Related papers: A Dynamical Systems Approach to an Inviscid and Th…
Sharpness-aware minimization (SAM) is a recently proposed training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains. Instead of minimizing the loss of the current…
Some memristors are quite interesting from the point of view of dynamical systems. When driven by narrow pulses of alternating polarities, their dynamics has a stable fixed point, which may be useful for future applications. We study the…
We investigate enstrophy variations by collapse of point vortices in an inviscid flow and, in particular, focus on the enstrophy dissipation that is a significant property characterizing 2D turbulent flows. Point vortex is an ideal vortex…
A thin gaseous disc with an almost keplerian angular velocity profile, bounded by a free surface and rotating around point-mass gravitating object is nearly spectrally stable. Despite that the substantial transient growth of linear…
The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…
Entangled magnetic fields entering into an accretion flow would very soon be stretched into a dominant toroidal component due to strong differentially rotating motion inside the accretion disc. This is particularly true for weakly viscous,…
We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $\delta$-scrambled set for some $\delta>0$ if…
We present the results of numerical integrations yielding the structure of and meridional flow in axisymmetric thin viscous accretion disk models. The solutions are obtained by simplifying and approximating first the equations, using…
We present steady-state solutions for a one-dimensional, magnetically-driven accretion disk wind model based on magnetohydrodynamic equations. We assume a geometrically thin, gas-pressure-dominated accretion disk, incorporating both…
The recent discovery of polymer diffusive instability (PDI) by Beneitez et al. (Phys. Rev. Fluids, 2023, 8: L101901) poses challenges in implementing artificial conformation diffusion (ACD) in transition simulations of viscoelastic…
The first spherical accretion model was developed 55 years ago, but the theory is yet far from being complete. The real accretion flow was found to be time-dependent and turbulent. This paper presents the minimal MHD spherical accretion…
We study mass flow rate through a disc resulting from a varying mass supply rate. Variable mass supply rate occurs, e.g., during disc state transitions, and in interacting eccentric binaries. It is, however, damped by the viscosity of the…
This paper studies the design of controllers for discontinuous dynamics that ensure the safety of non-smooth sets. The safe set is represented by arbitrarily nested unions and intersections of 0-superlevel sets of differentiable functions.…
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system…
Complex fluids such as emulsions, colloidal gels, polymer or surfactant solutions are all characterized by the existence of a "microstructure" which may couple to an external flow on timescales that are easily probed in experiments. Such a…
We consider an extreme case of disc accretion onto a gravitating centre when the viscosity in the disc is negligible. The angular momentum and the rotational energy of the accreted matter is carried out by a magnetized wind outflowing from…