

We present angular dependent magneto-transport and magnetization measurements on alpha-(ET)2MHg(SCN)4 compounds at high magnetic fields and low temperatures. We find that the low temperature ground state undergoes two subsequent field-induced density-wave type phase transitions above a critical angle of the magnetic field with respect to the crystallographic axes. This new phase diagram may be qualitatively described assuming a charge density wave ground state which undergoes field-induced transitions due to the interplay of Pauli and orbital effects.Comment: 11 pages, 4 figures, shown at the APS march meeting 2000, appears in the Ph.D. thesis of J. S. Qualls (Florida State University, 1999), and submitted to PR

Tomography of pairing symmetry from magnetotunneling spectroscopy -- a case study for quasi-1D organic superconductors

We propose that anisotropic $p$-, $d$-, or $f$-wave pairing symmetries can be distinguished from a tunneling spectroscopy in the presence of magnetic fields, which is exemplified here for a model organic superconductor ${(TMTSF)}_{2}X$. The shape of the Fermi surface (quasi-one-dimensional in this example) affects sensitively the pairing symmetry, which in turn affects the shape (U or V) of the gap along with the presence/absence of the zero-bias peak in the tunneling in a subtle manner. Yet, an application of a magnetic field enables us to identify the symmetry, which is interpreted as an effect of the Doppler shift in Andreev bound states.Comment: 4 papegs, 4 figure