Related papers: Attractor Bifurcation of Three-Dimensional Double-…
In this article, we describe a simple class of models of absorbed diffusion processes with parameter, whose conditional law exhibits a transcritical bifurcation. Our proofs are based on the description of the set of quasi-stationary…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…
The paper concerns with Wilson-Cowan neural model with impulses. The main novelty of the study is that besides the traditional singularity of the model, we consider singular impulses. A new technique of analysis of the phenomenon is…
The initial bifurcations in rotating Rayleigh-B\'enard convection are studied in the range of dimensionless rotation rate $0 < \Omega < 2150$ for an aspect-ratio-2.5 cylindrical cell. We used simultaneous optical shadowgraph, heat transport…
Diffractive scattering in the presence of a large momentum transfer is an ideal place to study the short distance rapidity gap producing mechanism. Previous studies (experimental and theoretical) in this area have focussed on gaps between…
Lorenz attractors play an important role in the modern theory of dynamical systems. The reason is that they are robust, i.e. preserve their chaotic properties under various kinds of perturbations. This means that such attractors can exist…
We study the bifurcation diagram of the R\"ossler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We…
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from…
In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…
Rayleigh-B\'enard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised setup to study thermal convection. Of special interest are the statistics of the turbulent…
Recently, it has been shown that properties of excitable media stirred by two-dimensional chaotic flows can be properly studied in a one-dimensional framework \cite{excitablePRL,excitablePRE}, describing the transverse profile of the…
We have designed and built an apparatus for real-time acoustic imaging of convective flow patterns in optically opaque fluids. This apparatus takes advantage of recent advances in two-dimensional ultrasound transducer array technology; it…
The coexistence of motions on various scales is a remarkable feature of solar convection, which should be taken into account in analyses of the dynamics of magnetic fields. Therefore, it is important to investigate the factors responsible…
In this paper, a class of high-order compact finite difference Hermite scheme is presented for the simulation of double-diffusive convection. To maintain linear stability, the convective fluxes are split into positive and negative parts,…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $\epsilon$…
The phenomenon of convection is found in a wide variety of settings on different scales -- from applications in the cooling technology of laptops to heating water on a stove, and from the movement of ocean currents to describing…
This study of spatio-temporal pattern formation in an annulus is motivated by two physical problems on vastly different scales. The first is atmospheric convection in the equatorial plane between the warm surface of the Earth and the cold…
We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves on finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave generically is a…