The special nonlinear effect of sinking bubbles is observed when the container partially filled with a liquid is excited by vibration. This paper is concerned with this interesting phenomenon in an incompressible viscous fluid under vertical vibration. We construct the theoretical model from the view of vibration mechanics and fluid mechanics. According to theoretical analysis, we derive the accurate model of the bubble moving in the liquid and the added mass caused by it. After that, the control equation of the bubble is given by the force analysis and the differential equation of variable-mass systems. Besides, the critical depth of the sinking bubble is derived based on the method of direct separation of motions. We further explore and analyze the specific reasons why the bubbles sink. At the same time, the conditions where the variable mass has a significant influence on the motion of the object are given. The main factors affecting the sinking of bubbles, density, frequency, and amplitude are numerically simulated and analyzed with different conditions. To prevent or weaken the effect of sinking bubbles in the oscillating fluid, feasible approaches are proposed. Meanwhile, the theory is validated experimentally.

In this research we analyze two models using the tensor network algorithm. The quantum correlations of a two-qubit system are first studied in different bosonic reservoirs. Both equilibrium and nonequilibrium scenarios are discussed. Non-Markovian effects can improve the survival time of the quantum correlations significantly and weaken the decoherence effect. Non-Markovian dynamics with existing memory can lead to entanglement rebirth in specific scenarios instead of the eventual entanglement decay or death seen in memoryless Markovian cases. The system reaches a steady state quickest in sub-Ohmic reservoirs and shows the most apparent non-Markovian behavior in super-Ohmic reservoirs. The Markovian approximation used in this paper is superior to that in the Bloch-Redfield master equation. The entanglement dynamics behaves similarly under different approaches when the system-bath coupling is weak and the memory effect is significant when the system-bath coupling is strong. We study not only the impact of the environment on quantum correlations, but also how to protect quantum correlations. Starting from a state in which the two ends are maximally entangled, a one-dimensional Aubry-André chain model is also studied. We identify distinct phases by monitoring the imbalance dynamics. When the chain is closed, the imbalance dynamics behaves differently in various phases and so does the entanglement evolution between the chain's ends. When the first site couples to a bath, we find that the imbalance dynamics can still be an effective indicator to differentiate various phases in an early evolution stage since the imbalance dynamics is only remarkably affected at relatively high temperatures. The distribution of the eigenenergy of the system can account for it. The entanglement of the chain ends decays rapidly in all phases due to one of the ends being coupled to the bath directly. However, the entanglement of the chain ends will persist for a perceptible amount of time in the localization phase if the bath is coupled to the middle site of the chain. Our research shows that one can utilize the disordered environment as a buffer to protect quantum correlations.

We employ a typical genetic circuit model to explore how noise can influence dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure regions. We find that a quasiperiodic component, which is not allowed by deterministic dynamics, will be generated by noise inducing in the first two regions, and this quasiperiod will be more and more stable along with the increase in noise. In particular, in the second region the quasiperiod will compete with a stable limit cycle and perform a new transient rhythm. Furthermore, we ascertain the entropy production rate and the heat dissipation rate, and discover a minimal value with theoretical elucidation. In the end, we unveil the mechanism of the formation of quasiperiods, and show a practical biological example. We expect this work to be helpful in solving some biological or ecological problems, such as the genetic origin of periodical cicadas and population dynamics with fluctuation.

The understanding of neural excitability and oscillations in single neuron dynamics remains incomplete in terms of global stabilities and the underlying mechanisms for phase formation and associated phase transitions. In this study, we investigate the mechanism of single neuron excitability and spontaneous oscillations by analyzing the potential landscape and curl flux. The topological features of the landscape play a crucial role in assessing the stability of resting states and the robustness/coherence of oscillations. We analyze the excitation characteristics in Class I and Class II neurons and establish their relation to biological function. Our findings reveal that the average curl flux and associated entropy production exhibit significant changes near bifurcation or phase transition points. Moreover, the curl flux and entropy production offer insights into the dynamical and thermodynamical origins of nonequilibrium phase transitions and exhibit distinct behaviors in Class I and Class II neurons. Additionally, we quantify time irreversibility through the difference in cross-correlation functions in both forward and backward time, providing potential indicators for the emergence of nonequilibrium phase transitions in single neurons.

Perceptual rivalry, where conflicting sensory information leads to alternating perceptions crucial for associated cognitive function, has long attracted research attention. Despite progress being made, authors of recent studies have revealed limitations and inconsistencies in our understanding across various rivalry contexts. We develop a unified physical framework, where perception undergoes a consecutive phase transition process encompassing different multistate competitions. We reveal the underlying mechanisms of perceptual rivalry by identifying dominant switching paths among perceptual states and quantifying mean perceptual durations, switching frequencies, and proportions of different perceptions. We uncover the underlying nonequilibrium dynamics and thermodynamics by analyzing average nonequilibrium flux and entropy production rate, while associated time series irreversibility reflects the underlying nonequilibrium mechanism of perceptual rivalry and link thermodynamical results with neuroelectrophysiological experiments. Our framework provides a global and physical understanding of brain perception, which may go beyond cognitive science or psychology but embodies the connection with wider fields such as decision-making.

In this research, we analyze two models using the tensor network algorithm. The quantum correlations of a two-qubit system are first studied in different bosonic reservoirs. Both equilibrium and nonequilibrium scenarios are discussed. Non-Markovian effects can improve the survival time of the quantum correlations significantly and weaken the decoherence effect. Non-Markovian dynamics with existing memory can lead to entanglement rebirth in specific scenarios instead of the eventual entanglement decay or death seen in memoryless Markovian cases. The system reaches a steady state quickest in sub-Ohmic reservoirs and shows the most apparent non-Markovian behavior in super-Ohmic reservoirs. We not only study the impact of the environment on quantum correlations but also how to protect quantum correlations. Starting from a state in which the two ends are maximally entangled, a one-dimensional AA chain model is also studied. We identify distinct phases by monitoring the imbalance dynamics. When the chain is closed, the imbalance dynamics behave differently in various phases, and so does the entanglement evolution between the chain's ends. When the first site couples to a bath, we found the imbalance dynamics can still be an effective indicator to differentiate various phases in an early evolution stage since the imbalance dynamics is only remarkably affected at relatively high temperatures. The distribution of the eigenenergy of the system can account for it. The entanglement of the chain ends decays rapidly in all phases due to one of the ends being coupled to the bath directly. However, the entanglement of the chain ends will persist for a perceptible amount of time in the localization phase if the bath is coupled to the middle site of the chain. Our research shows that one can utilize the disordered environment as a buffer to protect quantum correlations.