Related papers: Rough basin boundaries in high dimension: Can we c…
The spherical limit of strongly commensurate dirty-bosons is studied perturbatively at weak disorder and numerically at strong disorder in two dimensions (2D). We argue that disorder is not perfectly screened by interactions, and…
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the…
Turbulent flows are strongly chaotic and unpredictable, with a Lyapunov exponent that increases with the Reynolds number. Here, we study the chaoticity of the Surface Quasi-geostrophic system, a two-dimensional model for geophysical flows…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
Grain boundary roughness can affect electronic and mechanical properties of two-dimensional materials. This roughness depends crucially on the growth process by which the two-dimensional material is formed. To investigate the key mechanisms…
The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated…
In this paper, we define new fractal dimensions of a metric space in order to calculate the roughness of a set on a large scale. These fractal dimensions are called upper zeta dimension and lower zeta dimension. The upper zeta dimension is…
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…
The turbulent boundary layer scaling parameters for the velocity profile are usually associated with either the inner viscous region or the outer boundary layer region. It has been a long-held view that complete similarity of the velocity…
We consider the stability of two-dimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner…
We theoretically investigate the pattern formation observed when a fluid flows over a solid substrate that can dissolve or melt. We use a turbulent mixing description that includes the effect of the bed roughness. We show that the…
We report results of lattice Boltzmann simulations of a high-speed drainage of liquid films squeezed between a smooth sphere and a randomly rough plane. A significant decrease in the hydrodynamic resistance force as compared with that…
We give the explicit estimates of order $\gamma^{-d}$ (with logarithmic correction in the 1D case) for the fractal dimension of the attractor of the damped hyperbolic equation (or system) in a bounded domain $\Omega\subset \mathbb R^d$,…
Wind tunnel tests of 2D rough cylinders are presented. The goal is to simulate the alternate vortex shedding in flow regimes encountered in wind engineering applications, where the full scale Reynolds number is larger than the one that can…
Every volume-preserving centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (1) has two distinct centre Lyapunov exponents, or (2) exhibits an invariant continuous line field (or pair of line fields) tangent…
"Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Its effect on quasi-regular motion is quantified here with four different measures,…
Polymer chains composing a polymer solution in strict two dimensions (2D) are characterized with irregular domain boundaries, whose fractal dimension ($\mathcal{D}^{\partial}$) varies with the area fraction of the solution and the solvent…
We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough…