Related papers: Front d'onde et propagation des singularites pour …

We study the distribution of the Hodge spectral exponents of an irreducible plane curve by comparing it with a continuous distribution. We provide a closed formula for this difference in terms of numerical invariants of the curve. We…

We use sequences which depend on two parameters to define families of ultradifferentiable functions which contain Gevrey classes. It is shown that such families are closed under superposition, and therefore inverse closed as well.…

Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the…

For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on…

Let X be a smooth real algebraic variety. Let $\xi$ be a distribution on it. One can define the singular support of $\xi$ to be the singular support of the $D_X$-module generated by $\xi$ (some times it is also called the characteristic…

We introduce the wave-front set for distributions with respect to Fourier images of weighted translation invariant Banach function spaces. We prove that usual mapping properties for pseudo-differential operators hold in the context of such…

The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that…

This paper is concerned with the propagating speeds of transition fronts in $R^N$ for spatially periodic bistable reaction-diffusion equations. The notion of transition fronts generalizes the standard notions of traveling fronts. Under the…

We investigate the singularities of the trace of the half-wave group, $\mathrm{Tr} \, e^{-it\sqrt\Delta}$, on Euclidean surfaces with conical singularities $(X,g)$. We compute the leading-order singularity associated to periodic orbits with…

In this paper we describe the propagation of singularities of tempered distributional generalized eigenfunctions of many-body Hamiltonians under the assumption that no subsystem has a bound state and that the two-body interactions are…

All the leading-twist parton distribution functions are calculated in a spectator model of the nucleon, using scalar and axial-vector diquarks. Single gluon rescattering is used to generate T-odd distribution functions. Different choices…

This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…

We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of…

Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…

The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…

We study the propagation of uniformly translating fronts into a linearly unstable state, both analytically and numerically. We introduce a perturbative renormalization group (RG) approach to compute the change in the propagation speed when…

We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equation $u_t = u_{xx} + f(u)$ with $f(0)=f(1)=0$, and $f>0$ in $(0,1)$, which permits, in principle, the calculation of the exact speed for…

We introduce and study a new class of fronts in finite particle number reaction-diffusion systems, corresponding to propagating up a reaction rate gradient. We show that these systems have no traditional mean-field limit, as the nature of…

In a previous paper [Phys. Rev. A 105, 042205 (2022)], the distribution of resonance poles in the complex plane of the wavenumber $k$ associated to the multiple scattering of a quantum particle in a random point field was numerically…

We introduce discrete wave-front sets with respect to Fourier Lebesgue and modulation spaces. We prove that these wave-front sets agree with corresponding wave-front sets of "continuous type".