The slow passage problem through a resonance is considered. As a model problem, we consider a damped harmonically forced oscillator whose forcing frequency is slowly ramped linearly in time. The setup is similar to the familiar slow passage through a Hopf bifurcation problem, where for slow variations of the control parameter, oscillations are delayed until the parameter has exceeded the critical value of the static-parameter problem by an amount that is the difference between the Hopf value and the initial value of the parameter. In sharp contrast, in the resonance problem there is an early onset of resonance, setting in when the ramped forcing frequency is midway between its initial value and the natural frequency for resonance in the unforced problem; we term this value the jump frequency. Numerically, we find that the jump frequency is independent of the system's damping coefficient, and so we also consider the undamped problem, which is analytically tractable. The analysis of the undamped problem confirms the numerical results found in the damped problem that the maximal amplitude obtained at the jump frequency scales as A~ε(-1/2), ε being the ramp rate, and that the jump frequency is midway between the initial frequency at the start of the ramp and the natural frequency of the unforced problem.
This article reports a numerical study of double-diffusive convection in a fluidsaturated vertical porous annulus subjected to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio (λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly.123 754 M. Sankar et al.
Using the nematode C. elegans germline as a model system, we previously reported that PUF-8 (a PUF RNA-binding protein) and LIP-1 (a dual-specificity phosphatase) repress sperm fate at 20°C and the dedifferentiation of spermatocytes into mitotic cells (termed "spermatocyte dedifferentiation") at 25°C. Thus, double mutants lacking both PUF-8 and LIP-1 produce excess sperm at 20°C, and their spermatocytes return to mitotically dividing cells via dedifferentiation at 25°C, resulting in germline tumors. To gain insight into the molecular competence for spermatocyte dedifferentiation, we compared the germline phenotypes of three mutant strains – fem-3(q20gf), puf-8(q725; fem-3(q20gf), and puf-8(q725); lip-1(zh15). Both fem-3(q20gf) and puf-8(q725); fem-3(q20gf) mutants produced excess sperm like puf-8(q725); lip-1(zh15) double mutants. Our results show that spermatocyte dedifferentiation was not observed in fem-3(q20gf) mutants, but it was more aggressive in puf-8(q725); lip-1(zh15) than in puf-8(q725); fem-3(q20gf) mutants. These results suggest that MPK-1 (the C. elegans ERK1/2 MAPK ortholog) activation by removing the function of LIP-1 in the absence of PUF-8 promotes spermatocyte dedifferentiation. This idea was confirmed using Resveratrol (RSV), a potential activator of MPK-1 and ERK1/2 in C. elegans and human cells. Notably, spermatocyte dedifferentiation was significantly enhanced by RSV treatment, and its effect was blocked by mpk-1 RNAi. We, therefore, conclude that PUF-8 and MPK-1 are normally required to inhibit spermatocyte dedifferentiation and tumorigenesis. Since these regulators are broadly conserved, we suggest that similar regulatory circuitry may control cellular dedifferentiation and tumorigenesis in other organisms, including humans.
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 timeindependent 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.
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