Related papers: High dimensionality and h-principle in PDE
We use a perturbative approach to evaluate transition amplitudes corresponding to quantum friction, for a scalar model describing an atom which moves at a constant velocity, close to a material plane. In particular, we present results on…
The properties of decaying turbulence is studied with the help of a Generalized Hydrodynamic (GHD) fluid model in the context of two dimensional visco - elastic medium such as a strongly coupled dusty plasma system. For the incompressible…
What does it mean to study PDE(=Partial Differential Equation)? How and what to do "to claim proudly that I'm studying a certain PDE"? Newton mechanic uses mainly ODE(=Ordinary Differential Equation) and describes nicely movements of Sun,…
The Gross-Pitaevskii (GP) model, also known as the nonlinear Schr\"odinger equation, is arguably the most universal model in classical and quantum physics, describing spectrally narrow or long-wavelength distributions of interacting waves…
We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor…
We construct a discrete shell-model for two-dimensional turbulence that takes into account local and nonlocal interactions between velocity modes in Fourier space. In real space, its continuous limit is described by the one-dimensional…
Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario…
An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…
We show that a complex projective manifold X which satisfies the Gromov's h-principle is `special', and raise some questions about the reverse implication, the extension to the quasi-K\" ahler case, and the relationships of these properties…
In this paper we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the…
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…
Some features of hot and dense gas of quarks which are considered as the quasi-particles of the model Hamiltonian with four-fermion interaction are studied. Being adapted to the Nambu-Jona-Lasinio model this approach allows us to…
The higher dimensional cosmology provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Here we discuss two situations where starting with an ordinary matter field without any equation of state…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars,…
In this work, we study a Dark Energy (DE) energy density model which depends on the Hubble parameter squared $H^2$ and on its first, second and third time derivatives $\dot{H}$, $\ddot{H}$ and $\dddot{H}$. Considering a scale factor $a$…
For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the…
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…