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We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.
It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control.
Syngas fermentation, the bioconversion of CO, CO[subscript 2], and H[subscript 2] to biofuels and chemicals, has undergone considerable optimization for industrial applications. Even more, full-scale plants for ethanol production from syngas fermentation by pure cultures are being built worldwide. The composition of syngas depends on the feedstock gasified and the gasification conditions. However, it remains unclear how different syngas mixtures affect the metabolism of carboxidotrophs, including the ethanol/acetate ratios. In addition, the potential application of mixed cultures in syngas fermentation and their advantages over pure cultures have not been deeply explored. In this work, the effects of CO[subscript 2] and H[subscript 2] on the CO metabolism by pure and mixed cultures were studied and compared. For this, a CO-enriched mixed culture and two isolated carboxidotrophs were grown with different combinations of syngas components (CO, CO:H[subscript 2], CO:CO[subscript 2], or CO:CO[subscript 2]:H[subscript 2]).
Results
The CO metabolism of the mixed culture was somehow affected by the addition of CO[subscript 2] and/or H[subscript 2], but the pure cultures were more sensitive to changes in gas composition than the mixed culture. CO[subscript 2] inhibited CO oxidation by the Pleomorphomonas-like isolate and decreased the ethanol/acetate ratio by the Acetobacterium-like isolate. H[subscript 2] did not inhibit ethanol or H[subscript 2] production by the Acetobacterium and Pleomorphomonas isolates, respectively, but decreased their CO consumption rates. As part of the mixed culture, these isolates, together with other microorganisms, consumed H[subscript 2] and CO[subscript 2] (along with CO) for all conditions tested and at similar CO consumption rates (2.6 ± 0.6 mmol CO L[superscript −1] day[superscript −1]), while maintaining overall function (acetate production). Providing a continuous supply of CO by membrane diffusion caused the mixed culture to switch from acetate to ethanol production, presumably due to the increased supply of electron donor. In parallel with this change in metabolic function, the structure of the microbial community became dominated by Geosporobacter phylotypes, instead of Acetobacterium and Pleomorphomonas phylotypes.
Conclusions
These results provide evidence for the potential of mixed-culture syngas fermentation, since the CO-enriched mixed culture showed high functional redundancy, was resilient to changes in syngas composition, and was capable of producing acetate or ethanol as main products of CO metabolism.