Convection in nanofluids with a particle-concentration-dependent thermal conductivity

Thermal convection in nanofluids is investigated by means of a continuum model for binary-fluid mixtures, with a thermal conductivity depending on the local concentration of colloidal particles. The applied temperature difference between the upper and the lower boundary leads via the Soret effect to a variation of the colloid concentration and therefore to a spatially varying heat conductivity. An increasing difference between the heat conductivity of the mixture near the colder and the warmer boundary results in a shift of the onset of convection to higher values of the Rayleigh number for positive values of the separation ratio psi>0 and to smaller values in the range psi<0. Beyond some critical difference of the thermal conductivity between the two boundaries, we find an oscillatory onset of convection not only for psi<0, but also within a finite range of psi>0. This range can be extended by increasing the difference in the thermal conductivity and it is bounded by two codimension-2 bifurcations.Comment: 13 pages, 11 figures; submitted to Physical Review

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared to the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinise the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points and it pinpoints the crucial need of considering this effect when investigating critical transitions

Networks of coupled oscillators: From phase to amplitude chimeras

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 113124 (2018) and may be found at https://doi.org/10.1063/1.5054181.We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains coexist with incoherent domains and coherence/incoherence referring to both amplitude and phase or only the amplitude of the oscillators, respectively. By changing the coupling strength, the two types of chimera patterns can be induced. We find numerically that the amplitude chimeras are not short-living transients but can have a long lifetime. Also, we observe variants of the amplitude chimeras with quasiperiodic temporal oscillations. We provide a qualitative explanation of the observed phenomena in the light of symmetry breaking bifurcation scenarios. We believe that this study will shed light on the connection between two disparate chimera states having different symmetry-breaking properties. Chimera states are emergent dynamical patterns in networks of coupled oscillators where coherent and incoherent domains coexist due to spontaneous symmetry-breaking. In oscillators that exhibit both phase and amplitude dynamics, two types of distinct chimera patterns exist, namely, amplitude-mediated phase chimeras (AMCs) and amplitude chimeras (ACs). In the AMC state coherent and incoherent regions are distinguished by different mean phase velocities: all coherent oscillators have the same phase velocity, however, the incoherent oscillators have disparate phase velocities. In contrast to AMC, in the AC state, all the oscillators have the same phase velocity, however, the oscillators in the incoherent domain show periodic oscillations with randomly shifted center of mass. Surprisingly, in all the previous studies on chimeras, a given network of continuous-time dynamical systems seems to show either AMC or AC: they never occur in the same network. In this paper, for the first time, we identify a network of coupled oscillators where both AMC and AC are observed in the same system, and we also provide a qualitative explanation of the observation based on symmetry-breaking bifurcations.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Non-darcian Effects on Double Diffusive Convection in a Sparsely Packed Porous Medium

The linear and non-linear stability of double diffusive convection in a sparsely packed porous layer is studied using the Brinkman model. In the case of linear theory conditions for both simple and Hopf bifurcations are obtained. It is found that Hopf bifurcation always occurs at a lower value of the Rayleigh number than one obtained for simple bifurcation and noted that an increase in the value of viscosity ratio is to delay the onset of convection. Non-linear theory is studied in terms of a simplified model, which is exact to second order in the amplitude of the motion, and also using modified perturbation theory with the help of self-adjoint operator technique. It is observed that steady solutions may be either subcritical or supercritical depending on the choice of physical parameters. Nusselt numbers are calculated for various values of physical parameters and representative streamlines, isotherms and isohalines are presented

Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoids

Numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory. Continuation techniques have been employed in all branches of the natural sciences as well as in engineering to analyze ordinary, partial and delay differential equations. Here we show that the deterministic continuation algorithm for equilibrium points can be extended to track information about metastable equilibrium points of stochastic differential equations (SDEs). We stress that we do not develop a new technical tool but that we combine results and methods from probability theory, dynamical systems, numerical analysis, optimization and control theory into an algorithm that augments classical equilibrium continuation methods. In particular, we use ellipsoids defining regions of high concentration of sample paths. It is shown that these ellipsoids and the distances between them can be efficiently calculated using iterative methods that take advantage of the numerical continuation framework. We apply our method to a bistable neural competition model and a classical predator-prey system. Furthermore, we show how global assumptions on the flow can be incorporated - if they are available - by relating numerical continuation, Kramers' formula and Rayleigh iteration.Comment: 29 pages, 7 figures [Fig.7 reduced in quality due to arXiv size restrictions]; v2 - added Section 9 on Kramers' formula, additional computations, corrected typos, improved explanation