Related papers: Superexponential dissipation enhancement on $\math…
We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…
Motivated by the work of D. Hoff and K. Zumbrun (Indiana Univ. Math. J. 44: 603-676, 1995), we investigate the diffusion wave phenomena in three-dimensional incompressible viscoelastic flows. By employing the representation formula of the…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
We extend the superembedding formalism for 4D N=1 superconformal field theory (SCFT) to the case of fields in arbitrary representations of the superconformal group SU(2,2|1). As applications we obtain manifestly superconformally covariant…
Given a finite sequence of times $0<t_1<...<t_N$, we construct an example of a smooth solution of the free nonstationnary Navier--Stokes equations in $\R^d$, $d=2,3$, such that: (i) The velocity field $u(x,t)$ is spatially poorly localized…
We consider reaction-diffusion equations with combustion-type non-linearities in two dimensions and study speed-up of their pulsating fronts by general periodic incompressible flows with a cellular structure. We show that the occurence of…
We study drag-induced diffusion of massive particles in scale-free velocity fields, where superdiffusive behavior emerges due to the scale-free size distribution of the vortices of the underlying velocity field. The results show qualitative…
Inverting an evolving diffusive scalar field to reconstruct the underlying velocity field is an underdetermined problem. Here we show, however, that for two-dimensional incompressible flows, this inverse problem can still be uniquely solved…
We construct a smooth velocity field $u$ on $\mathbb{R}_+ \times \mathbb{T}^3$ that exhibits kinematic dynamo action, causing exponential growth in solutions to the magnetohydrodynamic induction equation, with a rate that is uniform in…
In this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
Using analysis for 2-admissible functions in weighted Sobolev spaces and stochastic calculus for possibly degenerate symmetric elliptic forms, we construct weak solutions to a wide class of stochastic differential equations starting from an…
We study by Variational Monte Carlo an extended Hubbard model away from half filled band density which contains two competing nearest-neighbor interactions: a superexchange $J$ favoring d-wave superconductivity and a repulsion $V$ opposing…
Advection-diffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent…
We present an approach for computing extensions of velocities or other fields in level set methods by solving a biharmonic equation. The approach differs from other commonly used approaches to velocity extension because it deals with the…
We consider a variant of the kinematic dynamo problem. Rather than prescribing a velocity field and searching for high-growth magnetic fields via an eigenvalue problem, we treat the seed magnetic-field structure as given and ask which…
The usual heat equation is not suitable to preserve the topology of divergence-free vector fields, because it destroys their integral line structure. On the contrary, in the fluid mechanics literature, on can find examples of…
This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function exp(x)is selected as the structural function to construct the local structural derivative diffusion equation model. The…
We consider two-dimensional flows above topography, revisiting the selective decay (or minimum-enstrophy) hypothesis of Bretherton and Haidvogel. We derive a 'condensed branch' of solutions to the variational problem where a domain-scale…
This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and…