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We study the subharmonic frequency response of a generalized driven oscillator excited by a nonlinear periodic force. We take a magnetic pendulum called the Doubochinski pendulum as an example. So-called “amplitude quantization,” i.e., the existence of multiple discrete periodic solutions, is identified as subharmonic resonance in response to nonlinear feeding. The subharmonic resonance frequency is found to be related to the symmetry of the driving force: Odd subharmonic resonance occurs under an even symmetric driving force, and vice versa. We obtain multiple periodic solutions and investigate the transition and competition between multistable orbits via frequency response curves and Poincare maps. Experimentally observed phenomenon can easily be reproduced in a student laboratory. This provides a perfect example to demonstrate the rich dynamics related to the effect of nonlinear driving within the scope of undergraduate physics.

We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to the mechanical one's when a piecewise linear model is used to simplify the diodes I-V curve. We derive series solutions to the differential equation under weak nonlinear approximation which can describe the resonant response as well as amplitudes of superharmonic components. Experimental results are consistent with series solutions. We also present the phenomenon of hysteresis. Theoretical analysis along with numerical simulations are conducted to explore the stick-slip boundary. The correspondence between the mechanical and electric oscillators makes it easy to demonstrate the behaviors of this nonlinear oscillator on a digital oscilloscope. It can be used to extend the linear RLC experiment at the undergraduate level., Comment: 14 pages, 7 figures

The rotating saddle not only is an interesting system that is able to trap a ball near its saddle point, but can also intuitively illustrate the operating principles of quadrupole ion traps in modern physics. Unlike the conventional models based on the mass-point approximation, we study the stability of a ball in a rotating-saddle trap using rigid-body dynamics. The stabilization condition of the system is theoretically derived and subsequently verified by experiments. The results are compared with the previous mass-point model, giving large discrepancy as the curvature of the ball is comparable to that of the saddle. We also point out that the spin angular velocity of the ball is analogous to the cyclotron frequency of ions in an external magnetic field utilized in many prevailing ion-trapping schemes.

We discuss the sign and energy dependence of second to tenth order susceptibilities of the baryon number, charge number, and strangeness for the analysis of critical conditions in heavy ion collisions in the LHC and RHIC by applying a modified Nambu-Jona-Lasinio model. This model is fitted to the quark condensate of the lattice QCD result at finite temperature and zero baryon chemical potential. The presence of a critical point made these susceptibilities deviate considerably from a Hadron-Resonance-Gas model that shows no criticality. The sign, magnitude, and energy dependence of these higher order fluctuations hint towards the existence and location of a critical point that could be discovered in future heavy ion collision experiments.

Conserved charge fluctuations can be used to probe the phase structure of strongly interacting nuclear matter in relativistic heavy-ion collisions. To obtain the characteristic signatures of the conserved charge fluctuations for the quantum chromodynamics (QCD) phase transition, we study the susceptibilities of dense quark matter up to eighth order in detail, using an effective QCD-based model. We studied two cases, one with the QCD critical end point (CEP) and one without owing to an additional vector interaction term. The higher order susceptibilities display rich structures near the CEP and show sign changes as well as large fluctuations. These can provide us information about the presence and location of the CEP. Furthermore, we find that the case without the CEP also shows a similar sign change pattern, but with a relatively smaller magnitude compared with the case with the CEP. Finally, we conclude that higher order susceptibilities of conserved charge can be used to probe the QCD phase structures in heavy-ion collisions.

We evaluate the second to fourth-order baryon, charge and strangeness susceptibilities near a chiral critical point using the Nambu–Jona-Lasinio model under different temperatures and baryon chemical potential. Baryon number susceptibilities are found to be of the greatest magnitude, offering the strongest signal. Whereas the strangeness susceptibilities have the smallest divergence dominating area, owing to the large strange quark mass. We also make an attempt to compare our results with experiment data. The trend at high collision energy is found to be consistent between theory and experiment. The model calculation predicts more complex behavior at low collision energies, near the postulated critical end point.