Related papers: Probing Non-Integer Dimensions
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
Using a generalization of vector calculus for the case of non-integer dimensional space we consider a Poiseuille flow of an incompressible viscous fractal fluid in the pipe. Fractal fluid is described as a continuum in non-integer…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…
We study some non-parabolic diffusion problems in one-space dimension, where the diffusion flux exhibits forward and backward nature of the Perona-Malik, H\"ollig or non-Fourier type. Classical weak solutions to such problems are…
This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on the real line exist. When the existence…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent…
We perform an exhaustive study of the simplest, nontrivial problem in advection-diffusion -- a finite absorber of arbitrary cross section in a steady two-dimensional potential flow of concentrated fluid. This classical problem has been…
The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear…